10th 1040105_A2 Mathematics QP

8/4/2019 10th 1040105_A2 Mathematics QP

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Class - X

MATHEMATICS

Time : 3 to 3 hours Maximum Marks : 80

: 3 3 : 80

Total No. of Pages : 17

c : 17

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

1040105 - A2

1 P.T.O.


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SECTION A

Question numbers 1 to 10 are of one mark each.

1. The lengths of the diagonals of a rhombus are 24 cm and 32 cm. The perimeter of therhombus is :

(A) 9 cm (B) 128 cm (C) 80 cm (D) 56 cm

2. The[HCF3LCM] for the numbers 50 and 20 is

(A) 10 (B) 100 (C) 1000 (D) 50

3. The value of k for which the pair of linear equations 4x16y21=0 and 2x1ky27=0 representsparallel lines is

(A) k53 (B) k52 (C) k54 (D) k522

4. If one of the zeroes of the quadratic polynomial (k21) x21kx11 is (23), then k equals to :

(A)4

3(B)

4

3 (C)

2

3(D)

2

3

5. The value of2

2tan30

1 tan 30

equals to :

(A) cos608 (B) sin608 (C) tan608 (D) sin308

6. Which of the following numbers has terminating decimal expansion ?

(A)37

45(B) 3 6

21

2 5(C)

17

49(D) 2 2

89

2 3

7. Sin (6081u)2cos (3082u) is equal to

(A) 2cosu (B) 2sinu (C) 0 (D) 1

8. The value of [(secA1tanA) (12sinA)] is equal to

(A) tan2A (B) sin2A (C) cosA (D) sinA


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9. If sinA1sin2A51, then the value of cos2A1cos4A is

(A) 2 (B) 1 (C) 22 (D) 0

10. In fig. 1 the value of the median of the data using the graph of less than ogive and more thanogive is

(A) 5 (B) 40 (C) 80 (D) 15

SECTION B

Question numbers 11 to 18 carry 2 marks each.

11. In fig.2, A, B and C are points on OP, OQ and OR respectively such that AB ??PQ and AC??PR.Show that BC??QR.


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12. If sec4A5cosec (A2208) where 4A is an acute angle, find the value of A.

OR

If 5 tanu=4, find the value of5 sin 3 cos

5 sin 2 cos

M M

M M.

13. In figure 3, ABCD is a parallelogram. Find the values of x and y.

14. In figure 4, Two triangles ABC and DBC are on the same base BC in which A5D5908.

if CA and BD meet each other at E, show that AE3CE5BE3DE.

15. If a and b are the zeroes of x217x112, then find the value of

1 12 9:

9 :.


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16. Convert the given cumulative frequency table into frequency distribution table :

Marks Number of students

0 and above 12020 and above 108

40 and above 90

60 and above 75

80 and above 50

100 and above 24

120 and above 9

140 and above 0

17. Find the mode of the following data:

Class 0 - 20 20 - 40 40 - 60 60 - 80

Frequency 15 6 18 10

18. Check whether 6n can end with the digit O for any natural number n ?

SECTION C

Question number 19 to 28 carry 3 marks each.

19. If a and b are zeroes of the quadratic polynomial x226x1a; find the value of a if 3a+2b=20.

20. Find HCF of 180, 252 and 324 using Euclids Division Lemma.

21. Prove that 7 is an irrational number.

OR

Prove that 3+ 5 is an irrational number.

22. Prove that

2sec tan 1 sin

sec tan cos

M M M

M M M


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23. In DABC, in fig.5, a PQ meets AB in P and AC in Q. If AP51 cm, PB53cm, AQ51.5 cmQC54.5 cm, prove that area of DAPQ is one sixteenth of the area of DABC.

24. In figure 6 P and Q are the midpoints of the sides CA and CB respectively of DABC right

angled at C. Prove that 4 (AQ21BP2)55AB2.

25. The sum of digits of a two digit number is 15. The number obtained by interchanging thedigits exceeds the given number by 9. Find the number.

OR

Solve for x and y :

2a b

yx

ax2by5a2

2b2

26. Find the mean of the following data :

Classes 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 50 - 55 55 - 60

Frequency 14 22 16 6 5 3 4

OR


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Find the median of the following data :


0 and above 80

10 and above 77

20 and above 72

30 and above 65

40 and above 55

50 and above 43

60 and above 28

70 and above 16

80 and above 10

90 and above 8

100 and above 0

27. The mean of the following frequency distribution is 50. Find the value of P.

Classes 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100

Frequency 17 28 32 P 19

28. In figure 7, DABC is right angled at B, BC57cm and AC2AB51cm. Find the value ofcosA2sinA


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SECTION D

Question numbers 29 to 34 carry 4 marks each.

29. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squaresof the other two sides.

OR

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio oftheir corresponding sides.

30. Without using trigonometric tables, evaluate the following :

2 22

2 2

cos 20 cos 702cosec 58 2cot58 tan32 4tan13 tan37 tan45 tan53 tan77

sec 50 cot 40

OR

Prove that :

sinA cosA1

secA tanA 1 cosecA cotA 1

31. What must be added to the polynomial f(x) 5x412x322x21x21 so that the resultingpolynomial is exactly divisible by x212x23 ?

32. Check graphically whether the pair of linear equations 4x2y2850 and 2x23y1650 isconsistent. Also, find the vertices of the triangle formed by these lines with the x-axis.

33. If 2cosu2sinu5x and cosu23sinu5y. Prove that 2x21y222xy55.


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34. Draw a less than ogive for the following data :


Less than 20 0

Less than 30 4

Less than 40 16

Less than 50 30

Less than 60 46

Less than 70 66

Less than 80 82

Less than 90 92

Less than 100 100

Find the median of the data from the graph and verify the result using the formula.

- o O o -


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U -

1 10 1

1. Z 24 cm32 cm

(A) 9 cm (B) 128 cm (C) 80 cm (D) 56 cm

2. 5060[HCF3LCM]

(A) 10 (B) 100 (C) 1000 (D) 50

3. k 4x16y21=02x1ky27=0 ;(A) k53 (B) k52 (C) k54 (D) k522

4. m (k21) x21kx11 (23) k

(A)4

3(B)

4

3 (C)

2

3(D)

2

3

5. 22tan301 tan 30

(A) cos608 (B) sin608 (C) tan608 (D) sin308

6. ?

(A)37

45(B) 3 6

21

2 5(C)

17

49(D) 2 2

89

2 3

7. sin (6081u)2cos (3082u)

(A) 2cosu (B) 2sinu (C) 0 (D) 1

8. (secA1tanA) (12sinA)

(A) tan2A (B) sin2A (C) cosA (D) sinA


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9. sinA1sin2A51, cos2A1cos4A

(A) 2 (B) 1 (C) 22 (D) 0

10. 1,

(A) 5 (B) 40 (C) 80 (D) 15

U -

11 18 2

11. 2 OP, OQOR A, BC S AB??PQAC??PR BC??QR


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12. sec4A5cosec (A2208),4A , A

5 tanu545 sin 3 cos

5 sin 2 cos

M M

M M

13. 3ABCD xy

14. 4, ABCDBC BC A5D5908 CABDD S , AE3CE5BE3DE.

15. x217x112 a, b , 1 1

2 9:9 :


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16.

s S h

0 120

20 108

40 90

60 75

80 50

100 24

120 9

140 0

17.

0 - 20 20 - 40 40 - 60 60 - 80


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22. Uh

2sec tan 1 sin

sec tan cos

M M M

M M M

23. U5 UDABC UPQ, AB UP U AC Q AP51 cm, PB53cm,AQ51.5 cm, QC54.5 cm, U h DAPQ U , DABC U

24. 6DABC C PQ CABC h 4 (AQ21BP2)55AB2.

25. 15 S 9

xy

2a b

yx

ax2by5a22b2


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26.

25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 50 - 55 55 - 60

77 14 22 16 6 5 3 4

N c

0 80

10 77

20 72

30 6540 55

50 43

60 28

70 16

80 10

90 8

100

0

27. 50 P

0 - 20 20 - 40 40 - 60 60 - 80 80 - 100


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U -

29 34 4

29. h Z

h M

30.

2 22

2 2

cos 20 cos 702cosec 58 2cot58 tan32 4tan13 tan37 tan45 tan53 tan77

sec 50 cot 40

h

sinA cosA1

secA tanA 1 cosecA cotA 1

31. f(x) 5x412x322x21x21 (x212x23) ?

32. m 4x2y28502x23y1650 x - m

33. 2cosu2sinu5xcosu23sinu5y h 2x21y222xy55.


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34.

N c

20 0

30 4

40 16

50 30

60 46

70 66

80 82

90 92

100 100

m

- o O o -

10th 1040105_A2 Mathematics QP

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