10th 1040106_B2 Mathematics QP

8/8/2019 10th 1040106_B2 Mathematics QP

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Class - X

MATHEMATICS

Time : 3 to 3 hours Maximum Marks : 80

: 3 3 : 80

Total No. of Pages : 13

c : 13

General Instructions :

1. All questions are compulsory.

2. The question paper consists of 34 questions divided into four sections A, B, C and D.Section - A comprises of 10 questions of 1 mark each. Section - B comprises of 8 questions of2 marks each. Section - C comprises of 10 questions of 3 marks each and Section - Dcomprises of 6 questions of 4 marks each.

3 . Question numbers 1 to 10 in Section - A are multiple choice questions where you are to selectone correct option out of the given four.

4. There is no overall choice. However, internal choice has been provided in 1 question of twomarks, 3 questions of three marks each and 2 questions of four marks each. You have toattempt only one of the alternatives in all such questions.

5. Use of calculator is not permitted.

6. An additional 15 minutes time has been allotted to read this question paper only.

1.

2. 34 , U , , U - 10 1 U - 8 2 U - 10 3 U - 6 4

3. 1 10 4. , 1 2 , 3 3 2

4

5.

6. - 15 - -S

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1 P.T.O.


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7. If sec u2tanu51

3, the value of (sec u1tanu) is :

(A) 1 (B) 2 (C) 3 (D) 4

8. If one of the zeroes of the quadratic polynomial (k21)x21kx11 is 23, then the valueof k is

(A) 2 4 3 (B)4

3

(C) 2 3 (D) 22

3

9. The measures of central tendency which cant be found graphically is :

(A) mean (B) median (C) mode (D) none of these

10. In fig.2, if D is mid-point of BC, the value of x

y

tan

tan

is

(A)1

3(B) 1 (C) 2 (D)

1

2

SECTION B

Question numbers 11 to 18 carry 2 marks each.

11. Find the median class and the modal class for the following distribuion.

C.I 135-140 140-145 145-150 150-155 155-160 160-165f 4 7 18 11 6 5

12. Write the following distribution as more than type cumulative frequency distribution:

C.I 50-55 55-60 60-65 65-70 70-75 75-80

frequency 2 6 8 14 15 5


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13. Simplify : (sec u1tan u) (12sin u).

14. In fig. 3, ABABC, DEAAC and GFABC. Prove that DADEDGCF

15. In a quadrilateral ABCD, B5908. If AD25AB21BC21CD2,

prove that ACD5908.

16. a, b are the roots of the quadratic polynomial p (x)5x22(k16)x12 (2k21).

Find the value of k, ifa1b1

2a b.

17 . Solve 37x143y5123, 43x137y 5117.OR

x16

y 56, 3x28

y 55.

18. In the adjoining factor tree, find the numbers m, n :


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SECTION C


19.

In fig. 4, LM??AB. If AL5x23, AC52x, BM5x22, BC52x13, find the value of x.

20. Find the median of the following frequency distribution :

C.I. 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75

Frequency 2 3 5 7 4 2 2

21. Find the mean of the given frequency distribution table :

Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70

Frequency 3 8 10 15 7 4 3

22. Find the zeroes of 23 2 13 6 2x x and verify the relation between the zeroes andcoefficients of the polynomial.

23. Show that 51 2 is an irrational number.

OR

Prove that 3 1 5 is irrational.

24. Show that 5n cant end with the digit 2 for any natural number n.


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25. If A,B,C are interior angles of DABC, show that

2 2B C Asec 1 cot2 2

OR

Prove that :1cos(90 ) sin (90 )

2cosec1 sin(90 ) cos (90 )

M M M

M M

26. If tan(A1B)5 3 , tan(A2B)51

3, 0 < A 1 B [ 908, A > B,

find A and B.

27. The taxi charges in a city consists of a fixed charge together with the charge for thedistance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journeyof 15 km, the charge paid is Rs. 155. What are the fixed charges and the charges perkm ?

