dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010,...
Transcript of dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010,...
![Page 1: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/1.jpg)
![Page 2: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/2.jpg)
(AS-1)
4 Marks
24 15
0.4234123567 pq
pq
log102= 0.3010, log103 = 0.4771, 366
16 25 817log + 5log + 3log15 24 80
pq
(AS-1)
2 Marks
2
![Page 3: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/3.jpg)
N
X=a2b3c4 Y=a3 b c2 X,Y
log3(7x+3) = log3(5x+9)
log25+3log5-5 log5
110 101000
1 x x 1100log log log
log25+log 9 -log3 = logx xUse logritham laws to simply following :
2
2 28x + log 2xy
yl0g
log2
4 256 log
10 2= 0.3010 log
1016
A Blog2 = 0.3010 (x = 42018)log x (AS-1)
1 Mark
2+log23 23
2log27
3
![Page 4: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/4.jpg)
a = 132, b = 11 a = bq + r q,r
1 0 08 1
x xlog 10 10 1050+ 20+ 100log log log 5 5625- 125log log log27+log3- log32 1og100.001
31log
243
5x = 4log x2x=5x-1 22+log 23 (AS-1)
1/2 Mark
375324327428 A) 2432 B) 28375374 C) 2837 D) 2357
n n A) B) C) D)
A) B) C) D)
A) B) C) D)
4
![Page 5: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/5.jpg)
2 256 A) B) C) D)
A) B) C) D)
19256 =............
A) 0.015 B) C) D) 0.02356
A) B) C) D)
p0.7 =q p+q=...............
A) B) C) D)
(3 + 2)(3 - 2) = A) 9 - 2 2 B) C) D)
63
A) 3 B) 2 C) 2 3 D) 3 2
A) 3.12 B) 12 C) 7 D) 34
A) B) C) D)
px =q xq
A) 2n5m B) 2n3m C) 3m.5n D) 3n.4n
log8512 A) B) C) D)
log34349=
A) 23 B)
72 C)
32 D)
27
5
![Page 6: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/6.jpg)
3 3243log =
A) 103 B)
152 C) D)
232log A) B) C) D)
52
2 2 2
1lo g lo g lo g 1 6
A) B) C) log 2 D) log 16
2 log3-3log 2 A) log 0 B) log 1 C )
9log8
D) log(72)
log102+ log105 A) B) C) D)log10125 + log108
A) B) C) D)
A) B) C) D)
A) B) C) D) 7 5
A) B) C) D)
45
1 66 2 5l o g =
A) B) C) D) log20182018=
A) B) C) D) log21024= .........
A) B) C) D)
19log 361 =
A) B) C)12 D)
6
![Page 7: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/7.jpg)
(AS-2)
4 Marks
3 7 + 3 2 m m
2 -12 +1
q 6q + 16q + 36q + 5
7 + 11
logx=m+n logy = m-n 2
10xlog = 1- m + 3ny
x2+y2= 10xy2log(x-y) = 2log3+logx+logy
“n”“m”3 m x 2nnn, n+2n+4 log2x=a, log3y =a, (72)a =x3. y2 log23=x log25=y log211.25 log2log 100
nm
bb
mlog a = log an
log x- b log y = 2 log 3 xa = 9yb
7 11
7
![Page 8: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/8.jpg)
2 45 + 3 205
(AS-2)
2 Marks
7x11x13+13 3 2 n n 4n 8 (17112)+ (17115)
12
2 3 + 5
(AS-2)
1 Mark
a=bq+rr=obqn6n
log103log10100
8
![Page 9: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/9.jpg)
(AS-2)
1/2 Mark
A) B) C) D)
p/q q A) B) C) D) (B), (C)
a = 3 + 2,b = 3 - 2 A) (a+b) B) (a-b)
C) ab D) ab
(A) (i) & (ii) (B) (i) & (iii) (C) (ii) & (iii) (D) (iii) & (iv)
n8n- 3n A) 8 B) C) 5 D) 3
3 5 A) B) C) D)
289 A) B) C) D)
log3A) B) C) D)
log105 + log102 A) B) C) D)
Y=ax A) Y B) X C) D)
A) 2434 B) 2632 C) 2533 D) 2236
9
![Page 10: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/10.jpg)
a=bq + r b,r A) b = r B) r b C) b r D) b = o, r = o
3 + 5
A) 23 + 5 B) 3 - 5 + 2 15 C) 3 - 5 D) 23 - 5
3x = 4l o g x=
A) B) C) D)
log 2020101+log 202020 =
A) B) C) D)
log15= A) B) C) D)
A) B) C) D)
6100 A) B) C) D)
38
A) B) C) D)2332 2233
A) 2232 B) 2333 C) 2332 D) 2233
233251223 52 A) B) C) D)
2 3
A) 65 B)
34 C)
32 D)
95
A) B) C) D)
189125
A) B) C) D)
10
![Page 11: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/11.jpg)
61250
A) B) C) D)
271600
A) B) C) D)
m a A) 3m + 1 B) 3m
C) 3m + 1,3m +2 D) 3m, 3m + 1, 3m + 2
(n2-1)n A) B) C) D)
A) 11
3000 B) 91
270 C) 3 2 3
34 32 x5 x7 D) 4 5
3 12 x 3
2323
52
A) B) C) D)
2.35 A) B) C) D)
A) 5 - 3 B) 3 2 C) 2 + 3 D) 5 + 4
(AS-3)
4 Marks
log x 3y 2 24 3
32
xlo gy
A) 0.3 B) 0.125 C) 0.12.5 D) 0.0875
11
![Page 12: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/12.jpg)
A)227 B)
34 C)
38 D)
16
P p ‘’
a,b‘’
(AS-3)
2 Marks
3 logx +12 logy=2 yx
65x+117y
A) 2 2
72183 x5 B) 99
625
625log81
12
![Page 13: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/13.jpg)
5q+1
A) 43.12345679 B) 27.142857
(AS-3)
1 Mark
78
log 1000 log x2y3 z4 a = bq + rY=ax y a,xlog2 32 = xlog91log a + log b
1725
log143 log 81
256
13
![Page 14: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/14.jpg)
(AS-3)
1/2 Mark
A) 3p 3p+1 3p+2 B) 3p C) 3p+1 D) 3p+2
0.49 =
A) 4919 B) 49
100 C) 12 D) 45
99
A) 36 B) 35 C) 34 D) 38
198
A) B) C) D)
343log125
A) 7(log 5 -log 7) B) 4(log 5 - log 7)
C) 2(log 7 -log 5) D) 3(log 7 - log 5)
x=5n+1x2 A) 25m + 1 B) 5m + 1 C) 25m + 5 D) 25m + 1
A) 8q + 1 B) 8q + 3 C) 8q + 6 D) 8q + 5
A) a + b
2 B) 2 2
2a b C)
2 2+2
a b D) 2
+2
(a b)
A) LCM HCF = a b B) LCM a=HCF b
C) LCM a = HCF b D)
14
![Page 15: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/15.jpg)
- A) B) C) D)
2 A) B) C) D)
225=5b A) log5100=225 ` B) log5225=b
C)log225b =5 D) log2255=b
A)1625
B) 0.04
C) D)
A) B) C) D)
12
A) B) C) D)
2
3
x ylogz
A) log x+ logy+logz B) 2log x+ logy+logz
C) log x+ logy-3logz D) log x+ logy-logz
q A) 6q B) 6q+1 C) 6q+2 D) 6q+4
A) B) C) D)
log71=.............. A) 3 B) 2 C) 0 D) 7
15
![Page 16: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/16.jpg)
625 = 25
A) 251log 625 =2 B) 625
1log 25 =2
C) 251log = 6252 D)
152 =225
A) 2log 225 = 15 B) 15log 2 = 225
C) 225log 15 = 2 D) 15log 225 = 2
263 =125
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) A, B D)
6100 A) B) C) D)
38
A) B) C) D)
A) B) C) D) 2 3
A) 65 B) 3
4 C) 32 D)
95
16
![Page 17: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/17.jpg)
189125
A) B)C) D)
61250
A) B) C) D)
271600
A) B)C) D)
ma = A)3m + B) 3m
C)3m +3m + D)3m, 3m +3m +(n2 - 1)n
A) B) C) D)
A) 11
3000 B) 91270 C) 3 2 3
3432 x5 x7 D) 4 5
312 x3
3 2
232 x5
A) B)C) D)
2.35 A) B) C) D)
(AS-4)
4 Marks
XX
x - log 48 + 3 log 2= 13 log 125-log3 x
17
![Page 18: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/18.jpg)
a - b 1log = (loga + logb)2 2 a2+b2
logx=2m-n, logy=n-2mlogz=3m-2n 2 3
4
x ylo gZ
log (x+5)+log(x-5)=4log2+2log3 x
xx
4-x5 5log - 2log x = 1 0 < x < 4 x
(AS-4)
2 Marks
log10 (2x2-1) = 2 x
log2 x = mlog5y = n2m-33n+2
3. log6x+log6(x-9) = 2
x + y 1log = (logx + logy)3 2 (x+y)2
( )5log 3x - 8 = 0 xlog
8 x
3=11x
18
![Page 19: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/19.jpg)
(AS-4)
1 Mark
A) 0.3 B) 0.125C) 12.5 0.0875
A) 227 B) 3
4 C) 38 D)
16
2y=3y-5 9
2n- 4
2n , n N
6n- 5
n , (n N)
27 P P
pq ‘q’
(AS-4)
1/2 Mark
a2b3c, a4b3ca3bc3 A) abc B) a3b4c3 C) a3b3c3 D) a6b8c6
2 log(x+3)= log 81x =....... A) B) C) D)
x2+ y2=27xy
x - ylog =5
A) logx-logy B) logx+logy
C) 1 logx + logy2 D)
logaa-1=....... A) +1 B) C) D)
19
![Page 20: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/20.jpg)
xx,x2,x3 A) x B) x2 C)x3 D) 0
3log(x+3)=log27 x A) B) C) D)
x,y A) B) C) xy D) x+y
12 1
A) 94 B)
34 C)
54 D)
74
9 - 0.9 = ....... A) 8.1 B) 8.1 C) 8 D) 0.1
a c = ac A) a=1 B) a=c C) c=1 D) a = -1
81 811log + log 3481 =
A) B) C) D)x,y
A) x-y B) x C) y D) 1
1132
A) B) C) D) 5 + 2 - 7
A) B) C) D) 9604 = 98 0.009604 =........
A) 9.8 B) 0.98 C) 980 D) 0.098
m n =a
A) n
ma B) m
na C) mn a D)
1mn a
20
![Page 21: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/21.jpg)
A) 225
30103045 B) 7
14050780
C) 130
1567565 D)
A) log
10 Tan 450 B) log
10 sin 0
C) log10
Sec245 D)
A) B) log C) log cos 900 D) 02log sin45
100log 0100 x
A) Sin 900 B)Tan 450 C) Cos 900 D) A B(AS-5)
4 Marks
2, 3, 5, 6, 7, 8, 10, (AS-5)
2 Marks
7
21
![Page 22: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/22.jpg)
(AS-5)
1/2 Mark
2
A) B)
C) D)
724
A)
B)
C)
D)
AC
A) B) C) D) A C
724
2424
724
724
A B
C
22
![Page 23: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/23.jpg)
![Page 24: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/24.jpg)
(AS-1)
4 Marks
A = { 3, 6, 9, 12, 15, 18, 21 }, B = { 4, 8, 12,16, 20 } C = { 2, 4, 6, 8, 10, 12, 14,16 },D = A {5, 10, 15, 20}
(i) A - B (ii) B - A (iii) C - A (iv) D - A (v) B - C (vi) B - D
(vii) C - B (viii) D - B
(ix) (A - B) (B - A) (x) (AB) - (AB)
A = { 1, 2, 3, 4, 5, 6 }, B {4, 5, 7, 8, 9, 10}(i) AB (ii) AB
(iii) A - B (iv) B - A(v) A - ( BC) (vi) (A -B) ( A-C)
A = { x : x}B = { x : x }C = { x : x }D = { x : x, 5 }
(i) A B (ii) AB (iii) C - D (iv ) AC
A = { 1, 2, 3, 4, 5, 6, 7, 8, 9,10}, B { 2,4, 6, 8,10 } C = { 1, 3, 5, 7, 9 }, D = {2,3, 5, 7 }
(i) AB (ii) BC (iii) (AB) C (iv) A ( BC) (v) AB
(vi) BC (vii) (AB)C (vii) A ( BC)
A = { 1, 2, 3, 4, 5, 6, 7, 8, 9,10 } B = { 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 } C = { 3, 6, 9, 12, 15, 18, 21, 24, 27, 30} D = { 1, 2, 3, 4, 5, 6, 7, 8, 9,10 }(i) AB (ii) AC (iii) AAB (iv) BC (v) BD (vi) CD
(vii ) AD (viii ) AAC (ix ) AAD (x ) B C (xi ) B D
(xii ) CD
24
![Page 25: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/25.jpg)
AB
2 8 -3 3(i)A = x : -2 x , B = -2. , , 33 3 2, 4
(ii) A = {}B = { }
A ={x/11 x 50, x }G = { }H = { }K = {}(i) GH (ii) HK
(iii) GHK
A = { MARVELLOUS }B = { }C = {MOUSE }(i) A (BC) (ii) A (BC)
A = {1, 2, 4 }, B = {6, 7, 8, 9, 10 }, C = {a, b, c, d, e, f, }(i) n (A), (ii) n (B), (iii) n (C),(iv) n(AB),(v) n (A (BC)),
(vi) n (A (BC))
XY
XY XY(AS-1)
2 Marks
V = { a, e, i, o, u }, B = { a, i, k, u } V - B B - V
A = { a, b, c, d, e }B = { c, f, g, b, h }A B
25
![Page 26: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/26.jpg)
A = { 2, 4, 6, 8, 10 }, B = { 1, 2, 3, 4, 5, 6} AB, AAB
A = { 1, 2, 3, 4, 5 }, B = { 6, 7, 8, 9, 10}n (AB), n (AB)
K = { p, q, r, s, t, u}, L = {q, s, t }M = { p, q, s, t, w }
(i) KL (ii) KM
A = { 6, 8, 11} = { }A , AA
A = { 3, 6, 9, 15, 18, 21} B = { 4, 8,12, 16, 20}C = { 2, 4, 6, 8, 10, 12, 14}(i)C - A (ii) C- B (iii) A - C (iv) B - C
A = {x:x }B = {x:x }A B, B - AA
(AS-1)
1 Mark
A = { a, b, c, d, e}, B = { a, c, e }AB, AAB
A = { 1, 3, 5, 7,9}, B = { 2,4,6,8,10 }AB
A = {},B = {}AB
A = { 1, 2, 3, 4, 5}A, AA
A = {x }B = {x }AB, AAB
A = { }B = {} C = {}n (A), n(B), n(C)
A = { 1, 2, 3, 4} B = { 2, 4, 6, 8}n (AB), n(AB)
A = {}B = {}AB, n (AB)
26
![Page 27: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/27.jpg)
A = { 1, 2, 3, 4} B = { 2, 4, 6,}A - B, B - A
AB, AAB
A - B, B - A
AB
(AS-1)
1/2 Mark
A = { 1, 2, 3, 4, 5 } B = { 2, 4, 5, 6, 7 }AB [ ]
A) { 2, 4, 5 } B) { 2, 3, 4 }
C) { 1, 4, 5 } D) { 5,7 }
A = { 1, 2, 3, }, B = { 12, 0, 5,}A - B
A) B B) { 5 } C) A D)
BA
A B
B
A
27
![Page 28: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/28.jpg)
= { x : 10 x 20, x }
A = {}B = {}n ( AB)
A) B) C) D)
P = {}Q = {}n ( AB) =
A) B) C) D)
A = {1, 2, 3, }, B = {3, 4, 5, 6}( A - B) (B - A)
A) {1, 2, } B) {4, 5, 6 }C) {1, 2, 4, 5, 6 } D)
A = {1, 2, 3, }, B = { 3, 4, 5, 6}( AB) - (AB) =
A) {3 } B){1, 2,} C){5,6} D) {1, 2, 4,5,6}
A = {a, e, i,o, u}, B = {p, q, r, s,t}AB =
A) {0} B) {} C) D)
n(AB) = 51, n(A) = 20, n(AB) = 13,n(B) =
A) 80 B) 44 C) 40 D)
P = {}Q = {}n(PUQ) =
A) B) C) D)
P = {a, e, i, o, u}, B = { a,i,u}PB =
A) P B) B C) D)
A){3, 17} B) {1, 3, 17} C) {1,3,17,51} D){ }
28
![Page 29: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/29.jpg)
n (A) = 13, n (B) = 16, n (AB) = 33n (AB)
A) B) C) D)
A = { }B = {} n (A) - n (B)
A) B) C) D)ABn (AB) =2
n (AB) =
A) B) C) D)
A = {E, X, A, M }, B = { P, R, I, N, C,I, P, A, L} AB =
A) { E} B) { A } C) { M } D) { P }
(AS-2)
4 Marks
A = {3, 6, 9, 12, 15, 18, 21 }, B = { 4, 8, 12, 16, 20}
(i) AUB = BA (i) A - B = B - A
n (AB) = n (A)
+ n (B) - n (AB)
A = {1, 2, 3, 4, 5, }, B = {2, 4, 6, 8} n (AB)
n (AB) = n (A) + n (B)
i) A ={} ii)B = {} iii)C = {} iv)D = {}
BA
29
![Page 30: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/30.jpg)
(i){x : XN(x - 1) (x - 2 ) = 0}(ii){x : XN x}(iii){x : XN x2 = 4}(iv){x : XNx}
(i)
(ii)
(iii)‘0’
(iv)(AS-2)
2 Marks
A = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}, B = {2, 3, 5, 7} AB AB = B
P = {1, 2, 3, 4,}A = {a, b, c} (i) F ={}(ii) P ={ x : 3.5 } (A) (B)1. {x : x2 = 4, XN}2. {x : x2 + 1 = 0, XN}3. {x : x < 5 , XN}4. {x : x }
30
![Page 31: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/31.jpg)
A,B
A,B
A = {p, q, r }, B = {q, p, r}A = B
A = {1, 2, 3 -----}N A, N
B = {}P = {}
B, P
A = {x, y, z }
A = {1, 2, 3, 4 }, B = {1, 2, 3, 5, 6} ABBA
ABn (B - A) = n (B) n (AB)
B = {x : x + 5 = 5}
“ ACB AB = B ”
A B
A B
31
![Page 32: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/32.jpg)
(AS-2)
1 Mark
A = {x, y, z}
i) A = {} ii) B = {}iii) C = {} iv) D = {}
{0}
A = {}B = {}AB, AAB
AB, AAB
A = {FOLLOW } B = {FLOW} A= B
A = {x :x } B = {x :x }A, B
A = {x},B = {x, y },C = {x, y, z}
A = {2, 4, 6, 8},B = { 1, 3, 5, 7 }A - B, B - AA - B = B - A
(AS-2)
1/2 Mark
AB A- B =
A) B B) C) A D) B - A
A = {1, 2, 3}B = { 1, 2, 3, 4}A, B
A) B)C) D)
32
![Page 33: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/33.jpg)
A = {x / x + 5 = 5}A =
A) {5} B) {0,4} C) {0,7} D) {0}A = {1, 2, 4 }, B = {3, 5, 6}
A) AB = B) AB = C)AB ={3 } D)
N = {}W = {} N W
A) B) C) D)
A = {x/xN, x< 6}B = {x/xN, 3 < x < 8}B - A =
A) { } B){6,7 } C){3,4,5 } D{1, 6, 7}A = {x : x Nx < 20}B = {x : xNx 5}n(A - B) =
A) B) C) D)n(A) = 23, n(B) = 17
A) AB B) BA
C) n (AB) = 6 D)
A = {2, 3, 5, 7 }, B = {},A, B
A) B) C) D)
AA A) B) C) D)
P = {}Q = {} R = {}
A) PQ B) QR C) RP D)PR
A) { }= B) = 0 C) 0 = {0} D){ }= 0
33
![Page 34: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/34.jpg)
A BAUB = A) B) C) A D) B
{x : x x }
A) B) C) D)
A) B) C) D)
A){x : xN x2 = 9}B){}C){}D){}
A B
A) x A x B B) x B x A
C) xA x B D) X A xB
AB
A) X A X B
B) X A XBX
C) X A XB X
D) B A
A B
A) B A
B) A B
C) B A
D) A B
34
![Page 35: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/35.jpg)
A = {}B = {}A, B
A) B) C) D)
A = {R, I, C, E }, B = {M, I, C, E}n (A - B)n (B - A)
A) B) C) D)AB
A) A - B = B) A B = AA C) AB = B D) A B = B
A)
B)P = {x : x - 8 = -8 }
C)D)
A) A= A = AA
B)A= A = C) A - B , AB, B - AAD)
A = {}B = {}
A) AB = 5
B) AB
C) AB = {}D)AB = {}
AUB = A A) A B B) B A C) AB = D) B =
A = {5, 7, 8 }, B = {8, 9, 10 }{5,7 }
A) AB B) AB C) A - B D) B - A
35
![Page 36: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/36.jpg)
A - B = B - A = (A,B ) A) AB = B) A B C)B A D) A = B
A) B){x : 1 < x < 2, xN }C){} D) {x : x 2 = 4, x }
A,B A) (AB) A B) AAB) C) (A - B)A D)A (A-B)
(AS-3)
4 Marks
(i) A = {x, y, z } (ii) B = {1,4,9,16 }
(i) A = {x : x }(ii) A = {x : x }(iii) A = {x : x }(iv) A = {x : x, }
x ‘A’
‘d’ B
A
P
(i) A = {}B = {} C= {} BC
(ii) A = {} B = {}
36
![Page 37: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/37.jpg)
1. A = {x : x = 2n + 1 xN } 2. A = {x }3. A = {x : x }4. A = {x ASSASSINATION}(AS-3)
2 Marks
A = {x : xN x < 20 }B = {x : xN x 5} A - B
1 1 1 1A = 1, , , ,4 9 16 25
(1) A = {x : xN, x x < 13}A
A = {2, 3, 4, 5 }, B = {1, 6, 8},B - A
(1)
(2)
A = {x : x}B = {x : x, }
A, B
ABn ( AB)
A = {0, 2, 4 }, A , A
37
![Page 38: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/38.jpg)
A = {3, 6, 9, 12 }B = {5, 25,125, 625}
(1) A, B
(2) A
(3) A
(4) P
(1)
(2)
(AS-3)
1 Mark
A = {2,3,5,7,11 }
A = {x : x+ 3 = 6, XN }A
A = {1, 4, 9, 16, 25 }
1 1 1 1A = 1, , , ,4 9 16 25
A = {1, 2, 3, 4 } B = { 5, 6, 7, 8 }AB
A = {1, 2, 3, }A , AA
A = {}A
“36 ”
38
![Page 39: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/39.jpg)
A, Bn ( AB)(AS-3)
1/2 Mark
B = {1,7, 2, 0, 6}n (B) = ( )
A) B) C) D) P = {1, 2, 3, 4, 5}P ( )
A) B) C) D)
1 1 1 1 1D = 1, , , , , ,2 3 4 5 6 ( )
A)
1P = x : x = ,n N,n < 7n
B) 2Q
1= x : x = ,n Nn
C) 3R
1= x : x = ,n Nn n 6
D)
1S = x : x = ,n W,n 0n
V = {x / x} ( )
A) {a, b, c,d} B) {a, e, o,u} C) {a, e, i, o, u} D) { }A = { 2,3,5,7,11} ( )
A){x / x } B){x / x x < 13}C){x / x x < 11} D){x / x x < 12}
P = { A, S, S, A, S, S, I, N, A, T, I, O, N }, Q = { S, T, A, T, I, O, N}P, Q ( )
A) B) P - Q = { S, A, T, O}C) Q - P = {O, N, I, T} D)
P = x : x = ,n N,n < 7
39
![Page 40: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/40.jpg)
( )
A) B) C) D)
A = {1, 2, 3, }, B = {4, 5, 6}n ( AB) ( )
A) B) C) D)
( )
A) B) C) D)
( )
A) B) C) D)
( )
A) B) C) D)
A = {p, q, r, s }, B = {s, r, q, p}A, B = ( )
A) B)
C) D)A B
A = {} B = {} ( )
A) A B = B) A = B C) A B D)B A
A B, B A A = B ( )
A) B)
C) D)
A = ( )
A) A B) C) D)
A, B ( )
A) n ( AB) = n (A) n(B) B)n ( AB) = n (A)
C) n ( A) = n (B) D) AB =
A = ( )
A) B) C) A D)
40
![Page 41: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/41.jpg)
{x : x A x B } ( )
A) A B B)AB C) A - B D)B - A
A - B = ( )
A) AB B)A B1 C)A B1 D)A1 B
( )
A) B) C) D)
A = {x : x FOLLOW} ( )
B = {x : x FLOW}
A) A = B B)A B C)A B D) B A
{ x : x A xB } ( )
A) A - B B) B - A C) A B D) AB
( A B ) - ( A B ) = ( )A) A - ( A B) B)( A - B) ( B - A)
C) ( A - B ) ( B - A) D) A B
{ x : x x < 10 } ( )
A) {1, 2, 3, 5, 7} B) {2, 3, 5, 7} C) {2} D) {2, 3, 5, 7, 9} A = {0, 2,4 } A=......... ( )
A) B) A C){ 2,4 } D)
A = {F, L, W, O}A ( )
(a) {x : x FOLLOW}(b) {x : x FLOW } (c) {x : x WOLF}(d) {x : x SLOW}
{x : x N , 1 x 5 } ( )
A) {1, 2, 3, 4,5 } B){2, 3, 4 } C){2, 3, 4, 5 } D){1, 2, 3, 4 }
41
![Page 42: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/42.jpg)
A = {x :x 42 },A ( )
A) B) C) D)
A = {2, 4, 6, 8, 10 } ( )
A) {x : x x < 12 }B){x : x x < 12}C){x : x x < 10 }D) {x : x x < 12 }
( )
A) B) C) D)
A, B ( )
A) n ( A B) = B) n ( AB) = O
C) n ( AB) = n ( A B) D) n ( AB) = O
( )
A) B) C) D)
(AS-4)
4 Marks
A = {x / x N, x 10}B = {x /x , x 10}C = {x /x, x 10}D = {x /x, x 10}
A B, A B, AAC, AAC, AAD, AAD, CD, CD
A = {x /xx 20}B = {x:x= 2y +1, yWy 9}
(i) A B (ii) A B (iii) A -B (iv) B - A
42
![Page 43: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/43.jpg)
A = {x / xN, 1 x 10}B = {x / xNx2 4}C = {x /x ,40 }D = {x / xW, 0 x 9}
A = {} B = {}C = {} D = {} (i) CD (ii) CD (iii) BC (iv) A - C
A = {x : x 2 = 4 3x = 9}{}A = {x FOLLOW}B = {x FLOW}C = {x WOLF}A , B , C,
A = {a, b, c, d}, B = {d, c, a, b}, AB BA A,B
(ii) P = {10, 20, 30----}, Q = {10,15,20,25 ------}P, Q
(i) A = {0, 2, 4} A AA
(ii) A = {2, 3, 5, 7, 11, 13-----} B = {4, 6, 8, 9-----}A,B
43
![Page 44: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/44.jpg)
(AS-4)
2 Marks
A = { x : x2 = 1, xN} B = { x : x2 = 1, xZ}
AB AAB
A = { } B = {
} C = {}
(i) A - B (ii) A - C (iii) BC
A = { ‘1’ } B = { ‘O’ }
(i) AB (ii) AB
A = {x :x x2 - 5x + 6} B = { x : x x2 - 6x + 9 }A , B
(i) (ii)(iii)(iv)
A = {x : x pq }
B = {x : x }A,B
{x : x + 5 =5 }‘x’
(AS-4)
1 Mark
44
![Page 45: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/45.jpg)
A = {1, 2, 3, 4, 5, 6, 7, 8, }
AB = B A,B
AB = B AB = A A - B
(A-- B) (B-- A)
{x : x + 5 = 0 } ‘x’
(AS-4)
1/2 Mark
A = {P,R, I, C,E }B = {P, R, I, Z E }A,B
A) B)
C) A B D)
A) B)
C) D)
l n P
A) , , ,a b c d
B) , , ,a c b d
C) , , ,d g c f
D) , , ,b g c h
A) , , ,c d g f B) , , ,a b h e
C) , , ,b c a d D) , , ,g h e f
P
n
lab
g eh e
c d
45
![Page 46: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/46.jpg)
‘’
A) A = {K, L, M } B) {A, B, C}
C) B = {P, Q, R} D) {P, A, M}
A) A, B B) A, C
C) B, D D) BC(AS-5)
4 Marks
= {a, b, c, d, e, f, g, h}A = {a, c, d, e }, B = {a, c, f, g} (i)AB(ii) AB
={x/11 x 50,x }G ={} H ={}
GH GH
A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 4, 6, 8, 10} (i) A - B(ii) B - A
A = {1, 3, 5, 7, 9, 11, 13, 15}, B = {2, 4, 6, 8, 10, 12, 14, 16}(A -B) ( B - A)
( AB) -(AB)
(N, W, Z, Q, S, R)
A
B
KL
M
D CR
PQ
D C
A B
46
![Page 47: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/47.jpg)
(AS-5)
2 Marks
A = {1, 2, 3,4, 5, 6 }, B = {2, 4, 6, 8}( AB) , (AB)
A = {1, 3, 5, 7, 9 }, B = {2, 4, 6, 8, 10}A - B, B - A,
(A - B) (B - A)
A - ( BC ), (A - B) ( A - C)
R, Q, Z, W, N
A = {x : x }B = {x : x}C = {x : n }A, B, C
(AS-5)
1 Mark
A = {1, 2, 3, 4, 5 }, B = {1, 3,5}AB
A = {1, 4,6,9,10}, B = {}AB
A = {a,b,c,d}, B = {c, d, e, f} A - B, B - A
AB , A - B, B - A,AB
ABAB
A BAB
47
![Page 48: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/48.jpg)
(AS-5)
1/2 Mark
AB
A){5, 6} B){5, 6, 7, 8}C) D){7,8}
A) A B B) B A
C) A,B D) B
A) A - B B) B - A
C) AB D) (AB) - (AB)
A) A - B B) B - A
C)AB D) AB
A) B - A B) A - B
C) AB D)AB
BA
BA
BA
BA
BA
48
![Page 49: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/49.jpg)
(BA
)
A) A - B B) B - A
C) AB D)AB
A) AB B)ABC) A - B D) B - A
A) AB B) AB
C) A - B D) B - A
A B
A) A - B = B) B - A =
C) AB = AA D) AB = B
A) AB ={ d, g } B)A - B = { a, b, h }C) B - A={ c, e, f} D)
abc
dg
cef
BA
B
A
BA
A B
A
B
49
![Page 50: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/50.jpg)
![Page 51: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/51.jpg)
(AS-1)
4 Marks
A) 3x2 + 5x -2 B) x2- 6x + 9
13
‘O’ 5 , (x ) = ax 2 + bx + c2 + 2
1 1
(x) = 6x2 + 4 + x - 2 ,
3 26x + 2x -10x - 4 2 2 (z) = 9z3 + 4z2+ 3z - 4 g (z) = z3 - 4z + a (z - 3)‘a’ 3 2x - 3 5x +13x - 3 5 (x - 5) (x) = abx2 + (b2 - ac) x - bc
(A) - 2 3, -9-3 1(B) , -
22 5
x3 + 3x2- 2x - 6 - 2 2 2x4 + 7x3- 19x2 - 14 x + 30 2 - 2
51
![Page 52: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/52.jpg)
x4 + x3- 34x2 - 4 x + 120 2-2 (x) = x2- 8x + kK(x) = x2+ Px + 45P (x) = ax2+ bx + C, a o, c o (x) = kx2+ 4x + 4, 2+ 2 =K (x) = x3- 5x2 - 16x + 80x3- 3x2 + x + 2g(x)(x - 2)(-2x + 4) g(x)(AS-1)
2 Marks
2x2- 7x + 3 ,
2 + 5
2x2+ 2px + 5x + 10 (x + p) P
15 - 2
P(x) = x3- 2x2 - 4x + 8P(2) P(x) = x2- 5x + K-1 K
P(x) = 6x3- 11x2 + Kx - 20 4x =3 K
P(z) = z3- 1 P(-2), P(2), P(-1), P(1)
52
![Page 53: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/53.jpg)
P(x) = x4- 16(u) =4u2+ 8u
(x) =x2- px +q, 1 1+
(t) =kt2+ 2t + 3kK (x) = 4x2- 8kx - 9KP (x) = x2+ 5x + 60, 5 x3- 3x2 + 5x + 3 (x + 2) y = ax +b a = 2, b = -3Y(AS-1)
1 Mark
P (x) = x2+ 5x + 6 (x) = x2- 16
14 - 1
5
-1 3,3 2
3x - 5 x2+ 5x + 6 5x3+ 3x2 + 6x + 7 P(t) = t3 - 1 P(1), P(-2), P(0), P(-1)
x2- 2x - 8 1 1+
53
![Page 54: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/54.jpg)
(t) = t2- 153 x - x2 + 5
1 3,2 2
x3- 3x2 + 5x - 3x2- 2 - x3+ 3x2 - 3x + 5 -x2 + x - 1r (z) = z3P (x) = x2 - 1P(m) = m2- 3m +1P(-1) P(1)(AS-1)
1/2 Mark
2x + 3
A) 3 B) 32 C)
-32 D)
-23
3x2 - 1
A) - 1 B) - 2 C) 3 D) -13
3, - 3 A) x2 - 3 B) x2 - 9 C) x2 + 3 D) 3x2 - 1
x2 + 1 A) + 1 B) 0,1 C) 1,1 D)
6x2 - 1
A) 0 B) 16 C) 6 D)
-16
3x3 -5x2-11x - 3
A) 1 B) - 3 C) -113 D)
53
A) x2 - 5x - 6 B) x2 + 5x + 6 C) x2 - 5x + 6 D) x2 + 5x - 6
54
![Page 55: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/55.jpg)
x - x-
A) B) C) D)
y = x3 - x x- ( 0,0)( 1,0)
A) B) C) D)f (x)(x + a)
A) (a) = O B) (- a) = O
C) f
1 = Oa D) f
-1 = Oa
A) B) C) D)
f (x) = 5x2 + 13x + k
A) O B) 5 C) 16 D) 6
, P (x) = x2 - 5x + k; - = 1k = A) 4 B) - 6 C) 6 D) 5
, , (x) = ax3 +bx2 + Cx + d
1 1+
1+ = .......
A) bd B)
cd C)
-cd D)
-ca
, , a x3 + bx2 + cx + d + + =
A) -ba B)
ba C)
ca D)
da
55
![Page 56: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/56.jpg)
, , ax3 + bx2 + cx + d =....
A) da B)
-da C)
-ba D)
ba
x2 - 9, + A) B) C) D) 9
2x2 + 5x + 1 2+ 2=
A) 4 B) 214 C)
254 D)
54
A) x2 - 5x + 4 B) x2 + 5x - 4
C) x2 + x - 20 D) x2 - 9x - 20
x2 + kx - 5K = A) 0 B) 5 C) - 4 D) 4
(x) = x2 +px + q , 1
1
A) qx2 + px + 1 B) qx2 + px + 10
C) px2 + qx + 1 D)
5 - 5 x3+ 3x2 - 5x - 15
A) B) C) D) 2x3 - 5x2 - 14x + 8
A) B) C) D) 2x2 + 3x + 1x + 2
A) B) C) D) x3 - 6x2 + 11x - 6
A) B) C) D)
56
![Page 57: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/57.jpg)
12x3 yn z7n A) B) C) D)
f (x) = 2x3 - 3kx2 +4x - 5K A) -1 B) 9 C) 0 D) 4
P (x) = 4x2 + 3x - 1
1P =4
A) 1 B) 0 C) -1 D)12
P q t2 - 4t +31 1 14+ - 2pq + =P q 3
A) 0 B) - 1 C) 2 D) 3
(x) = 14x2 - 42k2x - 9K
A) B) C) D) 3x2 - 8x +2k + 1 = 0K
A) 23 B)
13 C) 0 D) 1
, , P (x)+ + = 3
+ + = - 10 = -24 P (x) = A) x3 + 3x2 -10x + 24 B) x3 + 3x2 +10x - 24
C) x3 - 3x2 -10x + 24 D)ax3 + bx2 +cx + d0
A) -ca B)
ca C) 0 D)
-ba
3x2 + ax - 142x -b a - 2b = A) -2 B) 7 C) -8 D) -7
4 + 5 4 - 5 A) x2 - 8x + 11 B) x2 - 11x + 1 C) x2 - 8x + 3 D)
57
![Page 58: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/58.jpg)
2019 A) B) C) D)
x2 + 1 A) B) C) D)
x21x A) x2 B) x C) x3 D) x3 + 1
x3- x2 A) B) C) D)
x3- 4x A) 0,2,2 B) 0,+1 C) 0,+3 D) 0,0,0
(AS-2)
4 Marks
x3 + 3x2 -x - 3 P (x) = 3x2 - 5x2 - 11x - 3 -1
3 (x) = x2 - P(x + 1) - c, (+ 1) ( + 1)= 1 - c
K x2 - x - (2k + 2) 3x2 - x3 - 3x + 5 x -1 - x2 (A) - 2 x4 - 16(B) x2 + 9 (AS-2)
2 Marks
9x2 - 3x - 2 -13 2
3
(2x + 3), (3x - 2) 2x =3
58
![Page 59: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/59.jpg)
(x ) = x3 + 5x2 - 9x - 45 g (x ) = x3 + 8x2 + 15x (x ) = ax2 + bx + c
2
2 22
b - 2ac+ =a
(x ) = 3x2 - x3 - 3x + 5g (x ) = x -1 - x2 (x - 2) (x - 2) (x2 - x + 1)‘0’ x3 - 3x2 + 3x - 2
P (x ) = 4x2 + 3x - 1 14 - 1
x4 - 16
2
1x - 5x + 6
2x3 + x2 - 5x + 2 1 ,1, -22
x6 + 2x3 + x - 1( x2 - 1)K K > 1 x2+ kx + k P (x) g (x) ‘0’P(x)
g(x)3x2 - 2x - 1x = 1 ax2 + bx + c (AS-2)
1 Mark
x2 + 8x + 15
59
![Page 60: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/60.jpg)
P (x) = x2- x - 6
(i)
(ii) 22x - 3x +1 2
x2- 9 2x2+ 3x + 1 x + 2 2 2P (x) = x3- 2x (x2- 5)(x3+ 1)x2+ x + 3
-13,3 P (x) = 3x3- 5x2- 11x - 3
2
1x - 5x + 6
x2- 5x + 4(AS-2)
1/2 Mark
(x) = ax3- bx - a g(x) = x2+ bx + c, ab =
A)1 B) 7 C)-1 D) 0
, 9x2- 12 + 2 =
A) 19 B)
29 C)
13 D)
23
A) P (x) = 2x2 - 3x + 4 B) P (x) = x2 - 2x + 1
C) P (x) = 2x + 3 D) P (x) = 5
60
![Page 61: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/61.jpg)
a > 0 y = ax2 + bx + c
A) B)
C) D)
y = x3 x - x -
A) B) C) D)
A) x2 - 5x + 6 B) (x -2)2 + 4
C) 2x2 - 3 D) (x -3)(x -3) - (x2 - 5x)
ax2 + bx + c A) b o B) a o C) c o D) a = o
x - 2 P (x) = x2 + 4x - 12 K A) - 4 B) 4 C) 3 D) 2
nN,n32n + 7 A) B) C) D)
x - 1 A) x10 - 1 B) x11 - 1 C) 4x3 + 3x2 - 5x - 2 D)
A) x4 - 3x + 2 B) 2-3y + 6y2 - 2y3
C) x9/4 - 7x + 4 D) 5x2 - 6x + 2
y = ax2 + bx + c A) a < o B) a > o C) a < o D) a o
61
![Page 62: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/62.jpg)
A) B) n + 1 C) D)
A) 3x yt B) 3 x + 5 C) y2 + 8 D) x3+ 3
3x2 + 7x + 5xo A) B) C) D)
A) x2 + 5x + 6 B) x2 - 5x + 6
C) 1 + (x2 - 2x ) D) (x - 2 ) (x + 2 ) - (x2 + 5x )
ax2 + bx + c‘b’
A) B) C) D)
A) B)C) D)
(AS-3)
4 Marks
(x) =
A) (x) = 3x+ 1 B) g (y) = y3 C) r (m) = m 2- 1
P(x), g(x), r (x), deg p(x) =
deg q (x)
62
![Page 63: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/63.jpg)
-a a
ax2 + bx + c = oa > o a < o P (x) = g (x) x q (x) r (x) P (x) , g (x), q (x) , r (x)(AS-3)
2 Marks
x r(x) Op(x), g(x), q(x)
(AS-3)
1 Mark
i) 4 - y2 ii)5t - 3
63
![Page 64: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/64.jpg)
xx-x-x-x2 - 3 -x2 + 3x + 4(AS-3)
1/2 Mark
A) xyz B) 2x2 + 5x + 1 C) 2x + y D) 2 2y + + 9y
5x7 - 6x5 + 7x + 1 A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
64
![Page 65: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/65.jpg)
y = mx2 A) B)C) D)
A) A (x) = x2 + 7x + 30
B) A (x) = -x2 + 7x + 30
C) A (x) = x2 -7x + 30
D) A (x) = -x2 -7x + 30
A) B) C) D)
5x3 - 4x 2+ x - 2 A) B) C) D)
y = mx2 A) B) C) D)
2y2 - 3y + 4 A) B)C) D)
4x + 2 A) B)C) D)
A) B)C) D)
A) ax + b B)ax2 + bx + c
C) ax3 + bx2 + cx + d D)ax4 + bx3 + cx2 + d x + e
ax + b A) B) C) D)
D C
A B
10 -x
x + 3
65
![Page 66: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/66.jpg)
A) B) C) D)
ax +b
A) B) C) D)
A) B) C) D)2
(AS-4)
4 Marks
(x) = x3-12x2 + 39x -28
(x) = x3 - 12x2 + 39x + k A.Pk
(x) = x3 + 3px2 + 3qx + rA.P
(x) = 2x3 - 15x2 + 37x - 30A.P
(x) = ax3 + 3bx2 + 3cx + dA.P 2b3 - 3abc + a2 d = O
(x) = x3 - px2 + qx - rA.P
x3 - 6x2 + 3x + 10a,a + b, a + 2b a,b
(x) = x2 + px + q, (+ )2
(- )2
66
![Page 67: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/67.jpg)
(AS-4)
2 Marks
p(x) = 3x3 - 5x2 - 11x - 3 -13, -1,3
p (x) = 4x2 - 5x - 1 ,
2 + 2
(x) = 2x3-15x2+37x - 30 52, , 32 A.P
x2 + 4x + 3 , )i ii) 3, 3
sin450,cos450
, ,
ABC DE // BC, AD = (x + 2) , AE = (x) DB = (x -2) EC
(AS-4)
1 Mark
(x) = 5x2 + 13x+kK
(x) = ax3 + bx2 + cx +d, , 1 1 1
x2 + ax + 2b (x +2) a + b =4 a,b
(x) = x3 - 3x2 + x + 1a - b, a, a + b a,b
67
![Page 68: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/68.jpg)
(AS-4)
1/2 Mark
A) B) C) D)
A) B) C) D)
S = ut + 21 at2
A) B)C) D)
A) B) C) D)
A) B) C) D)
r2 A) B) C)r2 D)B C
A) B) C) D)
n A) B) C) n D) n
23
2x + + 7x + 4x
A) B) C) D)
A)B)C)D)
68
![Page 69: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/69.jpg)
x3 + px2 +qx + 5, , 1 1 1
A) pr B)
-pr C)
qr D)
-qr
ax3 + bx2 + cx + d, , 1 1 1
A) cd B)
-cd C)
bd D)
-bd
x3 - 3x2 + x + 1 , ,a a arr a
A) B) C) D)a - b, a, a+b x3-3x2 + x + 1 a =
A) B) C) D)(AS-5)
4 Marks
y = x2 - x -6
p (x) = x2 - 4x + 5
p (x) = x2 - 6x + 9
p (t) = t2 - 2t - 8
(n) = 2x2 + 3x + 1
(x) = x2 - 4
(x) = x2 + 5x + 4
ax2 + bx + c = o
(AS-5)
2 Marks
y = x2 - 3x - 4x - (- 1,0) (4,0)y = x2 y =2 x +3
69
![Page 70: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/70.jpg)
(AS-5)
1 Mark
(x) = x + 2 ‘2’
(AS -5)
a < oax2 + bx + c
A) B) C) D)
Y = P (x)
A) B) C) D)
1 2 3 4o-1
Y = P (x)
70
![Page 71: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/71.jpg)
(x)
A) B) C) D)
ax2 + bx +c
A) a > o, B)a < o, C)a < o, D) a > o,
A) B)
C) D) ax2 + bx +c a < o, b > o, c > o
A) B)
C) D)
x
y
x
y
3 2 1 1 2 3
71
![Page 72: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/72.jpg)
y = ax2 + bx +c a < o, b < o c < o
A) B)
C) D)
72
![Page 73: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/73.jpg)
![Page 74: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/74.jpg)
(AS - 1)
4 Marks
1. 2x + y - 5 = 0
3x - 2y - 4= 0
2. 8x - 4y = 20
3x + 2y = 11
3. x + 7y = 15
7x - y = 5
4. 2x +3y = 13
5x - 4y = -2
5. 2x - 3y = 7
3x - 2y = -2
6. 2x + 3y = 1
3x - y = 7
7. 3 2+ = 11x y
2 3+ = 4x y
8. 2 3+ = 1x y
1 1+ = 2x y
9. 2x + 3y = 5
8x - 27y = -5
10. 3x + 4y = 7
8x - 6y = 2
}
}}
}
}}}}}
x, y
}74
![Page 75: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/75.jpg)
“ ”A B C D x ,y
(AS - 1)
2 Marks
x + y = 6, x - y = 2
6 8x + = 6, 3x - = 5y y
p px - 6y = 152x - 3y = 5 2x - (6-x) = 8 - x x
3x + y
x - 3y D C
A B
7
13
75
![Page 76: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/76.jpg)
2x + y = 10, x + 2y = 10 3x - 2y = 4, x + y -3 = 0 yx 2x + y = 8, x - y = 1 x y 2x + 3y = 101, 3x + 2y = 99(AS - 1)
1 Mark
x - 4y = 5 y = -1x 3x + y = 11 y = 2x -5 x 3x + 3 (x - 1) = 9 2 (x + 5) = 20x 3 x + 4y = 2 x = 2 y y = 2x - 8 ax + by = c3x + 2y - 11 = 0x,y
1 = P = 2x x
1 1 1 1= , =x 100 y 80 x,y
x + y = 14, x - y = 42x - (4 - x) = 5 - x (AS - 1)
1/2 Mark
A) B) C) D)
A) 3 + 2x = y B) x +2y = y C) 3- x = y2 D) x + y = 0
2 ( x + 4) = 16x A) B) C) D)
76
![Page 77: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/77.jpg)
x + 2y = 8 A) B) C) D)
A) B) C) D)
A) B) C) D)
2x + y = 5 A) ( 0,6) B) ( 1,6) C) ( 2,2) D) ( 1,3)
A) B) C) D)
A) B) C) D) B C
a x + b, y + c1 = 0 a2 x + b2y + c2 = 0
A) 1 1
2 2
a ba b B) 1 1 1
2 2 2
a b ca b c C) 1 1 1
2 2 2
a b c= =a b c D)
a1x + b1y + c1 = 0 , a2 x + b2 y + c2 = 0
A) 1 1
2 2
a ba b B) 1 1 1
2 2 2
a b ca b c C) 1 1 1
2 2 2
a b c= =a b c D)
a1x + b1y + c1 = 0 ,a2 x + b2 y + c2 = 0
A) 1 1
2 2
a ba b B) 1 1 1
2 2 2
a b ca b c
C) 1 1 1
2 2 2
a b c= =a b c D) 1 1 1
2 2 2
a b ca b c
77
![Page 78: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/78.jpg)
3x + 4y = 2
A) B) C) D) 12
7x - 2y = 19 x = 2 y = ?