OR

The monthly incomes of A and B are in the ratio of 5 : 4 and their monthly expendituresare in the ratio of 7 : 5. If each saves Rs. 3000 per month. Find the monthly income ofeach.

28. Prove that the area of the equilateral triangle described on the side of a square is halfthe area of the equilateral triangle described on its diagonal.

SECTION D


29. Solve the following system of equations graphically and from the graph, find the pointswhere these lines intersect the yaxis :

x22y52, 3x15y517.

30. Prove the following :

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of theother two sides.

OR

If a line is drawn parallel to one side of a triangle to intersect the other two sides indistinct points, the other two sides are divided in the same ratio. Prove it.


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31. Find all the zeroes of the polynomial x425x312x2110x28, if two of its zeroes are

2 , 2 .

32. Prove thatcot 1 cosec 1

cot 1 cosec cosec cot

M M

M M M M

OR

If tanu 1sinu5m and tanu2sinu 5n, show that

22 2m n 5 16mn

33. Prove that1 sinA

secA tanA1 sinA

34. Draw less than ogive for the following frequency distribution and hence obtain the

median.

Marks obtained 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of students 3 4 3 3 4 7 9

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U-

1 10 1

1. p, q LCM(p, q) (A) 1 (B) P (C) q (D) pq

2. kx13y1150, 2x1y1350

(A) k56 (B) kv 6 (C) k53 (D) kv 3

3. d5HCF(48, 72)d

(A) 24 (B) 48 (C) 12 (D) 72

4. (1), ACB 5908, BDC 5908, CD54.., BD53.., AC512 .. cosA2sinA

(A)5

12(B)

5

13(C)

7

12(D)

7

13

5. cosu 1 cos2u 5 1 (sin2 u 1 sin4u)

(A) 0 (B) 1 (C) 21 (D) 2

6. DABC#DRQP, A 5 808, B 5608 P (A) 608 (B) 508 (C) 408 (D) 308

7. sec u2tan u51

3 (sec u1tan u)

(A) 1 (B) 2 (C) 3 (D) 4


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8. m (k21)x21kx11 23 k

(A) 2 4 3 (B)4

3

(C) 2 3 (D) 22

3

9. m

(A) (B) (C) (D)

10. (2) D, BC xy

tan

tan

(A)

1

3 (B) 1 (C) 2 (D)

1

2

U-

11 18 2

11.

r


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13. (sec u1tan u) (12sinu).

14. - 3ABABC, DEAACGFA BCh DADEDGCF

15. ABCD,B5908AD25AB21BC21CD2 h ACD5908

16. a, b m p (x)5x22(k16)x12 (2k21) , k U

a1b51

2a b.

17 . 37x143y5123, 43x137y 5117.

x5 6y 56, 3x28

y 55.

18. mn


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U-

19 28 3

19.

(4), LM??AB. AL5x23, AC52x, BM5x22, BC52x13x U

20.

r


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24. 5n S 2 n

25. A,B,C

2 2B C Asec 1 cot

2 2

h 1cos(90 ) sin (90 )

2cosec1 sin(90 ) cos (90 )

M M M

M M

26. tan(A1B)5 3 , tan(A2B)5 1

3

, 0 < A 1 B [ 908, A > B

AB

27. 10.. 105L. 15.. 155 L. .. ?

AB 5 : 4 7 : 5 3000L

28. h

U-

29 34 4

29. m m yaxis

x22y52, 3x15y517

30. h Z

-


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31. x425x312x2110x28 2 2

32. h cot 1 cosec 1cot 1 cosec cosec cot

M M M M M M

tanu 1sinu5mtanu2sinu 5n 22 2m n 5 16mn

33. h 1 sinA

secA tanA1 sinA

34.

s 10-20 20-30 30-40 40-50 50-60 60-70 70-80

Sh 3 4 3 3 4 7 9

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10th 1040106_B2 Mathematics QP

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