A) B) 52 C) - 5 D)
52
3x + 2y =11 y =
A) 11 - 3x
2 B)11 3x2 C)
2311 x
D) 11 + 2x
3
A) ax2 + bx + c = 0 B) ax+ by + c = 0
C) ax2 + bx + c < 0 D) ax2 + by2 = 0
x + y = 12 x - y = 8x A) B) C) D)
x + y = 2 2x + 2y = 2 A) B) C) D)
2a + 3b = 13 a = 2 b = A) B) C) D)
10a + 2b = 4 1a =5 b
A) B) 12 C) 2 D)
25
4x - y = 6 6x + y = 6 A) B) C) D)
78
![Page 79: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/79.jpg)
( l, m ) A) B) C) D)
2x - 3y = 5 y
A) 5 - 2x
3 B)
5 - 2x3 C)
5 2x3 D)
5 2x3
1 1
2 2
a ba b
A) B) C) D)
1 1 1
2 2 2
a b ca b c
A) B) C) D) A B2x + 3y - 4 = 0 y = 1x
A) B) 12 C) D) B C
A) B) C) D)
2x + 6y + 7 = 0, 5x - 7y +10 = 0 A) B) C) D)
2x + 3y = 5 3x - 3y = 0x
A) B) C) D) 12
x - axis
lmy
79
![Page 80: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/80.jpg)
2 3+ = 15x y
1 1= p, = qx y
A) 2p + 3q = 15 B) 2 3+ = 15p q
C) 2p + 3q - 15 = 0 D) A Cx + y- 7 = 0
A) ( 2,5) B) (3,4) C) (0,0) D) ( 7,0)
2x - 4y + 14 = 0 A) ( 3,5) B) ( 3,4) C) ( 5,3) D) ( 4,3)
y = 3x A) ( 3,1) B) ( 9,3) C) (3,9) D) ( 2,5)
ax + by + c = 0 a, b, c, R A) a + b 0 B) a2 + b2 0 C) a2 + b2 = 0 D) a + b = 0
y = ax + b x
A)
bo,a B)
b ,oa C)
-bo,a D)
,-b oa
x + y = 8 3x + 3y = 12 A) B) C) D)
A) B) C) D) x = 2, y = 3
A) ( 0,2) B) (3,0) C) ( 2,3) D) ( 3,2)
y =3x A) ( 3,1) B) (3,9) C) ( 9,3) D) ( 2,6)
3x - 5y = -1 x = 2 y
A) 15 B)
65 C)
75 D)
-75
80
![Page 81: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/81.jpg)
2p + 3q = 18 q = 4 p A) B) C) D)
2x - 3y = 5 y = 0.5x
A) 6.52 B) 3.25 C)
6520 D)
99x + 101 y = 499, 101x + 99y = 501 A) (-3,-2) B) ( 8,9) C) ( 1,4) D) ( 3,2)
34y = 5, y = 1x x
A) B) C) D) 2x - y= 5 ; 3x + 2y = 11
A) B) C) D) 3x + 4y + 7 = 0 ; 5x - 7y - 2 = 0
A) x = -1 ; y = 1 B) x = 1 , y = -1 C) x = -1, y = -1 D) x = 1 , y = 1
2x + 3y = 18 ; x - 2y = 2 A) ( 3,4) B) ( 6,2) C) ( 0,6) D) ( 3,4)
5 (x - 2 ) = x + 18 x A) B) C) D)
x + y =5, x - y = - A) (1,2) B) ( 1,-3) C) ( 1,4) D) ( 0,5)
(AS -2)
4 Marks
1. 4x + 2y - 10 = 0
3x - 2y - 4 = 0
2. 3x + 2y = 6
9x + 6y = 12
}}
81
![Page 82: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/82.jpg)
3. 3x + 2y = 11
2x + 3y = 4
4. 2x +3y -1= 0
3x - y - 7 = 0
(AS -2)
2Marks
5 - x = y2 + 2x + 5y = 4
2x 3y = 8
3. x + y - 5 = 0
3x + 3y + 6 = 0
4. 2x -3y = 5 (7,3 ) x + y = 8 7x + 7y = 14
}
} }
} x = 5, y = -2
82
![Page 83: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/83.jpg)
6x + 5y + 12 = 018x + 15 y + 36 = 02x + 3y - 5 = 0 6x + ky - 15 = 0 KK x - 2y = 3, 3x - ky = 1 K 2x + 3y + 4 = 0 8x + 12y + k = 0 p 5x +3y + 7 = 010x + 6y + p = 02x + 3y - 5 = 0, 6x + ky - 15 = 0 K (AS -2)
1 Marks
x + y = 0 2t + 1 = 2t - 5p 2x + py = 5 3x + 3y = 6 2x + 3y = 5 4 x + 6y = 82x + 4y = 6 2x - 6y = 4 (2,0)
1 1 1
2 2 2
a b c= =a b c a1x + b1y + c1 = 0 a2x+ b2y + c2= 0
K 3x + 4y + 5 = 0 , 9x+ 12y + K= 0
83
![Page 84: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/84.jpg)
K 2x - ky + 5 = 0 , 4x+ 6y - 5 = 0 x + y = 1 . kx + y = 2 k + 1 p x + y + 2 = 0, 2x + 2y + p = 0
(AS -2) 1/2 Mark
1. A) B) C) D)
2x - y -3 = 0, 2kx + 7y - 5 = 0 x = 1, y = -1 k A) B) C) D)
13x +k y = k 39x + 6y = k +4 k A) B) C) D)
2kx + 5y = 7 6x -5y = 11 k A) k 3 B) k - 3 C) k 2 D) k 6
2x + 5y = k kx + 15y = 18 k A) k = 2 B) k = 4 C) k = 6 D) k = 18
ax + by = cl x + my = n A) am bl B) am = bl C) am = cn D) am cn
3 (7 -3p) + 4p = 16 p A) B) C) D)
4x + 3y = 110 A) ( 10,20) B) ( 10,30) C) ( 15,30) D) ( 20,10)
x + y = 7 A) ( 2,5) B) ( 3,4) C) ( 7,0) D) ( 0,0)
84
![Page 85: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/85.jpg)
A) B)C) D) B C
kx - 5y = 2, 6x + 2y = 7 k A) 15 B) -15 C) 5 D) - 5
2x + 3y = 5 4x + ky = 8 K A) 2 B) 4 C) 6 D) 8
K 3x + 4y +2 = 0 A) 3 B) 4 C) 5 D) 6
kx + 2y -1 = 0 5x - 3y + 2 = 0K
A) 103 B)
-103 C)
310 D)
-310
4x + 6y - 8 = 0kx + 3y +5 = 0 K A) B) C) D)
2x + 3y + 4 = 0 10x + 15y - k = 0 K
A) B) C) D) -3x + 2y = 12
A) ( 2,3) B) ( 1,4) C) (0,6) D) (4,0)
x + 2y - 3 = 0 ; 5x - ky + 8 = 0 K A) B) C) - D) -
8x + 5y = 9 ax + 10y = 15 a A) B) C) D)
2x + y - 5 = 0 A) ( 1,3) B) ( 2,1) C) (3,2) D) A B
85
![Page 86: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/86.jpg)
A) B) C) D)( 2, - 3)
A) 2x - 3y = 10 B) 2x + 3y = 13 C) 2x - 3y = 13 D) 2x + 3y = -13
l1 = x + 2y - 4 = 0 ; l2 = 2x + my - n = 0 l1 , l2 m + n =..........
A) B) C) D) (AS -3)
4 Marks
i) x + y = 5 ii) 2x + 3y = 12 iii) 3x + 2y = 5
3 x + 3y = 15 2x + y = 6 6x + 4y = 7
2x + 3y - 6 = 0
i) 2x + 3y + 4 = 0 ii) x + y - 10 = 0
5x + 7y + 9 = 0 3x + 3y + 6 = 0
3x + 2y = 5b1x + a1 y + c1 = 0 , b2 x + a2 y + c2 = 0
86
![Page 87: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/87.jpg)
(AS -3)
2Marks
a1x +b1y + c1 = 0 , a2 x + b2 y + c2 = 0a1x +b1y + c1 = 0 , a2 x + b2 y + c2 = 0 2x + y - 5 = 0, 3x - 2y - 4 = 0 (AS -3)
1 Mark
xy
87
![Page 88: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/88.jpg)
12
2 (AS -3)
1/2 Mark
x y A) ax2 + bx + c = 0 B) ax2 + by2 = 0
C) ax + by + c = 0 D) ax2 = by
A) B) C) D)
A) 1 1
2 2
a ba b B) 1 1 1
2 2 2
a b ca b c
C) 1 1 1
2 2 2
a b c= =a b c D)
A) 5x - 7y = 50 B) 5x - 7y + 50 = 0
C) 5x + 7y - 50 = 0 D)
A) a1x + b1y + c1 = 0 ; a2 x + b2 y + c2 = 0
B) a1x2 +b1y2 + c1 = 0 , ; a2 x2 + b2 y2 + c2 = 0
C) ax + by + c = 0 ; ax2 + by2 + c = o
D)
A) B) C) D)
88
![Page 89: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/89.jpg)
A) B) C) D)
5x - 4y + 8 = 0 7x + 6y + 9 = 0
A) B) C) D)x - 4y = 5
A) B) C) D) a1x + b1y + c1 = 0 , a2 x + b2 y + c2 = 0
A) 1 1
2 2
a b=a b B) 1 1
2 2
a ba b C) 1 1
2 2
b c=b c D) 1 1
2 2
b cb c
2x + 3y - 5 = 0 3x - 4y + 1 = 0 A) Q1 B) Q2 C) Q3 D) Q4
A) B) C) D) AB
4x + 3y - 4 = 0 a = ......, b = ....... A) B) C) D)
A) x -y = 44 B) x + y = 44 C) xy = 44 D)x = 44y
x - 4y = 5 A) B) C) D)
A) x - y = 4 B) x = 4y C) x + y = 4 D) y = 4x
‘x’‘y’ A) 10x + y B) 10y + x C) xy D) yx
89
![Page 90: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/90.jpg)
A) B) C) D) A&B
xy A) yx B) 10x + y C) 10y + x D) x + y
x + y = 14 , x - y = 4 A) B) C) D)
x = 5 A) x - B) y C) x,y D)
A) B) C) D)
2x + 4y - 11 = 0 ; 4x + 8y = 22 A) B) C) D)
(AS -4)
4 Marks
125 60+ = 2
x y 130 240 43+ =
x y 10 x,y
90
![Page 91: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/91.jpg)
kmkmkmkmkm
(AS -4)
2Marks
(AS -4)
1 Mark
91
![Page 92: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/92.jpg)
ABC o o oA = x , B = 3x , C = y 3y - 5x = 30 ,A, B, C 2x - 3y = 7 (a + b)x - (a + b - 3)y = 4a +ba, b
x y+ = 1a b
(AS -4)
1/2 Mark
A) B) C) D)
A) B) C) D)
pm ql px + qy = s, lx + my = t A) B) C) D)
(AS -5)
4 Marks
1. 2x +3y - 12 = 0
x - y - 1 = 0
2. x + 2y = 5
3x + 6y = 10
3. x + 2y = 6
2x + 4y = 12
4.11x + 15y + 23 = 0
7x - 2y - 20 = 0
}}}}
92
![Page 93: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/93.jpg)
(AS -5)
2Marks
2x + 3y = 7
x,y
2x +y = 5
i ) ii) iii)
x -y - 1 = 0
(AS -5)
1 Mark
2x - 3y
x + y
3
7
93
![Page 94: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/94.jpg)
(AS -5)
1/2 Mark
(-2,2)
2x + 3y = 7
A) B) C) D) A B
3 2 1 1 2 3 4321
321
3 2 1 1 2 3 4321
321
3 2 1 1 2 3 41
2
3
4
4
3
2
1
3 2 1 1 2 3 41
2
3
4
4
3
2
1
A) B)
C) D)
1 2 3 4
32
3 2 1 1 2 3 4
32
1 2 3
32
32
2 1
A) B) C) D)
94
![Page 95: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/95.jpg)
![Page 96: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/96.jpg)
(AS-1)
4 Marks
25x - 6x - 2 = 0 2 2 2a x - 3abx + 2b = 0 2(p +1)x - 6(p +1)x + 3(p + q) = 0,q -1 P 2(2k + 1)x - (7k + 2)x + (7k - 3) = 0 ‘K’
2px - 14x + 8 = 0 P
25x - 6x +1 = 0 α,β α β 1 1+ + 2( + )β α α β
2x + px - 4 = 0- 2x + px + q = 0 p
q
2x - x - 2 = 0 α,β (2α +1) (2β +1)
24x - 3x -1 = 0 α,β
4 23x - 1 3x - 1- 5 + 4 = 02x + 3 2x + 3
(x +1)(x + 2)(x + 3)(x + 4) = 120
4 29x - 29x + 20 = 0
26x - 7x + 2 = 0 12
23x + 10x + 7 3 = 0
2x - 3 3x + 1+ = 3x + 2 x + 3
96
![Page 97: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/97.jpg)
‘K’
2(4 - k)x + (2k + 4)x + 8k + 1 = 0
(3y + 5)(2y - 8) = (y - 4)(y +1)
(AS-1)
2 Marks
2kx - 6x - 2 ‘K’
2x + kx + 64 = 0 2x - 8x + k = 0 ‘K’
(x - 5)(x - 7)(x + 6)(x + 4) = 504
22x + 7x + 5 2
22x + kx - 6 = 0 ‘K’
29x + kx +1 = 0 ‘K’
12
2x - 2x = -2(3 - x)
22x - 5x + 3 = 0
2x - 3x -10 = 0
2x + 5 = -6x
1 1 11- =x + 4 x - 7 30
97
![Page 98: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/98.jpg)
(AS-1)
1 Mark
24x + 4 3x + 3 = 0
2 13x - 2x + = 03
2x - 3x -10 = 0
x 49=4 x x
221x +17x - 2 = 0 29
10 23x - 2x - 3 = 0 27y - 6y -13 7 = 0 y x(2x -1) = 0 2x -16 = 0 2x - 5x + 6 = 0 n ‘n’ 2x + x -1 = 3 x(x + 4) = 12 1x + = 3
x
22x - 4x + 3 = 0
(AS-1)
1/2 Mark
22x - 8x + p = 0 “p”
A) 8 B) 64 C) -8 D)-64
23x - 5x + 2 = 0
A) -1 B) 23 C)
2-3 D)
32
23x - 6x + 2 = 0
A) 3 ± 33
B) 3 ± 3 C) 3 ± 32
D) 3 ± 36
98
![Page 99: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/99.jpg)
23x - 4 3x + 4 = 0
A) 0 B) 1 C) 2 D) 3
kx(x - 2) + 6 = 0 K =
A) -1 B) -2 C) -3 D) -4
x(x + 4) = 12
A) 2 B) -6 C) A,B D)
A) B)
C) D)
A) 2x + 6x + 5 = 0 B) 2x + 6x - 5 = 0
C) 2x - 6x + 5 = 0 D) 2x = 5
22x - 5x + 3 = 0
A) 2 B) 0 C) 1 D) -1
(x - 4)(x + 2) = 0
A) 2 B) 4 C) +3 D) 5
22x - 6x = 0
A) (2,6) B) (0,2) C) (0,-3) D) (0,3)
2x - 6x + 8 = 0 p,q p q =
A) 8 B) -8 C) 6 D) -6
2x - 3x - k = 0 k =.........
A) 4 B) -4 C) 9 D) -9
23x - 6x = 0
A) 3 B) 6 C) 0 D) -2
99
![Page 100: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/100.jpg)
23x - 5x + 2 = 0
A) -1 B) 23 C) -
23 D)
32
2(2x + 3) = 0
A) 0 B) 1 C) 2 D) -3
22x - 4x - 3 = 0
A) -8 B) 8 C) 4 D) -4
2x - 7x +12 = 0
A) -7 B) 7 C) 12 D) 127
1x - = 0x
x
A) 0 B) -1 C) 1 D)
2x - 5x + 6 = 0 α,β 2 2α +β = .........
A) 13 B) -13 C) -31 D) 31
2x - 2x -1 = 0
A) 2 ± 1 B) 3 + 2 C) 2 -1 D) 3 -1
25x + 5x + 6 = 0 α,β (1 +α)(1+β) =
A)6-5 B)
65 C) 110 D) 2
26x = 1
A) 0 B) 6 C) 16 D)
16
24x = 8
A) 2 B) -2 C) 8 D) 4
2kx + x - 6 = 0 K =
A) 8 B) 6 C) 1 D) -1
2x + x - 5 = (x + 3)(x - 2) + k K =
A) -1 B) 1 C) -2 D) 2
100
![Page 101: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/101.jpg)
25x - px + 12 = 0 p =
A) 46 B) 36 C) 26 D) 16
1 1,3 2
A) 2 5x +1x +6 B) 2-6x - 5x +1 C) 2 5x -1x -
6 D) 26x - 5x -1
2x - 5x = 0
A) 0 B) 5 C) A B D)
x(2x -1) = 0
A) 0,2 B) 12 C)
1 ,02 D)
10, -2
2 13x - 2x + = 03
A) 3 B) 13 C) 0 D) -2
23x + kx + 4 = 0 K
A) 4 3 B) 3 C) -4 3 D) 3 3
2kx + 6x +1 = 0 ‘k’
A) 9 B) 7 C) 4 D) 0
2x + 4x + k = 0
A) 0 B) 16-4k C) 4k-16 D) 1
23x - 6x + 2 = 0
A) 3 B) 2 3 C) - 3 D) -2 3
(px + q)(rx + s) = 0
A) q s,p r B)
-q -s,p r C)
-p -r,q p D)
p r,q s
101
![Page 102: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/102.jpg)
(3x - 2)(4x +1) = 0
A) -2 1,3 4 B)
2 -1,3 4 C)
-2 -1,3 4 D)
2 1,3 4
21x - = 9x
A) 7 -5,2 2 B)
7 5,2 2 C)
-7 5,2 2 D)
-7 -5,2 2
22x + 7x + 5 2 = 0
A) -5 , - 2
2 B) 5 , 22 C)
-5 , 22 D)
5 , - 22
A) 14,15 B) 15,16 C) 16,17 D) 17,18
2 2x + (x - 7) = 169
A) -12,5 B) 12,5 C) -12,-5 D) 12,-5
1 1x - =3x 6
A) 26x - x - 2 = 0 B) 26x + x - 2 = 0 C) 218x + 3x + 6 = 0 D) x = 4
2x - 4x - 6 = 0
A) 49 B) 97 C) 0 D) 1
1x =x
A) 1 B) -1 C) A,B D)
A) 2x - 5x + 6 = 0 B) 2x - 3x + 6 = 0 C) 2x + x +1 = 0 D) 2x = 4
2x -11x +18 = 0
A) 9 B) 2 C) 9,2 D) 0,9
102
![Page 103: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/103.jpg)
22x - kx + 3 = 0 , k =
A) +2 6 B) -2 6 C) A,B D) 6 2
2x - kx +1 = 0 k =........
A) -2 B)+2 C) A,B D) 4
43
A) 23x - 4x - 3 = 0 B) 23x + 4x + 3 = 0
C) 2x + 4x + 3 = 0 D) 23x - 4x + 3 = 0
x = 2 22x - kx + 5 = 0 k =...........
A) 152 B)
132 C)
-132 D) 0
22x + kx - 6 = 0 k =..............
A) a B) b C) ab D) 0
(AS-2)
4 Marks
x + 3, 2x + 5, 3x + 2
310
2 2 2 2 2x (a + b ) + 2x(ac + bd) + (c + d ) = 0
2 2 2 2(c - ab)x - 2(a - bc)x + b - ac = 0 a = 0
3 3 3a + b + c = 3abc
a,b,c ac 0 2ax + bx + c = 0
2-ax + bx + c = 0
24x + 3x + 5 = 0
103
![Page 104: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/104.jpg)
(AS-2)
2 Marks
2(x - 2) +1 = 2x - 3
2x - 8x + p = 0 α,β 2 2α +β = 40 p
3. 2ax + bx + c = 0 ‘c’a,b
2px + 6x + 4p = 0 p
3x2 -5x - 2 1-3
3 2 2x - 4x - x + 5 = (x - 3)
12 22x - 5x + 3 = 0
23(x - 4) - 5(x - 4) = 12
24x + 3x + 5 = 0
ca
(AS-2)
1 Mark
‘K’ 26x + 6 = 4kx
kx(x - 2) + 6 = 0 K
x(x +1) + 8 = (x + 2)(x - 2)
22x - 4x + 3 = 0
23x + 4 3 + 4 = 0
3 2 3x - 4x - x +1 = (x - 2)
32 22x - 5x + 3 = 0
2x(2x + 3) = x +1
2x - 2x +1 = 0
104
![Page 105: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/105.jpg)
(AS-2)
1/2 Mark
A) 2 2x - 2 = x + 4 B) x(x +1) = (x + 2)(x + 3)
C) 2x(2x +1) = x +1 D) 2 2(x + 2) = 5
A) 2(2x + 1)(x + 1) = x - 2 B) (x + 1)(x + 2) = (x + 3)(x + 4)
C) 2x = 7 D) x(x + 1) = 0
1 1 2+ =x 2 - x 5
A) B) C) D)
A) B)
C) D)
2ax + bx + c = 0
K
A) 2 2ka = bc(1 + k) B) 2 2kc = ac(1 - k)
C) 2 2kc = ab(1 + k) D) 2 2kb = ac(1+ k)
(x - b)(x - c) + (x - a)(x - c) + (x - a)(x - b) = 0
A) B) C) D)
2x + kx - 25 = 0
A) 2k -100 0 B) 2k +100 0 C) 2k +100 0 D)
3 2(m +1)x + 6x + 5x = 16 ‘m’
A) 2 B) 1 C) 0 D) -1
105
![Page 106: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/106.jpg)
2kx - 6x + 9 = 0
A) k=0 B) k<1 C) k>1 D) 2k -1 = 0
33x + 6x + k = 0
A) k < 3 B) k > 3 C) k =3 D) k < 0
2 2x - k = 0
A) 3 B) - 3 C) 3 D) 9
2(2x + 3) = 0
A) 0 B) 1 C) 2 D) -3
22x - 8x + p = 0 P
A) 8 B) 64 C) -8 D) -64
A) 27x = 2x B) 2-6x - x - 4
C) (2x +1)(3x + 2) = 0 D)
2ax + bx + c = 0 (a 0) α,β (-α, -β)
A) 2ax - bx + c = 0 B) 2ax + bx - c = 0
C) 2-ax - bx - c = 0 D) 2-ax - bx + c = 0
22x 3x + 5 = 0 A) 22x + 3x + 5 = 0 B) 25x - 3x + 2 = 0
C) 22x - 3x - 5 = 0 D) 25x + 3x + 2 = 0
a 2ax + bx + c = 0
A) 3 B) 2 C) 23 D) 0
106
![Page 107: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/107.jpg)
(AS-3)
4 Marks
2ax + bx + c = 0
(AS-3)
2 Marks
25x - 7x + 3 = 0
2x + 4x - 60 = 0
2x + 5x + 6
x
107
![Page 108: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/108.jpg)
3 + 2, 3 - 2
2x + 7x +10
(AS-3)
1 Mark
25
43
(AS-3)
1/2 Mark
0b 2 3 2ax(x - 4) + dx = 2x + bx + 10, m
A) 0 B) 1 C) 2 D) -1
A) x(x - 27) = 182 B) x(x + 27) = 182
C) x(27 - x) = 182 D) x(27 - x) = 182(x + 27)
a 2(a + 2)x - ax - 2 = 0
A) 1 B) -1 C) 2 D) 0
22x - 2 2x + k = 0
A) 1 1,2 2 B) (1,1) C) 2, 2 D)
1 1,2 2
108
![Page 109: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/109.jpg)
A) 2ax + bx + c = 0 B) ax + by = 0
C) 3 2ax + bx + c = 0 D)
2ax + bx + c = 0
A) 2a - 4bc B) 2b - 4bc C) 2b - 4ac D) 2c - 4ab
D = 0 2ax + bx + c = 0
A) b b,2a 2a B)
-b -b,2a 2a C)
c c,2a 2a D)
-a -a,2b 2b
2ax + bx + c = 0
A) 2-b ± b - 4acx =
2aB)
2-b ± b + 4acx =2a
C) 2-b ± b + 4acx =
2D)
2-b ± b - 4acx =a
2ax + bx + c = 0
A) ab B)
-ba C)
ba D)
ca
2ax + bx + c = 0
A) b2a B)
-b2a C)
2b4a D)
2-b4a
2D = b - 4ac > 0 2ax + bx + c = 0
A) B)
C) D)
A) 2x + 2x = 56 B) 22x + x = 56
C) 2x + x = 56 D) 2x - x - 56 = 0
(AS-4)
4 Marks
109
![Page 110: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/110.jpg)
(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0
24x + 3x + 5 = 0
x + 3, 2x + 5, 3x + 2 ‘x’
22x + 45x - 47 = 0
cm cm
72
5x, 3x-1.
(AS-4)
2 Marks
,2 22x + px + 8 = 0 p(x + x) + k = 0 ‘K’ 22x - 5x + 3 = 0 25x - 6x - 2 = 0 22x - 2 2x +1 = 0 Sin 45
0
cm,
x+7, x cm
110
![Page 111: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/111.jpg)
9. 2x - 3x - 4 (AS-4)
1 Mark
2x - 2x +1 = 0 sin 900, tan450
23x + 2 5x - 5 = 0
3x - = 2x
2ax + bx + c ‘b’
(AS-4)
1/2 Mark
α,β 2ax + bx + c = 0 α β+β α
A) 2c - 2ab
ab B) 2
2b - 2ac
c
C) 2a - 2bc
bc D) 2
2a - 2bc
b
2= b - 4ac = cos90 0
A) B) C) D)
2x + ax + b = 0 a ba+b=
A) 1 B) 2 C) -2 D) -1
2ax + bx + c = 0 Sina Cosa 2b =
A) 2a - 2ac B) 2a 2ac C) 2a - ac D) 2a ac
111
![Page 112: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/112.jpg)
2ay + ay + 3 = 0 2y + y + b = 0 y=1
ab = ..........
A) 3 B)-72 C) 6 D) -3
6 + 6 + 6 + ......
A) 4 B) 3 C) -2 D) 3.5
a b 2 + bx +1 = 0ax
A) 10 B) 7 C) 6 D) 12
A) 8m, 10m B) 8m,12m C) 10m, 12m D) 14m,8m
A) 24 B) 29 C) 39 D) 37
3
5 A) 8m B) 9m C) 10m D) 11m
(AS-5)
4 Marks
2 + bx + c = 0ax
i) 2b - 4ac > 0 ii) 2b - 4ac 0 iii) 2b - 4ac 0
(AS -5) 1. ax2 +bx + c = 0, a, b, cR , b2- 4ac = 0
y
o xo
A) B)
o o
C) D)
112
![Page 113: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/113.jpg)
o
D)
o
C)
x
y
o x
A)
o
B)
o
B) y
xo
A)
o
C)
2 2ax + bx + c = o,b - 4ac > o
ax + by + c = o
y
o x
D)
y
y
x
x
y x
y
y
A)
o
B) y
x
o
C)o
D)
2p(x) = ax + bx + c = o,a < o a,b,c€R y
y y
xo
x
x
x
x
113
![Page 114: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/114.jpg)
y
o x
A) B)
o
C) y
x
y
o x
D)
y
x
114
![Page 115: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/115.jpg)
![Page 116: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/116.jpg)
(AS-1)
4 Marks
a2= 21 a7= -14 a1,a3, a5,a8,
116
![Page 117: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/117.jpg)
n
a ‘r’
i) ,1 1a = r =2 2 ii) a = 4 , r = 2
(AS-1)
2 Marks
AP ‘n’
8 6 42, , , .......AP5 5 5
AP n3 - 2nt =
4
4 + 7+ 10 + --------AP
6, 11, 16 ,... AP
AP
8K + 4 , 6K - 2, 2K - 7 AP K
AP 54, 51, 48 ----
AP ‘o’
a2 = 15, a4 = 5 a1, a3
1 + 2 + 3 + ------ + 100
AP
a = 24, b = 4 AP
AP
117
![Page 118: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/118.jpg)
(AS-1)
1 Mark
4, 1, -2, -5, ------AP
5 5 55, , , .......GP2 4 8
AP n3 - 2nt =
4 t5
GP n
Sn = n2a2
a, b, c APb
5 5 -5- , , .......GP2 4 8
GP a = 2 , r = 3, n = 6 an
1 + 2 + 3 + ------ + 10
0.4, 0.04, 0.004, ---------GP
0.5, 0.05, 0.005, ---------GP
GP 1 21 1a = ,a =8 2 a12
3,43
n = 55n
AP
APannn(n + 3)a =
n + 2 a10
APn
118
![Page 119: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/119.jpg)
(AS-1)
1/2 Mark
AP
A) B) C) D)
1 -1 -3 -5, , ,4 4 4 4
A) 1-4 B)
14 C)
1-2 D)
12
an = 3n + 7 d =
A) B) C) D)
an = 2n + 5 a5 =
A) B) C) D)
A) 1, 3, 5, 8,------ B) 2, 4, 6, 8, 10, --------
C) 1, 4, 9, 16,------ D) 1 1 11, , ,2 3 4 --------
a = -1d = -3a10 =
A) 28 B) -28 C) 26 D) -26
AP
A) 31 B) 35 C) -31 D) -35
x, y , z z =
A) 2x + y B) 2y + x C) x - 2 y D) 2y - x
AP
A) 6 B) 3 C) 1 D) 0
A) 30 B) 31 C) 32 D) 33
A) 54 B) 44 C) 34 D) 24
119
![Page 120: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/120.jpg)
a12 = 37 d = 3 a =
A) B) C) D)
A) -34 B) 34 C) -32 D) 32
A) 57 B) 22 C) 4 D)
AP a1 = - 4, a6 = 6
A) a5 B) a4 C) a7 D) a3
A) 249 B) 110 C) 119 D) 99
A) 200 B) 210 C) 220 D) 420
a1= 9 1r =3 a5 =
A) 19 B)
13 C)
127 D)
181
1 1 11, , , , - - - - -GP2 4 8
A) B) C) 12 D)
1-2
A) 512 B) 128 C) 2048 D) 256
n
A) n2 B)
n -12 C) n D)
n + 12
A) 55 B) 10 C) 50 D) 45
A) B) C) D)
120
![Page 121: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/121.jpg)
3,3 + 2,3 + 2 2,3 + 3 2, - - - - -AP
A) B) 2 C) 2 2 D) 12
ar2 ‘r’
A) ar4 B) ar5 C) ar6 D) ar7
5 5 5, , , - - - - -GP2 4 8 n
A) n
52 B)n C) n-1
52 D) n+1
52
1a = 5,r =5
A) 15 B) 5 C)
15 D)
A) B) 1
10 C) D) A B
A) 245 B) 490 C) 47 D) 295
A) 4920 B) 5920 C) 4290 D) 5290
A) 3, 9, 27 -------- B) 3, 6, 12, 24 --------
C) 3 3 33, , ,2 4 8 -------- D) 2, 6, 18, 54 --------
x, 4, 4x GP x =
A) B) C) 12 D)
1-2
2x, 3x, 4x, AP
A) 9 x B) 10 x C) 11 x D) 12 x
APan =
A) 2n + 2 B) 2n + 4 C) 6 - 2n D) 2n + 6
121
![Page 122: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/122.jpg)
5 72, ,3, ,4, ............2 2 A P
A) 12 B)
32 C)
13 D)
AP an = 3 + 2n
A) 9 B) 12 C) 21 D) 42
A) 46 B) 43 C) 40 D) 37
A) 766 B) 666 C) 718 D) 659
a = 4, d = -3,
A) -5 B) -8 C) 16 D) -2
2x, 4x, 6x, -----AP
A) x B) 2 x C) - x D) -2x
an = 3n +7 AP S2 = ?
A) 10 B) 13 C) 23 D) 33
A) 845 B) 745 C) 645 D) 945
3, -32, 33 -----GP
A) 3 B) -3 C) 13 D) 0.3
AP
A) -5, -7, -9 B) 5, 7, 9 C) 4,5,6 D) -9, -11, -13
A) 40 B) 60 C) 45 D) 85
A.Pan = 3n + 7 d = -----
A) 1 B) 3 C) 6 D) 9
G . Pa1 = 2 r = -3 a7 = ----
A) 1458 B) -1458 C) 729 D) -729
122
![Page 123: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/123.jpg)
G.P2,8,32 ------
A) 512 B) 128 C) 2048 D) 256
A) 4920 B) 5920 C) 4990 D) 5290
G P
A) 59 B) 510 C) 5 210 D) 5 29
A) 407 B) 500 C) 405 D) 400
1 1 1, , .....G.P16 64 256
A) 12 B)
116 C) D)
14
A . P
A) 31 B) 32 C) 34 D) 35
A . Pan = 2n + 3 a12 =
A) 165 B) 23 C) 27 D) 38
A) 59 B) 60 C) 61 D) 62
a12 = 37, d = 3 S12
A) 41 B) 256 C) 246 D) 276
A) 750 B) 7500 C) 5500 D) 8050
A.P
A) 1 B) -1 C) 2 D) -2
1 -1 -3, . , - - - - AP4 4 4
A) 14 B)
-14 C)
12 D)
-12
123
![Page 124: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/124.jpg)
a = - 1.25, d = - 0.25 a4=
A) B) C) D)
1a = 5,r =5
A) 15 B) 5 C)
15 D)
(AS-2)
4 Marks
‘’
1 -1 1, , , - - - - - -2 4 8
5,5,5 5, - - - - an = 3+ 2n a1, a2, a3 ------an x
x
‘x’
n Sn S30 = 3( S20 - S10)
124
![Page 125: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/125.jpg)
(AS-2)
2 Marks
------67 A.P
A.Pn n2 + 7nn 2n + 6
A.P G.P
1 1 1, , - - - - - GP2 4 8 1
1024
A.P A.Pan = 4+ 3n n a,b,cb + c, c + a , a + b
(AS-2)
1 Mark
A.PA . P a10= -31 ‘’an = 1 + n a1, a2, a3 , a4A . P
125
![Page 126: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/126.jpg)
A . Pan = 3n + 4Snn n
A . P Sn = 5n2 + 3n an
(AS-2)
1/2 Mark
A . P-
A) -40 B) -23 C) -32 D) 10
G . P 1 1 1, , , - - - - -3 9 27 1
2187
A) 12 B) 8 C) 7 D) 10
A) A P B) G P C) HP D)
A Pa1= 7, a13= 35 S13 = ----
A) 546 B) 464 C) 273 D) 672
A) 6, 12, 24,------ B) 1, 4, 9, 16,-----
C) 0, 3, 9, 27,------ D)
G P ar2r
A) ar4 B) ar5 C) ar6 D) ar7
A) 3, 9, 27------ B) 3, 6, 12, 24, -----
C) 2, 4, 10,12,------ D)
G . P
A) 1 1 1, , , - - - - -64 32 8 C)
B) D) A B
126
![Page 127: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/127.jpg)
G . P
A) -162 B) -108 C) 162 D) -216
A) 7 B) 6 C) 5 D) 8
an = 3 + 2nA . P
A) 9 B) 12 C) 21 D) 672
A) 55 B) 10 C) 50 D) 45
5 5 5, , , - - - - -Gp2 4 8 n
A) n
52 B) 5.2n C) n-1
52 D) n+1
52
an = 512 n
A) 6 B) 5 C) 7 D) 9
a1 = 9, r = 13 a5 =
A) 19 B)
181 C) 1 D)
127
G .P arn
A) n + 2 B) n - 1 C) n + 1 D) n
2x , x + 10, 3x + 2 A P x
A) 6 B) 3 C) 5 D) 4
x , 1, 1x -------G P
A) 1 B) 2
1x C) x D) 3
1x
127
![Page 128: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/128.jpg)
G P
A) 1 1 1, , , - - - - -64 32 8
B) 30, 25, 20, 15 ---------
C) 1, 4, 16, 64----------
D) A B
a7 = 4, d = 2 S8 = - 8 S9
A) -6 B) -12 C) -14 D) 0
A) 5050 B) 5049 C) 5115 D) 1155
x, x + 2, x + 6 G .P x
A) 2 B) -4 C) 3 D) 7
G.P ap + q= m, ap - q = n ap=.............
A) m2n B) mn C) mn D) m n
(AS-3)
4 Marks
n2n2+ 6nn
n
n
i) ii)
Sec 450, Cosec2 450, 4 Sin 450
128
![Page 129: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/129.jpg)
(AS-3)
2 Marks
AP tn =5n -1
a = 2, d = 4, n = 12 AP tn t10
an = 3 + 4 n a1, a2, a3,
a = 512, r = 12 GP a3
n
‘n’
(AS-3)
1 Mark
n n
APn
(AS-3)
1/2 Mark
a + 3d, a + d, a - d ------
A) a + 2d B) a - 2d C) a - 3d D) a - 4d
129
![Page 130: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/130.jpg)
G.Pan = arn - 1 r -----
A) B)
C) D)
A) B)
C) D)
n
A) n2 B) n(n +1)2
C) n (n + 1) D) n(n +1)3
(AS-4)
4 Marks
n i) n 3n - 2
ii) n, n + 2, n + 6 GPn
130
![Page 131: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/131.jpg)
cm
(AS-4)
2 Marks
KK + 2, 4K - 6, 3K + 2 GP
2 GP
GP n
GP 116 1
108
(AS-4)
1 Mark
131
![Page 132: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/132.jpg)
-2 -7, x,7 2 x
3, 6, 2 3, 2 6, a, b, c A.P ( a - b)
A P 1.2, 1.44, 1.728 - - - - -
(AS-4)
1/2 Mark
4x 5xx, , ,2x - - - - - -A.P3 3
A) x3 B)
x2 C) x D)
2x3
x, G.Px
A) 24 B) 26 C) 28 D) 30
x, 1,1x G.P
A) 1 B) 2
1x C) D) x
2, 8, 18, A) 36 B) 38 C) 32 D) 24
x,4, 4x G.P x
A) 2 B) 1 C) 12 D)
1-2
G.P
A) 0.1 B) 0.01 C) 0.001 D) 1
2, 8, 18, 32, - - - - - - G.P
A) 64 B) 72 C) 50 D) 84
31
x
132
![Page 133: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/133.jpg)
A.Pan = 7 - 2n d = -------
A) 7 B) -2 C) -7 D) 2
3,3 + 2, 3 + 2 2, - - - - - A P
A) B) 2, C) 2 2 D) 12
n
A) 3.2n - 1 B) 3.2n - 1 C) 2n + 1 D) 2.3n - 1
Sin230, Sin245, Sin260,
A) B) C) D)
x, x + 2, x + 6 x
A) 1 B) -2 C) 2 D) 0
(AS-5)
4 Marks
cm
133
![Page 134: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/134.jpg)
cm
i ii iii iv
134
![Page 135: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/135.jpg)
![Page 136: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/136.jpg)
(AS-1)
4 Marks
ABCD ABCDABCD,E,F BC,CA, AB ABCDEF AB A BAOB AB AOBA( -4,6) , B (3,8) A( 6,2) , B (3,-5)( -5, -1) P ( 2,3) , Q (-2,-3) R(4,3)PQR QR P 2x + 3y - 6 = 0A = (4,2) , B = (1,y), AB = 5y
136
![Page 137: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/137.jpg)
(AS-1)
2 Marks
AB C
32
AB AB C AP:BP = 2:1A
A (-2,0) , B = (3,4), C = (10,- 1), (-a,0),(a,0),(0,a)
P (4,3)
A (x,O)
B (o,4)
Y
XO
137
![Page 138: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/138.jpg)
(AS-1)
1 Mark
A B
A B “R”
A, B 10. A(3,2), B (2,1), C (4,-6)
(AS-1)
1/2 Mark
A)
51,2 B) ,1
52 C) (1,3.5) D) (0,0)
A) 7 B) 92 C) 10 D) 27
A ( x1, Y1)
O
Y
X1
XB ( O, Y2)
138
![Page 139: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/139.jpg)
A) B) C) D)
A) B) C) D)
AB AB
A)
1 1- , -2 2 B) (2,9) C)
1 9- , -2 2 D) (-2,-8)
(x1,y1) (x2,y2)
A) 2 1
2 1
y - ym =
x - x B) 1 2
1 2
y - yx - x C) 2 1
2 1
x - xy - y D) 0
A) -1 B) -5 C) 1-5 D) 11
5
‘X’ A) B) C) D)
A) B) C) D)
X = 2000, Y= 3000 A) B) C) D)
A) B) C) D)
2x+y = 8x A) B) C) D)
4x+3y = 12y- A) B) C) D)
A) B) C) D) 13
A) B) C) D)
139
![Page 140: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/140.jpg)
A) B) C) D)
A) B) C) D)
A,B,CABC
A) B) 12 C) D)
A) B) C) D)
A) A = s(s -a)(s - b)(s - c) B) A = a(a - s)(b - b)(c - s)
C) A = b(s-a)(s -b)(c-s) D) A = c(a - s)(b - s)(c - s)
A) B) C) D)
(x,y) (x,y)
A) B) C) D)
A) B)C) D)
A) B)C) D)
A) 55 B) 73 C) 5 D) 24
A) B) C) D)
140
![Page 141: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/141.jpg)
kk = A) B) C) D)
1-3 ,32
1-7,22
A) B) C) 1-7 D) 1
7
x,3 x= A) B) C) D)
A)
2 4,3 3 B)
1 2,3 3 C) (1,2) D)
A)
53,2 B) (-5,-4) C) (3,2) D) (-3,-2)
A) B) C) D)
A) B) C) D)
A=B C AB=
A) 2AC B) 3AC C) AC3 D) AC
x- A) 00 B) 300 C) 450 D) 600
A) B) C) D)
141
![Page 142: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/142.jpg)
y A) (o,y) B) (x,o) C) (x,y) D) (y,y)
x- A) (x,y) B) (x,o) C) (x,x) D) (o,y)
A B C O
A) B) C) D)y - (- 8,-7)
A) B) C) D)x
A) B) C) D) ABCA B C ABC
A) B) C) D)
A) 1 B) 0 C) 52 D) 52
y0y= A) 4 B) 0 C) 4 D) 2
A) B) C) D)
A) B) C) D)
x,y- A) 00 B) 900 C) 1800 D) 3600
A) B) C) D)
A) B) C)
8 17,3 3 D)
4 11,3 3
142
![Page 143: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/143.jpg)
A) B) C) D)
A) B) C) D) 52 . e TÖ\ _ + < ŠTe Ú q T+ & (x,y)
A) 2 2x + y B) 2 2x - y C) 2x D) 2y
KK A) B) C) D)
PP A) B) C) D)
A) B)C) D)
A)
3 7,2 2 B)
-3 -7,2 2 C)
-3 7,2 2 D)
3 -7,2 2
ABC
A) B) C) D)
ABC
A) 12 x1y2 B) 1
2 (x2y1) C) 12 x2y1 D) x1y2
X1
BY1
A
O
Y
O
B (4,3)
XA (4,0)
143
![Page 144: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/144.jpg)
(AS-2)
4 Marks
P(2,-1), Q(3,-4), R(-2,3), S(-3,-2)
(i)(ii)(iii)
a) (2,3) b) 2, 2 c) ,1 2 d) (5,6)
A (-3,-2), B(3,2), C -2 3,3 3
(4,7), (1,4), (3,2), (6,5)
A(-1,5),B(3,1), C(5,7), ABCD,E,FBC,CA, AB
ABC DEF
A(x1,y1), B(x2,y2 ), C(x3 ,y3 )
(4,-3), (1,3), (5,-5)
2A 2,3
-7B -3,2
5C 3,2
144
![Page 145: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/145.jpg)
A (-4,3) B(6,5) y(3,0), (0,2) (0,0)A (1,5), B (2,3)C(-2,-1)(-a,0),(0,-a),(a,0),(0,a)y=x+8 x- y-
(2,-2), (8,4), (5,7)(-3,-4), (12,5), (14,12)A (4,7) , B = (1,4), C = (3, 2),D = (6, 5)
(AS-2)
2 Marks
(-1,-1), (1,2), (-3,-4), (-1,7),(3,-5),(4,-8),(3,2), (5,-3), (0,0),A(2,1), B(0,3), C (-2,1), D (0,1),
145
![Page 146: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/146.jpg)
A (-3,2) , B (9,1)(1,3) (5,4)(9,-9),(8,-2),(1,-3),(1,-1),(4,1),(-2,-3)(5,8),(1,5),(13,14) (4,5),(7,6),(4,3),(1,2)
abc (a,a2), (b,b2), (c,c2)
(sin2, sec2), (cos2, tan2)
1 1,2 2
A(a.0), B(0,b);AB P(x,y) x y+ = 1a b
A(0,3), B(2,1) ,C(0,-1),D(-2,1)A (7,5) , B = (2,4), C = (6,10), A B = AC A (0,0) , B = (2,2), C = (0,4),P (9,-9) , Q = (8,-2), R = (1, - 3),S (1,2) , A = (-3,4), T = (7, - 1) A (-1,5) , B = (3,1), C = (5,7),ABCD,E,F A B ABCDEF (AS-2)
1 Mark
A(2,-3), B(5,0), C (0,-5), D(1,3)
A(4,2),B(8,6)
146
![Page 147: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/147.jpg)
(5,0),(7,0) (x2-x1)
A(7,5), B(2,3), C(6,-7),
(-2,3), (8,3), (6,7)
(5,-6)(-1,-4) y-
-130,3
(2,0),(0,2)
“ (-9,0) y-”
(AS-2)
1/2 Mark
A,B,C
A) AB + BC AC B) AB + AC = BC C) AC + BC = AB D)ABC = O
(1,2),(4,y),(x,6)(3,5)
xy
A) B) C) 3 , 62 D)
A,b,C ABC
A) B) C) D)
A) B) C) D)
147
![Page 148: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/148.jpg)
l
A) x = 2 B) y = 2 C) x = 0 D) y =0
A) B) C) D)
A) (4,-7) B) (-5,2) C) (4,3) D) (-6,-2)
xA) (4,2) B) (-6,3) C) (3,0) D) (0,8)
y A) (2,4) B) (-3,-6) C) (0,5) D) (8,0)
(x,-y)Q4(-x,y)
A) Q1
B) Q2
C) Q3
D) Q4
A) x = 2 y - B) y = 4y - C) x = 4 x - D) y = 6 y -
A,B,C AB = 3 2 , BC= 5 2 , AC = 2 2 A) AC B B) AB C C) BC A D) BC A
3
2
0
0 1 2 3
Y
X
l
148
![Page 149: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/149.jpg)
(AS-3)
4 Marks
(6,4), (-4,-6)(4,6) (2,5), (3,-8), (9,10) P(-6,-9),Q(6,9) S(-8,2), T(3,2), AB AB x-(AS-3)
2 Marks
(-3,0), (-1,0), (2,-4)
A (2,3), B (-1,0),C (2,-4)AB,BC, AC, (x,y)(7,1)(3,5)x y
A,B (-2,-2)(2,4) 3AP = AB7 P AB
P ' 'AB ‘P’
149
![Page 150: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/150.jpg)
(AS-3)
1 Mark
1
A =2
bh Somu A(x
1,k)B (x
2,k)‘0’
Q(x,y)(x,y) x - y -x - y - x -y -(AS-3)
1/2 Mark
A) x- B) y- C) D) x,y
A) y- B) x- C) D)
y = 6 A) B) C) D)
x A) x=0 B) y=0 C) D)
y- A) y= 0 B) x=0 C) 0 D)
150
![Page 151: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/151.jpg)
x- A) B) C) D)
y- A) x-0 B) y-0 C) D)
A) (2,-3) B) (5,0) C) (0,-5) D) (1,3)
(2,3) , (2,-3) A) x- B) y- C) D)
x- A) B) C) D)
(0,0), (1,0), (0,-4) A) B)C) D)
x-
A) B) C) 3 D) 13
y-
A) (0,c) B) (0,0) C) (c,0) D)
y = mx
A) B) (0,c) C) (c,0) D) (1,1)
y = mxY
X
Yy = mx + c
O
151
![Page 152: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/152.jpg)
y-
A) (2,0) B) C) D)
(AS-4)
4 Marks
P (0,-2), Q (4,2), R (0,6),
A(1,a), B (7,-4), P (3,0)
‘a’
(-1,4), (5,2)
A (8,-10),B(7,-3), C(0,p), B
‘P’
ABC C A (1,-6), B (-5,2)
ABC D E F
A,B,CD,E,FBC, AC, AB
Y
2
1
1 2
152
![Page 153: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/153.jpg)
x,y
x-y+1=0
-a,a0,a+a 3 x-
(2,3), (4, -2)xA(4,0), B (a,b)P (0,0), Q (a,b),a,b
P (6,-1), Q (1,3), R (x,8) PQ = QR ‘x’
A(4,6), B (-7,-1) x-A(-3,2), (6,1)y- A(1,1), B (-7,-4) P (3,0)(AS-4)
2 Marks
P(2,5), Q(x,-7), PQ=10 units‘x’
A(6,5), B (-4,3), x-
T (2,5),S (x,3), x
(1,K),(4,-3),(-9,7), ‘K’
153
![Page 154: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/154.jpg)
(t,2t), (-2,6), (3,1),t
(4,6),(-7,-1),x
P (2,5), Q (x,-7); PQ=13‘x’
(0,0), (a,0), (0,6) ‘a’
(x,y)(3,0)(0,4)x,y
P (a cosθ , 0),Q (0,asinθ ) AB
R (b+c,c+a)S (c+a,a+b)RS
ABC AD
A(-2,5), B (3,2) A = 2BCC‘C’ P(t,2t), Q (-2,6), R (3,1), ‘t’ F(4,8), A (7,5), S (1,-1), T (-2,K) K (AS-4)
1 Mark
(2,K),(-1,7),K
(a,0),(0,b),(1,1), 1 1+a b
(2,0) x-A(5,1)B (-1,5) ‘P’
B (3,-2)
A (4,-6)
C (5,2)D
154
![Page 155: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/155.jpg)
(4,6)(-7,-1)x(6,1) (-3,2) y-A (4,2), B (1,y)AB = 5 y(1,x) 10 xP(x,y)A(3,6)B(-3,4) 3x + y = 5(2,1),(p,-1)(-1,3),‘p’y- cos 900 (3,-2),(-2,8) (0,4) cot 900
(2,3)O (0,0) , A (4,0), B (0,6)
2x + y = 8x-
(sec 450, sin 300), (log11121,log3243)(tan 450, cot 450) , (cosec2 300, sec2 450)(a cos ,0),( 0, a sin ) (a cos ,0),( 0, a sin )(AS-4)
1/2 Mark
(sinθ , cosθ )
A) cosθ B) tan θ C) sinθ D) 1
(0,0)(cos, a sin)
A) 1 B) a C) D) 1
155
![Page 156: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/156.jpg)
x- A) -450 B) 450 C) 300 D) 600
(1,1) AB , A (4,5) B =
A) B) C) 52 D)
A) 1 + 2 B) 2 +1 C) D) 2 + 2
F4,7
A) B) C) D) x,yx,y
A) -5,-1 B) 5,1 C) 1,5 D) 0,0y = 4
A) sin0 B) cos0 C) tan0 D) A Cy -
A) sin 900 B) cos 900 C) tan 900 D) sin00
A) N B) W C) Z D) R
KK A) 3 B) 4 C) 13 D) 12
A-1,3B 2,PC 5,-1P = A) 4 B) 3 C) 2 D) 1
3a,4-2,2b2,2a + 2b A) 2 B) 4 C) 6 D) 8
1,2-1,x2,3 ‘x’ A) 0 B) 1 C) 2 D) 3
C
156
![Page 157: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/157.jpg)
-2,-1a,04,b1,2a,b A) 1,3 B) 2,3 C) 0,0 D) 5,4
a,bb,cc,a0,0a3+b
3+c
3=
A) abc B) 2abc C) 3abc D) 12 abc
x- 600 A) 3 B)
13 C) 3
2D)
13
KK =
A) -5 B) 5 C) -7 D) 7
(AS-5)
4 Marks
A (-3,6) B (0,4) C (3,0) D (6,0)A(2,0), B (0,2) A(3,4), B (-2,5) C (17,-12),ABC A(0,3), B (0,0) C (5,0), (1,2), (-1,m) , (-3,-4), ‘m’ A(4,2), B (6,5) C (1,4) ABCAD D A(4,p), B (1,0) P AB
P (3,-5), (-7,4), (10,y), (2, -1), y
157
![Page 158: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/158.jpg)
(AS-5)
2 Marks
A (3,6), B (3,2), C (8,2) ABCDDA (-1,-2), B (1,0), C (-1,2), D (-3,0) P (2,3) Q (x,3), ‘x’Rs A(3,2), B (-8,a) ‘a’ AB
(AS-5)
1 Mark
y = x + 4 P (3,-5), Q (2,1), R (5,-1), S (1,2) A (-4,5) , B (3,5), C (-4,-6), D (3,-6)ABC AD
(AS-5)
1/2 Mark
x
L X
YM
oA) B) C) D) A B
158
![Page 159: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/159.jpg)
x
3. ç¿ì+~ y { ìý Ë y \ T ‘’
‘’
A) B) C) D)2G1
B A
O
A) B) C) D) l
X1 X
Y
Y 1
M
A) B) C) D)
lY
Y 1X1 X
M
A) B) C) D) lM
N
P
A) B) C) D)21
1 2
P
1 2
2
1
1 N
l
Y X
P Y
X
Y
YA) B) C) D) B C
159
![Page 160: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/160.jpg)
![Page 161: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/161.jpg)
(AS-1)
4 Marks
AB//CD//EF AB= 7.5 c.m.CD = ycm, EF = 4.5cm xy
28 cm, 26 cm, 48 cm
ABC AD, BE, CF A, B, C
AB = 5cm, BC=8cm, AC=4cm
AE, CD, BF
ABCD‘0’ AB//CD, AO = 4cm, OC = 4x-2, BO = x+1,
OD=2x+4 ‘x’
30cm, 40cm
AP, BQ, CR, DS, l
PQ= 6cm, QR= 9cm, RS =12cmAD =36cm
AB, BC, CD
A
B CD
F E
A
B D E
F
4. 5cmy cm
C 3 cm
x cm7.5 cm
A B C D
lP Q R S
161
![Page 162: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/162.jpg)
A,B
PQRPQ PRM N PM = 4,
QM = 4.5, PN = 4 NR
(AS-1)
2 Marks
8cm, 9cm
2.5cm, 5cm
‘x’
DEF A.B.C BE, EF, DF DEF 14.4cm2
ABC
A Bx 2x
R
Q
X
3
2 5100 80
P
162
![Page 163: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/163.jpg)
(AS-1)
1 Mark
ABC AD 2= , AC = 18cmDB 3 AE
ABCADBAC ABAC
PQRPS PT=SQ TR PQ‘S’ PT : TR
(AS-1)
1/2 Mark
( )
A) 2:3 B) 4:9 C) 81:16 D) 16:81
ABCPQRA=500 Q+R = ( )
A) 400 B) 500 C) 1300 D) 1400
ABCD.E AB,ACDE BC ( )
A) 4:1 B) 1:2 C) 1:1 D) 2:1
ABCDEFDE=3 cm, EF= 2cm, DF=2.5cm,BC= 4cm ABC ( )
A) 18 cm B) 20cm C) 12cm D)15cm
ABCDEF, BC=3cm, EF=4cm ABC54cm2DEF ( )
A) 96cm2 B) 108cm2 C) 100cm2 D) 48cm2
163
![Page 164: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/164.jpg)
ABCPQR, ABC =4 x PQR BC = 12cmQR= ( )
A) 6cm B) 8 cm C) 9 cm D) 10cm
ABCAB2= 2AC2C ( )
A) 300 B) 450 C) 600 D) 900
ABC C = 900,AC= 6cmAB ( )
A) 6cm B) 6 2 cm C) 4 2 cm D) 2 6 cm
ABCAD BC AD2 = ( )A) CD2 B) 2CD2 C) 3CD2 D) 4CD2
ABCDEF, AB = 3cm, BC = 2cm, AC = 2.5cm, EF= 4 cm DEF ( )
A) 7.5cm B) 15cm C) 22.5cm D) 30cm
ABCC= 600,AC= 3 BCA ( )
A) 300 B) 450 C) 600 D) 900
( )
A) 2:5 B) 5:2 C) 4:25 D) 25:4
25cm2, 36cm2, ( )
10cm A) 10cm B) 12cm C) 15cm D) 18cm
( )
A) 11m B) 13m C) 15m D) 17m
ABC AB//LM, AL= x-3, AC=2x, BM = x-2, BC= 2x+3 x ( )A) 7 B) 8 C) 9 D)
ABCBC//DF, AD 3=DB 5 , AC= 5.6cm AE ( )
A) 2.1cm B) 1.2 C) 1.8cm D) 3.5cm
( )
A) B) C) D)
164
![Page 165: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/165.jpg)
x+y+z =............
A) 14 B) 24 C) 22 D)15
‘A’ ( )
‘A’A) B) C) D)
ABC A AD, BC= a, AC = b, AB = c
BD = ( )
A) ac
a - c B) bc
b + c C)ac
a c D)ac
b + cCD = ( )
A) a
b + c B) ab
b + c C) aba + b D)
bcb + c
BD = ....................CD ( )
A) ab B)
bc C) c
b D)ac
( )
A) 1 :1 : 2 B) 1 :1: 2 C)1 : 3 : 2 D) 1 :1 : 3
a : b ( )
A) a : b B) b : a C) a : b D) b : a
ABC BCM AMB
A) B) C) D)AMB ( )
A) 000 B) 000 C)000 D)000
AMB ( )
A) B) 1 : 3 : 2 C) D)
x ( )
A) B) 253 C)25
2 D)65
5X
23
X5
6
Y
3
Z
165
![Page 166: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/166.jpg)
ABC, PQR AB BC AC= =PQ QR PR ΔABCΔDEF ( )
A)
2ABPQ B)
BCQR C)
BCPR D)
BC.PRAC.QR
ABCPQR A + Q + R = ( )
A) 900 B) 1800 C) 1200 D)150
a,bA) 1:1 B) a:b C) a2: b2 D)a : b ( )
(AS-2)
4 Marks
ABCBC//DE ABC,ADED,E AB,AC
ABCB = 900 BE= 23 BC 9(AC2-AE2)= 5BC2
ABCDAB2+BC2+CD2+AD2= AC2+BD2ABC‘D’, BC9AD2=7AB2ABCBCADAB2 - BD2 = AC2- CD2ABC‘A’ BL, CM AC, AB9 (BL2 +CM2) = 13 BC2
=
166
![Page 167: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/167.jpg)
ABC P,Q AB,ACPQ//BC ADPQ
AB//CD//EF =AE BFED FC
ABC ‘O’AOC,BOC,COAAB, BC,ACD,E,FADxBExCF= DBxEFxFA
XP//YQ
ABC‘C’AB2=2AC2‘B’ABCADBCAC2=AB2+BC2+2BC. BDBABC BCAD AC2=AB2+BC2-2BC. BDABCAB=AC ‘D’ BCAB2-AD2=BD.CD
E F
B
C
A
D
B
X A
P
Y
Q
167
![Page 168: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/168.jpg)
ABC‘D’BCADC= BAC =CA CBCD CA
ABCD‘O’ =AO COBO DO
PQRPQ PRM N PQ = 1.28, PR = 2.56, PM = 0.16, PN = 0.32 MN QR ABCDBD‘x’ xDA AB yDCBC Z YZ,AC(AS-2)
2 Marks
ABCD,E AB,ACDE//BC, BD=CEABC
LM//BC, MN//AB,LN//AC
ABC = =AB BDAC DC
A
B C
1 2
D
M
L
B
CA
N
1 2
168
![Page 169: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/169.jpg)
AP//BC, =RA RACA RQ
PR//BO, QR//CO, =AP ARPB RO
AD//GE, AB//GF,
=CE CFED RO
ABC ADBC
S,Q
B
R
P
Q CA
B C
A
RQP
O
FB
CA
ED
G
X 3 X
2X
RQ
TS
P
169
![Page 170: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/170.jpg)
ABC BC//DEBDE, CDE
ABCD.E AB,ACABC ADE =AB AEAD EC
BC,DE(AS-2)
1 Mark
cmcmcm(AS-2)
1/2 Mark
( )
A) B) C) D) ( )
A) B) C) D) ( )
A) B) C) D)
B C
A
D E
6080
80 40
40
60
170
![Page 171: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/171.jpg)
( )
A) B)C) D)
ABC,DEF = =AB BC CADE FE FD ( )
A) FDE CAB B)FDE ABC
C) CBA FDE D)BCA FDE
( )
A) B)C) D)
( )
A) B) C) D)
CABCAB=P, BC-q, p-q=1AC= ( )
A) 2q-1 B) 2q+1 C) 2q -1 D) 2q +1
ABCD.E AB,AC AD=1.5cm DB= 6cm, AE= 1.8cm,
BC//DE CE = ....... ( )
A) 7cm B) 8cm C) 7.2cm D) 6.8cm
( )
A) B) C) D)
( )
A) B) C) D)
p : ( )
q :A) p q B) q pC) p,q D) p,q
Assert : ( )
171
![Page 172: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/172.jpg)
Reason: A) p q B) p q C) p q D)
( )
A) B) C) D)
ABC AB ( )
A) AC2 =AB2+BC2 B) AB2 = BC2+AC2
C) BC2 = AB2+AC2 D) AC2+ AB2+BC2=0
( )
A) B)C)D)
( )
A) B)C) D)
( )
A) B) C) D)a c
( )
A) B) C) D) a c ( )
A) B) C) D) A CABC AB, BC, AC D,E,F BDFE = ( )
A) DEF B) 14 ABC C)ABC D)
13 ABC
172
![Page 173: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/173.jpg)
( )
A) B) C) D) ABC B AD BC
A) AC2 =AB 2+BD2 +2.AB.BD B)AB2 =AC 2+BD2 +2AB.AC
C) BC2 =AB 2+BC2 +2AB.BC D) AD2 =AB 2+BC2 +CD2
( )
A) B) C) D) ( )
A) B) C) D)
( )
A) B) C) D)
AD=DC, CD=2.DE ADC,DEC ( )
A) B) C) D) a b
ADB BDC ( )
A) BD B) BD C) a b D) a c
B C
A
D
E
DA
C
B
173
![Page 174: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/174.jpg)
POS ROS ( )
A) PS//QR B) PR PS C) QR SR D) PQ BR
ABC BC 7 AMB ( )
A) B) C) D)(AS-3)
4 Marks
PQR R RS
QS ‘p’x,y,z
a,b ‘P’
p,a,b
‘x’a,b,c
R
QP
S
O
RQ
x
Z
P
p
ys
L
pa x
b400 400
KM C
N
174
![Page 175: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/175.jpg)
(AS-3)
2 Marks
ABCBC//DE =AD AEDB EC
ABCD AB//CD AOOB
=PL PMPQ PR
(AS-3)
1 Mark
2
3 2
3 5
3
DE
C
BA
A
CD
B
O
RQ
P
L M
175
![Page 176: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/176.jpg)
(AS-3)
1/2 Mark
( )
A) B) C) D)a:b ( )
A) a:b B) b:a C) a2:b2 D)b2:a2
( )
A) B) C) D)
( )
A) B) C) a c D)
( )ABC, PQR ( )
A) ABC PQR B) ABC PQR
C) A B D) A, B
176
![Page 177: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/177.jpg)
ABCDCD‘E’ABE = ( )
A) 12 ADE B)
12 BCE
C) 12 (ADE+BCE) D) ADE (ADE+BCE)
ABCD BD B,D ( )
A) AB=BC B) =AB ADBC CD C) =AB AD
CD BC D) AD=BD
‘a’ ( )
A) 23 a2 B) 23 a
4 C) 2a32 D) 23 a
4
ABCAAD ΔABDΔACD
( )
A) ACBD B) C)
BCAC D)
ABAC
AAD BC BD = ......DC ( )
A) ABAD B)
ABAC C)
2ABAD D)
2ABAC
cmcmcm ( )
A) B) C) D)ABCD 4AB2-AC2= ( )
A) 2BD2 B) 12 BD2 C) 3BD2 D) BD2
( )A) B) C) D)
( )A) B) C) D)
=
177
![Page 178: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/178.jpg)
( )
A) B) C) D)
A) 1: 2 B) 2 :1 C) 1:2 D) 2:1(AS-4)
4 Marks
(BD)
Q
C A
E
P
D
B
15 m
2 m 2 m 2 m
R
C
A
B
178
![Page 179: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/179.jpg)
(AS-4)
2 Marks
1. ABCD
ABCDAB//CD
x
ABCDE//BC, AD 3=DB 5 , AC = 5.6cmAE
(0,0) (0,12) (5,0)(wire) (wire)(AS-4)
1 Mark
OB//O1C, OA=3cm, OO1=7cm AB=4.5cm
BC
C
A
D
B
9
x-y3
x+y
B
C
A
3x-1
D6x-5
2x+1
5x-3
o
7 cm
C
A
B O1
3 0
179
![Page 180: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/180.jpg)
ABC
3cm, 10cm OBOX=5cm oy
DE “x’’
(AS-4)
1/2 Mark
‘d’ ( )A) B) C) D)
00 ( )
A) 2 B) C) D) 1 : 3 : 2
( )
A) B) C) D) ( )
A) B) C) D) (0.0), (3.0), (4.0) (0.0), (-6.0) , (0.-8) ( )
A) B) C) D) ( )
A) B) C) D)
A B
YX
O6
C
A
3x+19D
B
E
3x+4
x+3 x
180
![Page 181: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/181.jpg)
3 : 2 ( )
A) 3:2 B) 3 : 2 C) 3:4 D) 3 : 2
( )
A) B) C) D)
A(6,3),B (-3,5), C(4,-2), D(x,3x) ΔDBCΔABC = 1:2x = ..... ( )
A) B) 8
11 C) 118 D)
2x-y=5, y=2x+7 ( )
A) B) C) D) ( )
A) B) C) D) AOC DOB, COB=1100,
BDO= 600 OAC = ( )
A) 500 B) 600 C) 1700 D) 100
(AS-5)
4 Marks
cmcm
23
a=4cm , b=6cm, c=8cm
53
5cm 8cm. 11cm
23
m600
D B
CA
1100O
l
181
![Page 182: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/182.jpg)
6cm5cm
13
(AS-5)
2 Marks
6cm 6cm
8cm 13
7cm 35
(AS-5)
1 Mark
ABC 23
‘5’3cm 6cm7006cm(AS-5)
1/2 Mark
( )
A) B) C) D)3 2 4
3
55
3
2 4
13
2.51.5
5
400460
182
![Page 183: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/183.jpg)
AB ( )
A) B) C) D)
BC,DE ( )
A) B) C) D)
( )
A) B) C) D)
( )
A) B) C) D)
AC//BD ( )
A) XA XC=AB XD B)
XA XC=XB CC
C) XA XC=XB XD D)
XA XB=AB XC
BC//DE, AE:EC=4:7 BC:DE ( )
A) 11:4 B) 4:1 C) 11:3 D) 3:1
C
A
D
BX
XX
A B A AB B
X
A B
A1 A
2A
2
A1
A1
A2A
3A
3
A B1 B
A BB1
B1
B1 B
A
D2 3
A
A AB B B BC C
C CD
D
4
4E
400
400
E6
E2
8
3
44 2
12 3
133
5
6
108 5
C
A
E
B
D
183
![Page 184: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/184.jpg)
ABC C=900, CD AB ( )
A) 1 1 1= +P a b B) P=a+b
C) 2 2 2
1 1 1= +P a b D) P
2=a
2+b
2
OAxOB= OCxOD B= ( )
A) C B) B C) D D) ( )
A) 2K =3
B) K=O C) K=
D)3K =2
ABCDOPC
( )
A) B) C) D) R
Q
P
S
C
A
D
B
O
CA
O
DB
C
AD B
D Pa
184
![Page 185: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/185.jpg)
![Page 186: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/186.jpg)
(AS-1)
4 Marks
ABC
cmcm
AP = 3cm PC = 8cmCD
OQP = 600cm
A,B,C,D
A
B Cr r
CD
A
P
B
P
Q2
0600
186
![Page 187: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/187.jpg)
AB= 14 cm
‘O’ ABAT AOQ = 580 ATQ OTQ
ABC (AS-1)
2 Marks
3 5cm, 3cmcmcm AOB = 900
A
O
B
C
B
Q
TA
O
580
o
A
B187
![Page 188: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/188.jpg)
BA BC A,C AEC = 1100 DCE = 800 ABC
AC,0O ACO
AC‘O’ C OC
cm900
AP = 10 BP
O
2
A C4
P
A
B
3 cm
6 cm10 cm
1100
800
B
C
A
D E x
BO
CA 160
900
7cm
188
![Page 189: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/189.jpg)
cmcmAOC ACB = 600AB AAAT
BAT ‘O’L,M,N AB,BC AC B =700, C =600 LOM, ,LON MON OQ : PQ = 3:4 POQ, 60cm PQ,QR,OP
(AS-1)
1 Mark
cm900300cmcmcmrdp
APB =600 AOB
Q
O
R
P
A
P
B
O
189
![Page 190: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/190.jpg)
cmcm
ABC
4cm 5cm, 3cmcm900R,r
R,r(AS-1)
1/2 Mark
cmcm
A) cm B) cm C) cm D)cm
AP,BP1200 APO =....
A) 0 B) 0 C) 0 D)0
OPQ
A) 0 B) 0 C) 0 D)0
R r
5 cm
4 cm
6 cm
B C
A
Q
o
P
A
P
A
B
O
190
![Page 191: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/191.jpg)
cmcm
A) cm B) cm C) cm D)cm
‘O’ TPTQ OPQ 0
PTQ =.... A) 0 B) 0 C) 0 D)0
(x),‘x’
A) 0 B) 0 C) 0 D)0
A) B) C) D)
cmcm
A) B) C) D)
‘r’
A)
2π 3- r3 4 B)
2π 3- r3 2 C)
2π 3+ r3 4 D)
2π 3+ r3 2
‘O’ ‘P’ PA, PB0 POA
A) 0 B) 0 C) 0 D)0
P
B
A
O x
A B
C
o
191
![Page 192: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/192.jpg)
cm A) cm2 B) cm2 C) cm2 D)cm2
A) 239 cm2 B) 222 cm
7 C) 4 26 cm
5 D)cm2
cm0 A) cm2 B) cm2 C)cm2 D)
cm0 A) cm2 B) cm2 C) cm2 D)cm2
APB = 800 AOB
A) 0 B) 0 C) 0 D)0
x + y
A) B) C) D)
APO
A) 0 B) 0 C) 0 D)0
AB = cm BC
A) cm B) cm C) cm D)cm
A B
o
C
A
B
Po
o P
A
B
xy
A
B
Po 800
B
A450
o 7 cm
192
![Page 193: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/193.jpg)
BPO =400 BOP
A)0 B) 0 C) 0 D)0
(AS-2)
4 Marks
PAB, PCD PA.PB=PC.PD
PAPCDPA2= PC. PD
cmcmVerifyAP, AXAYAY = AX
PAO = 400 POA AP
PAB
C
D
A
P C D
C
D
X
Y
A
P
A
B
Po
P
A
o 400
193
![Page 194: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/194.jpg)
PQ PR‘O’ QPR = 900 PQOR
AB AOC AT BAT = ACB
ABCDEF 0ABC + CDE + EFA = 360 ABCD CA,CBD A (AS-2)
2 Marks
ABCD P, Q, R, S AB+CD=BC+DA (AS-2)
1 Mark
T
C
o
A
P
Q
o 900
R
B
194
![Page 195: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/195.jpg)
(AS-2)
1/2 Mark
cm
A) cm B)cm C) cm D)cm
A) B) C) D)
QP=4.5 cm
A) cm B)cm C)cm D)cm
‘O’A AP AQ A) AP=AQ B) APO =900 C) BPO =900 D)
A) B) C) D)
QP
R
195
![Page 196: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/196.jpg)
‘’ PA ‘A’ A) OAP =900 B) POA =900 C) OPA =900 D)
A) B) C) D)
OPA
A) 90c B) 1800 C) 450 D) 1200
A) B) C) D)
AP APO
A) 0 B)0 C) 0 D)0
cmcm
A) cm B)cm C) cm D)cm
cm
A) cm,6cmB)cm,67cm C) cm,4cm D)cm,8cm
cm A) cm B)cm C) cm D)cm
(i)(ii)
A) (i) B) (ii) C) (i) (ii) D) (i)(ii)
A
Po
o
A P1
2
1
196
![Page 197: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/197.jpg)
A) B)C) D)
A) B)C) D)
A) B)C) D)
r 1 r2
A) r 1+r2 B) r1- r2 C) 1
2
rr D) r 1* r2
A) B)
C) D)
A) B) 2 C) D) 3
A) B) C) D)
A) B) C) D)
O
197
![Page 198: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/198.jpg)
A) C)
B) D)
PAO,PBO
A) B) C) A B D)
AD = BEADBAEB
A) B)C) D)
(AS-3)
4 Marks
ABCD P,Q,R,SAB + CD, BC + DA
A
B
Po
A B
D E
198
![Page 199: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/199.jpg)
(AS-3)
2 Marks
(AS-3)
1 Mark
2 2d - r
0
(AS-3)
1/2 Mark
A) B) C) D)
199
![Page 200: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/200.jpg)
A) B)C) D)
A) 0 B)0 C) 0 D) 0
‘x’
A) π r2 B) 2π r C) 2.360
x r D) 2360
x r
‘r’ ‘d’
A) dr B) 2 2d + r C) 2 2d - r D) 2 2d .r
A) B) C) D)
A) B) C) D)
A) lr2 B)
l2r C) 2 l + r D) l + 2r
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
200
![Page 201: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/201.jpg)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) 0 B)0 C) 0 D)0
A) B) C) D)
A) p B) q C) r D)
A) B) C) D)
ACB
A) 0 B)0 C) 0 D)0
q
p
r
BA
C
O
201
![Page 202: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/202.jpg)
A) B) C) D)
0APB = 80 AOB = 80
A) 800 B) 1000 C) 1100 D) 1200
(AS-4)
4 Marks
cm0
0
0
cm
A B
o
A
P B0
A) B) C) D)
A) B) C) D)
202
![Page 203: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/203.jpg)
(AS-4)
2 Marks
ACB
0= 80APB AOB
PAQ
‘a’
0
V.I.P Lonze 0
63 m
A B
o
1200r
C
A
800 Po
B
P
o
7900aa
203
![Page 204: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/204.jpg)
(AS-4)
1 Mark
cm.
0
QcmQ cm
O PAPB0 POA
cm cm
cm x cmcm0 ACB
AOB
ABCD
1200 rr
A B
C
500
A
C
B
o
3.5cm
2cm
A B
CD
o 204
![Page 205: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/205.jpg)
(AS-4)
1/2 Mark
cm
A) 50 2 B) 100π C) 50 2
π D) 100 2π
PT PAB PT=6cm PA = 4cmAB ---- cm
A) cm B)cm C) cm D)cm
cm
A) 3 2 B) C) D) 6 2
cmcm
A) cm B)cm C) cm D)cm
cm0 A) cm2 B)cm2 C) cm2 D)cm2
AB;CD AOB =
A) COD B)BOC C) AOD D)07c
m
21cm
o
A B
D
A
C
B
o
205
![Page 206: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/206.jpg)
A)π B)π C) π D)πcm
A) B) C) D)
A) 2r B) r3 C) r5 D) r
ABCD PQRS AB=4cm CD=6cm
BC+AD= A) cm B)cm C) cm D)cm
APB + AOB =
A) 600 B) 900 C) 1200 D) 1800
A) 2 B) 2 -1 C) 12 D)
22 +1
‘O’ PT PA=3cm
PT = 6cm
A) cm B)cm C) cm D)cm
B
T
A Po
6 cm
3 cm
B
A
Po
D
A
C
B3cm
600
206
![Page 207: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/207.jpg)
A) cm B)cm C) cm D)cm
r A) r2 B) 2r2 C) r3 D) 2r3
cm
A) cm2 B)cm2 C) cm2 D) sincos
A) sin2- cos2 B) sin+ cos C) 1 D) 12
x
A) 0 B)0 C) 0 D)0
A) 50(π -2) B) 25(π -2) C) 25(π+2) D) 5(π -2)
A) 2a
4(π+2) B)
2a4
(π -2) C) 2a
4(π -1) D)
2a4
(π+1)
900aa
9005cmo
X
500
207
![Page 208: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/208.jpg)
(AS-5)
4 Marks
cmcmcmcm0
cm,cm
cmcmcm
AB = 3 , AD = 2.7 DB = 3.6 0B = 110 BC = 4.2 cm
ABCDABCDDB = 4.8 A1 BC1DABC 2/3AB = 4 , BC = 5 , AC = 6 AB = 3 BC = 6 AC = 4 AB = 2 ABCD
(AS-5)
2 Marks
AB
208
![Page 209: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/209.jpg)
(AS-5)
1 Mark
cm
(AS-5)
1/2 Mark
A) B) C) D)
A) B) C) D)
A) B) C) D)
209
![Page 210: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/210.jpg)
![Page 211: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/211.jpg)
(AS-1)
4 Marks
cm
cm cm cmmmmm
cm
cm2
12
mm
cm
cm cm
cm cm
cm
211
![Page 212: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/212.jpg)
(AS-1)
2 Marks
cm3 cm cm cm
cm cm cm cmcmcmcm3
cmcmcmcm3cmcm
cm cm2
cmcm3
cmcm
cmcm3
cm,cm
212
![Page 213: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/213.jpg)
cmcm
cm
cmcm
cm2cm2
cm
(AS-1)
1 Mark
cm cm cm
cmcm
cm3
cm
cm2cm
cm2cm
cmcm
cm,cm
cm3cm2
5cm
7cm
213
![Page 214: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/214.jpg)
cmcm
cm,cm
cm2cm
cm
cm,cm
cm
(AS-1)
1/2 Mark
cmcmcm
A) B) C) D)cmcm
A)cm3 B) cm3 C) cm3 D) cm3
5cmcmcmcm2
A) B) C) D)cmcmcmcm2
A) B) C) D)mm2
A) B) C) D)m
A)m2 B)m2 C) m3 D) m3
214
![Page 215: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/215.jpg)
Cm3 cm
A) B) C) D)
l=cm, b=cm, h=cm
A)cm3 B) cm3 C) cm3 D) cm3
m3
A)m B) m2 C) m2 D) m2
r = 3cm, h = 14cm
A) 132
7 cm2 B)cm2 C) cm2 D) cm2
d=7cm,cm
A) cm2 B)cm2 C) cm2 D) cm2
cm3cmcm
A) 92 B)
52 C) 7
2 D) 112
cmcm
A) cm3 B) cm3 C) cm3 D) cm3
cm,cm
A) cm2 B) cm2 C) cm2 D) cm2
cmcm3
A) B) C) D)
cm cm2
A) B) C) D)
cmcm cm
A) B) C) D)
cm ...............cm2
A) 14 B) 1
8 C) 34 D) 3
2
215
![Page 216: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/216.jpg)
cm2cmcm
cm
A) B) C) D)
cmcm
A) B) C) D)
cmcm
cm
A) B) C) D)
cm2cm
A)cm B)cm C)cm D)cm
cmcm
A) B) C) D)
cm3 cm
A) B) C) D)
cm3
A)cm B)cm C)cm D)cm
cm cm cm
A)cm B) cm C) cm D) cm
cm2cm
A) cm3 B) cm2 C) cm2 D) cm3
4 3 cm................cm
A) B) C) D)
216
![Page 217: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/217.jpg)
cmcmcm
cm2
A) B) C) D)
‘a’ cm cm2
A) a3 B)a C) a2 D) a2
cm cm2
A) B) C) D)
cmcm
A) B) C) D)
‘r’ ‘r’
A)r B)r C)r D)r
cm2 .............cm3
A) B) C) D)
cm3cm
A)cm B)cm C) cm D) cm
(AS-2)
4 Marks
m m
m x
217
![Page 218: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/218.jpg)
(AS-2) 2 Marks
i)
ii)
218
![Page 219: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/219.jpg)
cmcm
49507 cm
(AS-2) 1 Mark
2
25
5
219
![Page 220: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/220.jpg)
(AS-2)
1/2 Mark
m2 m3
A) B) C) D)
cm2cm3
A)156 B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
‘l’‘a’
A) l -2a B)l +2a C) l - a D)l + a
‘a’
A) a3 B)a2 C) a2 D) a2
A) B) C) D)
220
![Page 221: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/221.jpg)
A) B) C) D)
l,r h
A) l2 = h2 + r2 B)l = h + r2
C) 2h2 =r
D)l2 - h2 = r
(AS-3)
2 Mark
Km 37
‘l’ ‘l’
lh
r
l
r
h
h
bl
b
h l
221
![Page 222: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/222.jpg)
(AS-3)
1 Mark
(AS-3)
1/2 Mark
A) B)
C) D)l b
A) 2 2l + b B) l + b + h C) 2 2 2l + b + h D) 3 3 3l + b + h
=...........
A) B)
C) D)
h
r
222
![Page 223: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/223.jpg)
A)a B) 3 a C) 2 a D)2a
A) 2 2r + h B) 2 2r + l C) 2 2r + h D) 2 2r + l
=
A) 3 34 ( )3
R r B) 3 32 ( )3
R r C) 3 31 ( )3
R r D) 3 3( )R r
= ..............
A) B) 5 C) 2 D)1
‘d’
A) 31 πd6 B) 31 πd
3 C) 31 πd24 D) 34 πd
3
A) 21 π r h3 B) 2π r h C) 32 πr
3 D) 34 π r3
A) 24 πr3 B) 21 πr h
3 C) 2π r h D) 21 π r h2
Group A Group B ( )
a) 21 πr h3
b) 32 πr3
c) 2πr h
d) 24 πr3
A) 1-c, 2-d, 3-a, 4-b B) 1-a, 2-b, 3-c, 4-d
C) 1-c, 2-a, 3-d, 4-b D) 1-c, 2-a, 3-b, 4-d
223
![Page 224: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/224.jpg)
Group A Group B ( )
a) 23π r
b) 24 π r
c) πr(r + l)
d) 2πr(h + r)
A) 1-b, 2-a, 3-d, 4-c B) 1-c, 2-d, 3-a, 4-b
C) 1-c, 2-d, 3-b, 4-a D) 1-a, 2-b, 3-c, 4-d
A) 2 2πh(R - r ) B) πh(R - r) C) 2 2π(R - r ) D) 2 2πR - r h
A) 3πr B) 31 πr3 C) 32 πr
3 D) 21 πr3
A)lb + bh + hl B) b + bh + H2
C) (lb + bh + hl ) D)
A) 1:3 B) 3:1 C) 1:2 D)2:1
(AS-4)
4 Marks
224
![Page 225: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/225.jpg)
cmcmcm
5. 2cmcm
cm cm
cmcmcm
cmkgs
cmcmcmcm
23
cmm
cm cm cmcm
cmcmcm
225
![Page 226: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/226.jpg)
(AS-4) )
2 Marks
cmcm
cm
cm
cm cm
cm
cmcm
/
m cmm
cm
226
![Page 227: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/227.jpg)
(AS-4)
1 Mark
(AS-4)
1/2 Mark
A) B) C) D)
A) B) C) D)
A) B) C) Ring D) Frustrum
A) B) C) D)
A) B) C) D)
cmcm
A) B) C) D)
227
![Page 228: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/228.jpg)
cm cm cm cm
A) cm B) cm C) cm D) cm
cmcmcm
A) B) 3 C) 5 D) 6
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
cm
A)cm B)cm C) cm D) cm
A) B)
C) D)
A) B) C) D)
A) B) C) D)
cm
A)cm3 B) cm3 C) cm3 D) cm3
228
![Page 229: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/229.jpg)
cmcm
A) B) C) D)
xcm π cm2 x = .........
A) B) C) D)
cm
...........cm3
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) 1: 1 : 5 B) 2 : 2 : 5 C) 3 : 3 : 5 D) 4 : 4 : 5
229
![Page 230: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/230.jpg)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)(AS-5)
4 Marks
230
![Page 231: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/231.jpg)
(AS-5)
1 Mark
(AS-5)
1/2 Mark
l =........................ ( )
A) B) C) D)
3-D
A) B) C) D)
A) B) C) D)
A) B) C) D)
n
hl
231
![Page 232: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/232.jpg)
A) B) C) D)
A) B) C) D)
A
232
![Page 233: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/233.jpg)
![Page 234: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/234.jpg)
(AS-1)
4 Marks
15sinθ =17 15cotθ+17sinθ
8tanθ+16secθ
2
2cos θ- 3cosθ +2 = 1
sin θ
3cosθ =2
4 sin2θ + tan2θ+4 sec2θ
cosθ -sinθ 1- 3=cosθ+sinθ 1+ 3 θ
3cosθ =2
4 sin2θ + tan2θ
sinA = 3 sec2 A - tan2A
cot A = 3 sinA + cosAsinA - cosA
3(sinx-cosx)4 + 6(sinx+cosx)2+ 4 (sin6x + cos6x)
secθ + tanθ = p2
2p -1P +1
1cosθ cosθ+ = 4
1- sinθ sinθ
cosθ cosθ+ = 2cosecθ+1 cosecθ -1
2 2 332cot - 8sec + 8cot4 3 6
1 1tan(A - B) = ,sinA =3 2
1secθ + tanθ =5
(AS-1)
2 Marks
4Tan A = 3Sin A + Cos A 8Tan θ = 15Sin θ - Cos θ
Tan θ= 247 secA + cosecA
234
![Page 235: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/235.jpg)
4 cot A = 3 sinA + cosAsinA -cosA
cos θ = 12 sin2 θ + tan2 θ
0 0
0 0a
2 2
2 2
sin 30 + cos 30sec 60 t n 60
2tan2 450 + cos2 300sin2600 0 0 0cos0 + sin90 + 2sin45
Tan(A+B)=1, TanB=13 TanA
Tan(A+B) = 3 ,sinA = 12 A,B
sin(A-B)= 12 , sin (A+B) =1 (0 < A (or) B < 900)A,B
(1 - cosθ ) (1 +c osθ )(1 + cos2θ ) sin5θ = cos4θ , 5θ , 4θ θ Tan3an3θ ABCB = 900 AC = 10m CAB = 600 BC Cosecθ = n+1 cosθ
0 0
0 0
tan45 sec60+cosec30 cot45
(AS-1)
1 Mark
0θ0,
2 sin2θ=θ cos 3θ = 1θ sinθ = 1,0< θ <0cosθ sin7 A = cos (A-6) ‘A’Tan 2θ = cot θ θ cot 12. cot 38. cot 52. cot 60. cot 78 sin 6θ = cos 3 θ 0 6θ 3θ sinθ0 0
235
![Page 236: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/236.jpg)
ABC B =0 , AB = 60 mC =0C0cot θ+cosec θ=5 cos θ
sinθ cos θ = 12 θ
2 sin2θ = 12 00
θ0‘θ ’
mnm +nsecθ =2 sinθ
tanθ+cotθ=2tan2θ+cot2θ
sin2300 + cos2600 + tan2450
cosec2600+ sec2300 + cos2450
sin2600 + cos2300 + tan2600
2 0 2 0
2 0 2 060 + cos 6060 -cos 60
sinsin
2 0 2 0
2 0 2 0-+
30 cos 3030 cos 30
sinsin
coso0+ sin900 + 2 sin450
44
2 2
sin θ -cos θsin - cos θ
21sinθ = 3θcos
2
0
0
sin18cos72
(AS-1)
1/2 Mark
ΔABC B = 90 , AB =12cm, BC = 5cm, TanA
A)125 B)12
13 C) 512 D)
1315
236
![Page 237: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/237.jpg)
θ secθ =1312 Tananθ =..........................
A)1512 B)13
14 C) 1415 D)
125
ΔABCB = 900, AB =12cm, BC = 9cm, cosC=...........................
A)129 B) 9
15 C) 1215 D)
159
3sinA =5 cosA =........................
A) 34 B) 4
5 C) 54 D)
43
12cosA =13 TanA = .......................
A)5
12 B) 513 C)
125 D)
1213
1cosecθ
A) B) C) D) Sin450 + Cos 450 =
A) 2 B)12 C)
14 D) 1
4Sin300 Cos600 A) B) C) D)
θ Secθ 53 Tananθ + cot θ=............................
A)3512 B) 25
12 C) 1225 D)
2535
2cosecθ =3 θ
A)0 B)0 C) 0 D) 0
2Sin20 Cos2 0=........................
A) 32 B) 3
4 C) 32 D)
34
237
![Page 238: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/238.jpg)
θ=0Sin2θ
A)0 B)1 C) 21
D) 12
2Sin2θ=12 θ θ
A)900 B)600 C) 450 D) 300
2Cos θ = 12 2θSin
A)1 B)0 C) 12 D) 2
1
Sin 600 Cos 300+ Cos 600 Sin 30
A)1 B) 12 C)
32
D) 12
tan 2θ = cot (θ + 600)θ A)100 B)180 C) 200 D) 280
sec2A = cosec (A-21), (2A) A = A)0 B)0 C) 0 D) 0
cot (900 -θ )=...... A)tan(90 - θ ) B)tanθ C) Cotθ D) secθ
sin (50 + θ ) = cos (40 + θ ) θ= A)0 B)0 C) 0 D) 0
A,B cos2 A + cos2B =.... A) B) C) D)
cosec20 - cot2 0 =...... A) B) C) D)
sin20+ cot2 0 =...... A) B) C) D)
cos20 + cos2 0=......
A) 53 B)
23 C)
14 D)
24
238
![Page 239: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/239.jpg)
sinθ cos θ =12 θ=......
A)0 B)0 C) 0 D) 0
ABCBC = 3 ,CA = 4, AB = 5 cos A =
A) 35 B) 3
4 C) 45 D)
53
tan θ = 34 sin θ =..........
A) 37 B) 4
3 C) 35 D)
45
secθ + tenθ = cos θ =..........
A) 34 B) 3
5 C) 25 D)
23
cotθ + cosecθ = cosθ =..........
A)1213 B) 26
24 C) 5
13 D) 1312
2
2
1- cos A1 + cot A
=......
A)SinA B)Sin2A C) tan A D) SinAcosA
cos2θ = sin4θ θ θθ=......
A)0 B)0 C) 0 D) 0
2sin6A = cos 3A ,6A & 3A2A=.....
A)0 B)0 C) 0 D) 0
sinθ + cosθ= 2 θ=.........
A)0 B)0 C) 0 D) 0
cosecθ = 2, cotθ = 3p θ P=.........
A) B) C) 12 D) 3
tan 8A = cotA, 8A 8A =.........
A)0 B)0 C) 0 D) 0
239
![Page 240: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/240.jpg)
(1 + cot2θ ) (1 + cosθ ) (1-cosθ )
A) B) C) D)
tan450=....
A) B) 12 C) 2 D)
5tanθ = 4 5sinθ - 3cosθ5sinθ+ 3cosθ
A)19 B)
12 C)
17 D)
15
4cos3300 -3cos300 A) B) C) D)
sin2600 + cos2450 A) B) C) D)
1+ Tan2θsec4θ
A)cos2θ B) sec2θ C) tan2θ D) cosec2θ
AB =............................
A)60 3 B) 20 3 C) 20
3 D) 60
3
sin 810=
A) cos 90 B) cos 810 C) -cos 90 D) cos 810
Sec A = cosec B A + B =
A) 900 B) 1800 C) 3600 D) 00
0tan(15 + B) = 3 B
A) 600 B) 450 C) 300 D) 00
(sec 450 + tan 450 ) ( sec 450 - tan 450 )
A) B) C) D) 2 2
A
BC 60m300
240
![Page 241: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/241.jpg)
(AS-2)
4 Marks
Cosecθ+cotθ = p 2p +1 2Cosθ = p -1 p 0 2 2 2 2Tan θ +Cot θ + 2 = Sec θ.cosec θ
0
00
2cosθcosθ+sinθ = cosθ-sinθ = 2sinθ
A, XCosA =cosX A = X
+ = 2sinθ 1+cosθ1+cosθ sinθ cosecθ
=Tanθ+Secθ-1 1+SinθTanθ-Secθ+1 Cosθ
Sin A -B = SinAcosB -cosASinB
4 0 4 0 2 0 2 0Sin 30 + C os 60 - 3 C os 45 - S in 904 = 2
=Tanθ+Secθ-1 1+SinθTanθ-Secθ+1 Cosθ
2θ - 1Cotθ - tanθ = 2cos
Sinθcosθ
+ = 2Secθ1+Sinθ Cosθcosθ 1+Sinθ
= tancotβ -tanα α.cotβcotα - tanβ
Secθ+ tanθ = p 2
2
-1+ 1
pSinθ =p
241
![Page 242: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/242.jpg)
Sin A + B + Sin A - B = 2SinACosB A,B
2A + B + Cos A - B = cosAcosBCos A,B
2 2θ +Cos θ = 1Sin ‘θ ’
2 2Cosec θ - cot θ = 1‘θ ’
2 2Sec θ - tan θ = 1 ‘θ ’
4 0 4 0 2 0 2 04 Sin 30 + cos 60 - 3 Cos 45 sin 90 = 2
3 (sinx - cosx )4 + 6 (sinx + cosx )2 + 4 (sin6x + cos6x ) =13
cotθ -cosθ cosecθ -1=cotθ + cosθ cosecθ +1
sinθ - cosθ +1 1=sinθ + cosθ -1 secθ - tanθ
(cosec sinA ) ( sec A - cos A) = 1
tanA + cotA
21 + secA sin A=
secA 1- cosA
secA -1 1- cosA=secA + 1 1 + cosA
2
22
1 + tan A 1 + tanA= = tan A1+ c0t A 1+ cosA
2 2 2 2
2 22 2 2 2
cos β - cos α sin α - sin βtan α - tan β = =cos β - cos α cos β -cos α
0
0
tan47 = 1cot43
2 2(1 - cos θ)sec θ = tanθ
242
![Page 243: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/243.jpg)
%
2 2sec θ+cosec θ = tanθ +cotθ(AS-2)
2 Marks
A + B = cosA + cosBCos
3 3Cos θ+ sin θ = cosθ + sinθ 1- sinθcosθ
2
22
θ = Tan θθ -1
1- Tancot
=1-TanA cotA -11+TanA cotA +1
2 2 2 2Sec θ +Cosec θ = Sec θ.Cosec θ
2 2 2 2Tan θ -Sin θ = Tan θ.Sin θ
acosθ+bSinθ =m aSinθ-bcosθ = n 2 2 2 2a + b = m + n
1- Sinθ=Cosθ1+Sinθ Cosθ
2 2 2 2Sec θ +Cosec θ = Sec θCosec θ
2 2 2Sinθ +Cosθ Sinθ -Cosθ
cos6 + sin6
= 1-3 sin2 cos2
cos2A = cos2A - sin2A cos4A-sin4A = c0s2A
243
![Page 244: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/244.jpg)
(AS-2)
1 Mark
sincos
AA tan AA
A 5sinA =4
AsinAcosAAcosec AsecA A,B sinA= cosB A+B sinA, cosA sec 680. sin320. cos680. cosec320 = 1tanA = cot BA + B = 900 cos10. cos 20. cos 30.........cos 890.cos 900 = 0tan10.tan 20.tan 30........tan 880.tan 890 = 1(AS-2)
1/2 Mark
tanθ = 3 secθ=
A) B) C) D)
1cosecθ
A) B) C) D) tanθ
A) B) C) D)
sinθ
A) 12 B)
13 C) D)
244
![Page 245: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/245.jpg)
A) cosθ = 1cosecθ B)
1sinθ =secθ
C) tanθ = sinθcosθ D)
cosθcotθ =secθ
sin400 =...... A) sin x 40 B) sin + 400 C) sin20 + sin20 D)
ABC 0A = 90 CosB=
A) ABAC B)
ABBC C)
BCAC D)
BCAB
(see400 + tan400)(sec400 - tan400)=...... A) B) C) D)
cos10.cos20....cos990.cos1000=... A) B) C) D)
sin θ = cosθ =...
A) 0 B) 0 C) 0 D) 0
θ 3 sinθ - cosθ= 0 θ=....
A) 0 B) 0 C) 0 D) 0
tan A = 13 tanB= 3
A) A + B = 900 B) A - B = 300 C) B - A = 300 D) A C
tan 100. tan 200. tan 450. tan 700. tan 800=.....
A) 3
2 B) C) D) 3
cos 300. sin 600 + sin300. cos 600
A) B) C) D) 12
A=sin θ+ cosθ B= sin θ - cosθ
A) A2- B2 = 2 B) A2 + B2 =4 C) A2 + B2= 2 D) A2- B2 = 4
}
245
![Page 246: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/246.jpg)
P:Q = tanθ , Q:R =12 2P:R =......
A) tanθ B) 2tanθ C) 12 tanθ D) cosθ
A) sec2θ=1-tan2θ B) sin2θ+cos2θ=1
C) cosec2θ=1+cot2θ D) tanθ -cotθ=1
tanθ+cotθ=2sin θ =...........
A) 2 B) 21
C) 1 D) 0
ABC tan
A + B2 =......
A) sin C2 B) cos C
2 C) tan C2 D) cot C
2
sinθcosθ = tanθ
2 =...........
A) B)1 C) 3 D) 31
θ
A) 0 B) 0 C) 0 D) 0
A,B A B
A) sin A sinB B) cos A cos B
C) tan A tan B D) sec A sec B
A) sin (90 - )= cos B) cosec (90 - ) = tan
C) sec (90 - )= cosec D) tan(90 - ) = cot
A) sin 450 B) cot 00 C) tan 00 D) sec 450
0
θ
246
![Page 247: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/247.jpg)
(AS-3)
4 Marks
BF1, F2 F1
0F20
‘sinθ ’
‘cosθ ’
‘tanθ ’
‘cotθ ’
‘cosecθ ’
‘secθ ’
(AS-3)
2 Marks
2 0
02 030cos60 =30
1- tan1+ tan cos2θ
0
02 0
30tan60 =30
2tan1- tan tan2θ
‘A’
‘C’
A
BC
247
![Page 248: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/248.jpg)
(AS-3)
1 Mark
sin750+ cos65000 A00sinAcosA
‘θ ’ tanθ ABCB Csin A = sin x A sin A
secθ+ tanθ = 34 secθ - tan θ
sin730+ tan 730cos, cot
sin750+ cos 65000450(AS-3)
1/2 Mark
aSinθ =b Tanθ =
A) 2 2b - aa
B) 2 2a + ba
C) 2 2a - bb
D) 2 2b + ab
ΔXYZ & 0y = 90 XZ = A) 2xy B) 3xy C) 2XY D) XY2
‘θ ’ 1+ Cos θ A) B) C) D)
ΔABC 0ABC = 90 Sinc = ................
A) ACAB B)
ABAC C) BC
AC D) BCAB
31Cotθ =
2
2
θ = ...................θ
1-Cos1-Sin
A) 12 B)
45 C)
35 D)
13
248
![Page 249: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/249.jpg)
2
2
θ = ....................+1
1+ TanCot
A) Tan0θ B) - Cot0θ C) Cotθ D) Tanθ
ABCA,B 2 2A + Sin BSin
A) B) 2
2
AA
SinCos C) 2 2Sin A - Cos A D)
2
2
AA
CosSon
Secθ + Tanθ = m, Secθ - TanTanθ= nmn =.............................. A) B) C) D)
2 = ...................θ
Tanθ1+Tan
A) Sinθ B) Cosθ C) Tanθ D) Cotθ
2sinθ 1 + tan θ = ..... A) 1 B) sinθ cosθ C) tanθ D) cotθ
tanθ + cot θ=2 tan2θ + cot2θ =..... A) B) C) D)
(1 + tan2θ cos2θ = ...
A) tan2θ B) 2 2
1sin θ - cos θ C) sec2θ D) 1
cosθ . tanθ =..... A) sinθ B) cosθ C) cotθ D) sinθ cosθ
θ tanθ A) 0 B) 0 C) 0 D) 0
A) sin900 B) cos00 C) sec900 D) cos900
cotA
A) 1213 B)
1417 C)
512 D)
125
tanθ
A) 12 B)
12 C)
32
D) 12
A
B
C
1
θ
A
BC
13
12
5
249
![Page 250: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/250.jpg)
secθ=.....
A) 35 B)
45 C)
54 D)
53
sin A =......
A) ACBC B)
BCAC C)
ABAC D)
BCAB
C A
A) 600 B) 300 C) 900 D) 450
Tan θSec θ A) 21- sec θ B) 21 + sec θ C) 2sec θ -1 D) 2see -1
(AS-4)
4 Marks
cm0cmABC A ABCAD10cm
BD = 10cm, CD = 10 3 BAC
sin (A - B) = sin cos B - cos A. sin B sin 150
sin2θ +cos2θ
cosec2θ - cot2θ
sec2θ - tan2θ
x = 2 cosecθ ; y = 2cotθ ‘θ ’
3
A
B C
54 θ
A
B
C
A
B C
8m4m
250
![Page 251: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/251.jpg)
x = asecθ ; y =btanθ‘θ ’
x = cosθ+sinθ ; y = cosθsinθ ‘θ ’
x= cosθ+sinθ ; y = cosθ -sinθ ‘θ ’
x = asinθ -bcosθ ; y=acosθ+bsinθ ‘θ ’
xcosθ + ysinθ = a; xsinθ - ycosθ= b‘θ ’
tan (A-B)= .tanA - tanB
1 + tanA tanB A,B
tan150
tan (A+B)= .tanA - tanB
1 + tanA tanB A,B
tan750
tan (450+B) = 2 + 3 tanB B
cos20= 2
2
1- tan θ1 + tan θ
A,B
cas600
sinA=3
2,AA
ABC 0 0C = 90 , A = 30 AB = 40cm
15cos A - 8sin A = O,‘A’ sinA + cosA2cosA - sinA
000
251
![Page 252: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/252.jpg)
0000(AS-4)
2 Marks
cm0cm0
4cos2θ=1 2
2tanθ1 - tan θ
3 0
ABCA,B,C
A + Btan2
ABC A,B,C
A + Bcos2
(AS-4)
1 Mark
secθ = 3ktanθ = 3K 2
2
1K -K
x sin450 cos450+ tan2600= sec2 300 x
252
![Page 253: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/253.jpg)
AsinA = cosAAtanA
ABC
B + Csin2
coseθ - cotθ =14 coseθ + cotθ
8cosec2 A - 8 cot2A sin30, sin900, sec600
cot2
cosec
sec2 =2 tan
(AS-4)
1/2 Mark
ABCA,B,C
A + Btan = .....2
A) Ctan2 B)
Csin2 C)
Ccot2 D)
Ccos2
ABC Csin2 =....
A)
A + Bsin2 B)
A + Bsin 90 -2
C)
A + Bscos2 D) B,C
cosecθ - cotθ =14 cosecθ+cotθ=.....
A) 2 B) 4 C) -1 D) 0
1secθ - tanθ =.....
A) secθ+tanθ B) secθ -tanθ C) 1 D) 0
22
1cot θ - = ...sin θ
A) -1 B) 4 C) 3 D) 1
253
![Page 254: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/254.jpg)
sin300. sin 900. sec 600 A) AP. B) H.P. C) G.P D) A or C
tan (A + B) =1, cos (A + B) =12 .B = ....
A) 0 B) 0 C) 0 D) 0
sec 450
A) 2 B) 12 C) D)
cosθ - cotθ = 3 cosecθ+cotθ =.....
A) 13 B) 9 C) 3 D)
13
a coseθ+bsinθ=m a sinθ - bcosθ=n a2+b2=.....
A) m2-n2 B) 2
2nm
C) 2
2
mn
D) m2+n2
secθ -1secθ +1
A) 1 + cosθ1- cosθ B)
cosθ - 11 + cosθ C)
1 - cosθ1 + cosθ D)
1+cosθ1-cosθ
tan2θ=2tan2θ+1cos2θ+sin2θ
A) 0 B) 8 C) 2 D) 1
sin4θ -cos4θ=
A) -1 B) cosθ C) 2sin2θ -1 D) 2cos2θ -1
(cosec2θ -cot2)(1-cos2θ )
A) sin2θ B) tanθ C) cos2θ D) cotθ
3 A) 0 B) 0 C) 0 D) 0
0..... A) 2 3 m B) 5 3 m C) 10 3 m D) 4 3 m
254
![Page 255: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/255.jpg)
(AS-5)
4 Marks
00000
0
0
0
00
(AS-5)
2 Mark
‘l’0 0‘h’ ABBC‘’ ‘P’ AB, BC APB = 0ABA‘P’
AP = n. ABAB“C” CB P
0
255
![Page 256: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/256.jpg)
θ
(AS-5)
1 Mark
‘d’m
‘θ ’
m0
h1,h2ß d
(AS-5)
1/2 Mark
21sinθ =29
A) B)
C) D)
A) B) C) D)3
4
35 5
4
5
4
P Q
A
B C
29 2121
29 R
D
E F
2129
21
29
cotθ
256
![Page 257: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/257.jpg)
= 450
= 300
= 600
A) B) C) D)1
11
3
2 8
10
6
2 2 4
5
A) B) C) D)21
13
2
1
4
3
5
1
11
A) B) C) D) A B1 2
1
3 2
1
4
3
5
257
![Page 258: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/258.jpg)
![Page 259: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/259.jpg)
(AS-1)
4 Marks
(a)
(b)
(c)
(d)
(i)(ii)(iii)(iv)
(i) (ii) (iii) (iv)
x
(i)
(ii)
123
4567
8
259
![Page 260: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/260.jpg)
(i)(ii)(iii) (iv) (i) (ii)(iii)(iv) (i) (ii)(iii)
(i) P()P()P()P() (ii)
(i)(ii) (iii)(iv)
(i)(ii)(iii)(iv)
260
![Page 261: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/261.jpg)
(i) (ii)
(iii) (iv)
(i)
(ii)
(iii)
(iv)
(a)(b)
(i)(ii)(iii)(iv)
(i) (ii)(iii) (iv)
261
![Page 262: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/262.jpg)
(i) (ii) (iii) (iv)
(i)
(ii)
(i) (ii)
(iii) (iv)
(i)(ii) (iii)(iii)
262
![Page 263: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/263.jpg)
(i)(ii)(iii)(iv)
(AS-1)
2 Marks
(i) (ii)
(i) (ii)
(a) (b)
(i) (ii)
(i) (ii)
263
![Page 264: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/264.jpg)
(i) (ii)
PROBABILITY
(i)(ii)
(i) (ii) (AS-1)
1 Mark
P (E)P( E )
264
![Page 265: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/265.jpg)
n n n n P ( E ) =
113 P ( E )
n (AS-1)
1/2 Mark
A) B) C) 12 D)
265
![Page 266: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/266.jpg)
A) B) 136 C)
236 D)
336
A) 125 B) 3
25 C) 4
25 D) 8
25
A) B) C) D)
EPE = 25 E
A) 35 B) 2
5 C) 15 D)
45
A) 1
16 B) 126 C) 2
26 D) 3
26
A) B) C) 1-2 D)
12
A) B) C) 12 D)
A) 13 B)
16 C)
23 D)
45
A) B) C) D)
A) 3
13 B) 2
13 C) 1
13 D)
A) B) 2
26 C) 3
26 D) 126
A) B) 14 C)
24 D)
34
(A)
(A)
266
![Page 267: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/267.jpg)
A) 14 B)
1326 C)
211 D)
13
A) 14 B)
113 C)
13 D)
152
A) 25 B)
13 C)
12 D)
16
A) 16 B)
56 C)
136 D)
236
A) 45 B)
23 C)
16 D)
36
A) 130 B)
330 C)
215 D)
230
A) 1726 B)
926 C)
1126 D)
626
A) B) C) D)
A) 12 B)
34 C)
13 D)
14
P (E)+ P ( E ) = ............
A) 1 B) 0 C) 2 D) 4
A) 34 B)
13 C)
24 D)
14
267
![Page 268: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/268.jpg)
A) 13 B)
16 C)
23 D)
56
A) B) C) 13 D)
23
A) 16 B)
19 C)
112 D)
118
P (E) = 0.05 P( E ) = ...........
A) 0.95 B) 0.85 C) 1 D) 0
A) B) C) D)
A) 4052 B)
1352 C)
126 D)
P (E) = 1
13 P( E ) =
A) 2
13 B) 1213 C) D)
A) B) 12 C) D)
A) 2
13 B) 1
13 C) D)
A) 2
13 B) 1
13 C) D)
A) B) C) D)
A) B) 32 C)
12 D)
268
![Page 269: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/269.jpg)
A) 13 B)
16 C)
12 D)
112
A) 7
10 B) 9
10 C) 3
10 D) 5
10
A) 0 P (E ) B) 0 P (E )
C) 0 P (E ) D) P ( E)
“ ASTONISHED ”
A) 7
10 B) 69 C)
610 D)
810
A) 12 B)
14 C)
56 D)
13
A) 12 B)
18 C)
13 D)
23
A) 1
365 B) 1
366 C) 17 D)
27
A) 13 B)
12 C)
23 D)
16
‘ MOBILE’
A) 37 B)
12 C)
47 D)
13
A) 0.25 B) 0.50 C) 0.75 D) 0
269
![Page 270: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/270.jpg)
A) 0.10 B) 0.20 C) 0.30 D) 0.40
A) 0 B) 1 C) 2 D) 3
A) 126 B)
226 C)
14 D) 1
A) 140 B)
240 1
20 C) 1 D) 0
A) 17 B) 2
7 C) 37 D)
47
(AS-2)
4 Marks
(i) (ii)(iii)
4cm
270
![Page 271: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/271.jpg)
(i)
(ii)
(iii)
(iv) ‘’
(a) (b) (c) (d)
‘x’
‘x’
(AS-2)
2 Marks
(i)(ii) P ( E ) + P ( E ) = 1
0 P (E )
271
![Page 272: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/272.jpg)
P (E ) +P ( E ) (AS-2)
1 Mark
72
‘’‘’
272
![Page 273: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/273.jpg)
‘’
(AS-2)
1/2 Mark
A) 12 B)
13 C) 1
6 D) 23
A) 2126 B)
526 C) D)
A) 1
12 B) 2
12 C) D)
A) 12 B)
220 C) 3
20 D) 4
20
x
A) 17 B)
57 C) 2
7 D) 37
273
![Page 274: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/274.jpg)
A) 12 B)
13 C)
14 D)
34
A) 1
100 B) 1
1000 C) A, B D)
A) 17 B)
27 C) 5
7 D) 67
A) 0 B) 1 C) 2 D) 3
A) 3 B) 2 C) 1 D) 0
A) 750 B)
927 C) 3
50 D) 4
127
A) 79 B)
25 C)
45 D)
17
A) 49
192 B) 5041 C)
12 D)
4971
A) 14 B) 0 C) 1 D)
13
A) 0 B) 1 C) 2 1D) 0.5
P
A)P B) P - 1 C) P + 1 D) 0
274
![Page 275: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/275.jpg)
‘x’ 1x
A) B) C) D)
A) 0 P ( E) B) 0 P (E) C) 0 P (E ) D) 0 P (E)
A) ‘’ B) C) D)
A) B) C) D)
A) B) C)
D)
A) B) C) D)
A) 1
4B) 1
4C) 1
3D) 3
4275
![Page 276: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/276.jpg)
A) 113
B) 113
C) 352
D) 113
(AS-3)
4 Marks
(i) (ii)(iii)(iv)
x
276
![Page 277: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/277.jpg)
(AS-3)
2 Marks
‘CONGRATULATIONS’
(i) (ii)
(i)
(ii)
(Sample Space )
(Sample Space )
(Sample Space )
(Sample Space)
277
![Page 278: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/278.jpg)
(AS-3)
1 Mark
EE
34
78
(AS-3)
1/2 Mark
A) B) C) D)A B
A) B) C) D)
A) B) C) D)
A) B) C) D) a, c
278
![Page 279: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/279.jpg)
A) B) C) D)
A) B)C) D)
A) H B) ,H T C) T, H D) b,c
A) 1, 2,3 B) 4,5,6 C) 1, 2, 3,4,5 D) 0
A) B) C) D)
A) B) C) 1
4 D) 12
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C)
12 D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
279
![Page 280: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/280.jpg)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B)
C) D) ‘’
A) B)
C) D)
A) B)
C) D)
A) B)
C) D)
‘n’ A) n2 B) 2n C) 2n D) n + 2
280
![Page 281: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/281.jpg)
‘n’ A) n6 B) 6n C) 2n D) n + 6
A) B) C) D)
A) B) C) D)
(AS-4)
4 Marks
A B O O AB O A O B A
O B A O O A AB O A A
O O AB B A O B A B O
A , B, AB
(i)(ii)(iii)
281
![Page 282: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/282.jpg)
(i) (ii) (iii)(iv)
(i) (ii)(iii) (iv)
23
19
112
282
![Page 283: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/283.jpg)
(i) (ii) (iii) (iv)
(i) (ii)(iii) (iv)(v)
(AS-4)
2 Marks
“ ’’
x x2 < 2
(i) (ii)
‘ MATHEMATICS’ M,E
(a) P
(b)
283
![Page 284: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/284.jpg)
(AS-4)
1 Mark
tan ‘’ cos (AS-4)
1/2 Mark
A)
27 B)
57 C)
47 D)
37
A)
512 B)
711 C)
213 D)
917
A)
12 B) C) D)
14
A) B)
13 C)
24 D)
284
![Page 285: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/285.jpg)
cas A) B) C) D)
tan A) B) C) D)
(AS-5)
4 Marks
14
1184
285
![Page 286: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/286.jpg)
(AS-5)
2 Marks
1 1 1, ,2 4 4
(AS-5)
1 Mark
‘’
286
![Page 287: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/287.jpg)
(AS-5)
1/2 Mark
14
12
16
16
16
16
16
16
13
13
13
13
13
13
12
12
12
12
12
12
23
23
23
23
23
23
(D)
wwG
GGRR
R wGG
GGRR
W wwW
RRRG
GA B
(A) (B) (C)(D)
RwG
GGGR
R wwG
RRRR
W RRG
GGWW
WwwG
GGRR
R(A) (B) (C) (D)
(B)
(A)
(C)
287
![Page 288: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/288.jpg)
(D)
-22
-12 0
12 2
2
(A) (B)-
22
-12 0
12 2
2
-22
-12 0
12 2
2 32
-22
-12 0
12 2
2 32
42
(C)
-2 -1 0 1 2 -2 -1 0 1 2
-2 -1 0 1 2 -2 -1 0 1 2
(A)
(C)
(B)
(D)
-2 -1 0 1 2 -2 -1 0 1 2
-2 -1 0 1 2 -2 -1 0 1 2
(A)
(C)
(B)
(D)
14
34
12 1
2
34 1
4
13 2
3
(C) (D)
(A) (B)
288
![Page 289: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/289.jpg)
(A)
(C)
(B)
(D)
0 14
24
34 1 0
14
24
34 1
0 14
24
34 1 0
14
24
34 1
(A)
(C)
(B)
(D)
0 14
24
34 1 0
14
24
34 1
0 14
24
34 1 0
14
24
34 1
(A)
(C)
(B)
(D)
0 14
24
34 1 0
14
24
34 1
0 14
24
34 1
0 14
24
34 1
289
![Page 290: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/290.jpg)
![Page 291: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/291.jpg)
(AS-1)
4 Marks
P
0-10 10-20 20-30 30-40 40-50 50-60 60-70
52 76 35 92 23 74 48
0-20 20-40 40-60 60-80 80-100
15 18 21 29 17
P
291
![Page 292: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/292.jpg)
f1, f2
0 - 20 20 - 40 40 - 60 60 - 80 80 - 100
17 f1 32 f2 9 12
65 - 70 70 - 75 75 - 80 80 - 85 85 - 90 90 - 95
3 12 15 10 8 2
20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50
8 11 12 18 19 12
5 12 20 27 35 40
2 3 5 6 5 3 1
0 - 50 50 -100
100 -150
200 -250
250 -300
300 -350
150 -200
292
![Page 293: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/293.jpg)
f
‘a’
60 - 65 65 - 70 70 - 75 75 - 80 80 - 85 85 - 90
13 28 35 f 5 3
20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
15 16 38 15 9 7
8 15 32 26 12 7
0 - 50 50 -100
100 -150
200 -250
250 -300
150 -200
15 18 21 29 17
0 - 20 20 - 40 40 - 60 80 - 100 60 -80
293
![Page 294: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/294.jpg)
x,y
(AS-1)
2 Marks
6 7 10 8 9
0 - 10 10 - 20 20 - 30 40 -50 30 - 40
0 - 6 6 - 12 12 - 18 24 -30 18 - 24C .I
Frequency 4 x 5 y 1
C .I
Frequency 24 40 33 28 30 22 16 7
100 -150
200 -250
250 -300
300 -350
150 -200
350 -400
400 -450
450 -500
5 10 15 25 3020midvalues
Frequency 4 8 14 11 3 10
294
![Page 295: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/295.jpg)
7 14 19 25 20 10 5
800 860 900 920 820 980 1000
8 10 11 16 20 25 15 9 6
1 3 4 52 6 7 8 9
f
x
15 50 80 76 72 45 39 9 8 6
5 15 20 2510 30 35 40 45 50
46 x 38 y 10 5 200
0 2 3 4 1 5
295
![Page 296: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/296.jpg)
P
, , , ,2 5 1 5 15 3 3 6 6
(AS-1)
1 Mark
x x x xx, , , , ,5 2 4 3 ‘x’
x + 3, x + 1 , x , x - 1, x -3
‘’
5 8 7 12 28 20 10 10
37 39 40 41 38 42 43 44
7 P 10 9 13 6
0 - 20 40 - 60 60 - 8080 -10020 - 40
100 -120
3 4 3 2
5 5.2 5.4 5.6
296
![Page 297: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/297.jpg)
x,x
‘x’
‘’
n, n +1, n - 1 (n -)
3 2 1 5 7, , , ,4 4 4 4 4
a = 325, N = 50, fidi = - 600
3, 5, 0, x, 11‘’‘x’(AS-1)
1/2 Mark
a + 2, a, a - 2 A) 3a B) 2a C) a D) 0
x, x + 3 , x + 6, x + 9 x + 12 x = A) 1 B) 2 C) 6 D) 4
n A) n B)
n + 12 C)
n2 D)
n + 32
n A)
n2 B) n C) n2 D) n (n + 1)
n A)
n2 B) n + 1 C) n2 D) n
n 5n9 n
A) 5 B) 4 C) 9 D) 10
x y, A) x + y = 21 B)x + y = 19 C) x - y = 19 D) x - y = 21
297
![Page 298: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/298.jpg)
A) 5 B) 10 C) 15 D) 20
x + 2, x + 3, 30, 31, 34 x A) 27 B) 25 C) 17 D) 18
x,x A) 9 B) 9.5 C) 10 D) 10.5
A) 3 B) 4 C) 5 D) 6
A) 27 B) 28 C) 50 D) 100
A) 25 B) 35 C) 45 D) 65
a + 1 , a + 3, a + 4 a + 8 A) a + 1 B) a + 4 C) a - 3 D)
A) 19 B) 19.5 C) 20 D) 20.5
fi = 20, fixi = 2p + 20p A) 110 B) 240 C) 90 D) 310
A) 5 - 8 B) 7 - 6 C) 2 - 3 D) 4 - 5
A) 90 B) 95 C) 100 D) 105
A) 10 B) 15 C) 20 D) 30
A) 20 B) 21 C) 20.5 D) 21.5
A) 75 B) 76 C) 22 D) 28
298
![Page 299: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/299.jpg)
A) 1 B) 4 C) 9 D) 25
A) 9 B) 4 C) 5 D) 1
A) 163 B)
185 C)
112 D)
196
A) 70 B) 69 C) 71 D) 51
x x x x, , , , x3 2 5 4 x
A) 8 B) 16 C) 24 D) 32
x + 1, x + 2, x + 3, x +4, x + 5 ( x > 0) A) x + 2 B) x + 3 C) x + 4 D) x + 5
x + 1, x + 2, x + 3, x + 4, x + 5 ( x > 0) x A) 9 B) 10 C) 11 D) 13
x , x + 2, x + 8 x + 6 x
A) 9 B) 8 C) 7 D) 6
L = 20, f0= 5, f1 = 8, f2 = 10, c = 10 A) 50 B) 60 C) 20 D)
A) 5 B) 9 C) 2 D) 5
A) 14 B) 10 C) 12 D) 8
A) 9 B) 10 C) 15 D) 20
x,x A) 18 B) 18.5 C) 17 D) 19
299
![Page 300: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/300.jpg)
9, B) 10 C) 11 D)
A) B) C) D)
A) 17.5, 45 B) 21.5,16 C) 16,18.5 D) 19.5, 20
4 3 6 9 8, , , ,5 5 5 5 5
A) 65 B)
95 C)
35 D)
85
A) 45 B) 40 C) 50 D) 55
-3, -5, -8, 0, 3, 2, -10 A) -8 B) 0 C) -2 D) -3
x -1, x +1, x, x -2, x +2 x A) 15 B) 20 C) 25 D) 30
A = 15 fiui = - 6, N = 10, h = 10 A) 10 B) 9 C) 14 D) 12
L = 10, N = 50, cf = 15, f = 10, h = 10 A) 20 B) 30 C) 40 D)
x, x A) B) C) D)
A) 7 B) 10 C) 5 D)
A) 12.4 B) 15.4 C) 16.5 D) 13.5
A) 4 B) 4.6 C) 5.6 D) 5
300
![Page 301: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/301.jpg)
0 - 10 10 - 20 20 - 30
A) B) C) D)
A) B) C) D) (AS-2)
4 Marks
(AS-2)
2 Marks
"N"2
0 - 10 10 - 20 20 - 30 40 -50 30 - 40C .I
Frequency 5 x 20 15 y 5
50 - 60
301
![Page 302: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/302.jpg)
‘’‘’‘’(AS-2)
1 Mark
‘’‘n’‘’‘’(AS-2)
1/2 Mark
A) B) C) D)
302
![Page 303: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/303.jpg)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
x 1x m 2
2
1x ,x
A) m2 +2 B) 2m2 +1 C) 2m2 - 1 D) m2 - 2
2n
A) n2 - 1n
B) n -12 - 1
n
C) 2n + 12 - 1n + 1
D) n2 - 1
2 n + 1
n
A) 2n(n + 1)
4B)
2 2n (n + 1)4
C) 2n (n + 1)
2D)
n(n +1)(n + 2)6
303
![Page 304: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/304.jpg)
MR MG A) MR = MG B) MR > MG
C) MR MG D) MG MR
xi , fi A) B) C) D)
A)
B)
C)
D)
A) =
B) =
C) =
D) = (AS-3)
4 Marks
1 - 4 4 - 7 7 - 10 10 - 13 13 - 16 16 -19
6 30 40 16 4 4
304
![Page 305: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/305.jpg)
SA1‘n’ ‘n’(AS-3)
2 Marks
4 11 29 40 46 50
305
![Page 306: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/306.jpg)
(AS-3)
1 Mark
C. I
20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79
15 16 38 15 9 7
6
306
![Page 307: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/307.jpg)
(AS-3)
1/2 Mark
A) B) C) D)
= 1 2
Δ,CL +Δ +Δ Δ 1
A) f1 - f0 B) f1 - f0 C) f0 - f1 D) f0 - f2
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B)C) D)
A)
2xn
B) i
2
xn C)
ixn D)
2i
2
xn
A) 142 B)105 C) 121 D) 132
307
![Page 308: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/308.jpg)
A) 2 B) 8 C) 6 D) 4
A) 10 B) 20 C) 30 D) 40
A) 1 0
1 0 22f fl
f f f
xh B) 1 0
1 0 2
f flf f f
xh
1 0
1 0 22f fl
f f f
D) 1 0
1 0 22f fl
f f f
xh
A) B) C) D)
1 0
1 0 12f fL
f f f
xh L
A) B) C) D)
2N cf
Lf
xh h
A) B) C) D)
A) B) C) D)
642
2 4 6
1020
4030
10 203040
308
![Page 309: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/309.jpg)
A) 13 B) 11 C) 20 D) 25
A) B) C) D)
fiuiAn
xh A
A) B) C) D)
xi Ah
A) B) C) D)
(AS-4)
4 Marks
0-10 10-20 20-30 30-40 40-50 50-60 60-70
x 5 9 12 y 3 2
C .I
Frequency
1 - 10 11 - 20 21 - 30 31 - 40 41 - 50
x 12 16 14 y
309
![Page 310: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/310.jpg)
y
(AS-4)
2 Marks
x, y,x, y‘’‘’y = x + 3 , y = 2x + 3, y = 2x + 6, y = 2x + 5, y = 3x + 7,A = 1, B = 2 ------
6 8 15 y 8 4
x
f
P 3 20 31 17 10 q
30 - 39 40 - 49 50 - 59 70 - 79 80 - 89 90 - 99 60 - 69
x 15 17 19 20 + P 23
2 3 4 5P 6f
310
![Page 311: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/311.jpg)
x1, x22x1 x1< x2< 2x1A.Mx1, x2 x3. x1< x2< x3 x3 -x1 = 50x1, x2 x3
x x x, x, ,5 4 2 x
3 (x >o) x
20 21 22 23 24 25
4 5 12 15 6 8
20 25 30 35 40
4 4 7 3 2
311
![Page 312: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/312.jpg)
(AS-4)
1 Mark
x + 3, x +1, x + 4, x + 5, x + 8 ‘’‘x’
1x,x K 2
2
1x ,x
x2, 2x2 + 3x, 5x2+ 6x, 2x2, x ‘x’‘x’n‘n’(n. )
‘’sin 300 ; cos 600 ; tan 450‘’ 10 100 1000
10 10 10log , log , log 10 16 64 256 81
10 2 4 4 3log , log , log , log , log log2, log5 A = { } P (x) = x2 - x - 6 5 One day Cricket
x / x
312
![Page 313: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/313.jpg)
(AS-4)
1/2 Mark
10 100 100010 10 10log , log , log A) 1 B) 2 C) 3 D) 4
A) 15 B) 20 C) 25 D) 50
sin 900 ; cos 00; tan 450 A) 3 B) 2 C) 1 D) 5
x, x + 3, x +5, x + 7, x + 10
A) 2133 B)
1113 C)
1143 D)
1153
log 2, log 5
A) 1 B) 12 C)
14 D)10
x2 - x - 2
A) 12 B) 1
4 C) 15 D)
29
x x
A) 69 B) 72 C) 45 D)91
A) n + 1
6 B) (n +1)(2n +1)
6 C) 3n -12
D)2(n + 1)
4
(1,4),(2,-5),(6,-8),(-4, 5),(-3,-2),
A) Q1 B) Q2 C) Q3 D)Q4
313
![Page 314: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/314.jpg)
A) B) C) D)
A) B) C) D)AB
(AS-5)
4 Marks
0 - 8 8 -16 16 - 24 24 - 32 32 - 40
6 7 10 8 9
0 -10 10 -20 20 - 30 30 - 40 40 - 60 50 - 60
7 10 23 51 4 3
20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79
15 16 38 15 9 7
0 -10 10 -20 20 - 30 40 - 50 50 - 60 50 - 60
7 10 23 51 4 3
C. I
Frequency
314
![Page 315: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/315.jpg)
(AS-5)
2 Marks
3 5 9 14 28 32 35
0 - 10 0 -20 20 - 30 30 - 40 40 - 50
9 16 24 15 4
0 - 5 5 -10 10 - 15 15 - 20 20 - 25
4 7 3 5 6
0 - 8 8 -16 16 - 24 24 - 32 32 - 40
6 7 10 8
315
![Page 316: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/316.jpg)
(AS-5)
1 Mark
20 -29 30 -39 40 - 49 50 - 59 60 - 69 70 - 79
15 16 38 15 9 7
0 - 10 0 -20 20 - 30 30 - 40 40 - 50
9 16 24 15 4
6 20 24 28 15 4 2 1
6 20 24 28 15 4 2 1
316
![Page 317: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/317.jpg)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
(AS-5)
1/2 Mark
317
![Page 318: dcebnellore.comdcebnellore.com/wp-content/uploads/2018/10/K-Mathematics.pdf · log 10 2= 0.3010, log 10 3 = 0.4771, ... log2 log 100 ... 2 45 +3 20 5 ...](https://reader031.fdocuments.us/reader031/viewer/2022020115/5c885cb309d3f2ff638b68e5/html5/thumbnails/318.jpg)
A) B) C) D)
A) B) C) D)
A) B) C) D)
A) B) C) D)
318