10th 1040125_C2 Mathematics QP.pdf

7/29/2019 10th 1040125_C2 Mathematics QP.pdf

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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 - D comprisesof 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 , UU , , 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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SECTION - A

Question numbers 1 to 10 carry one mark each :

1. If tan u = cot u then the value of sec u is :

(A) 2 (B) 1 (C)23 (D) 2

2. In Fig. 1, DABC in right angled at B and cot A=3

4. If AC =10 cm the length of AB is

(A) 3cm (B) 4cm (C) 6cm (D) 8cm

3. The decimal expansion of7

125will terminate after how many places of decimal

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

4. The pair of linear equations 5 x14y520 and 10x18y516 have

(A) No solution (B) Many solutions (C) Two solutions (D) One solution

5. If sec A5 cosec B =5

3then A1B is equal to

(A) Zero (B) 908 (C) < 908 (D) > 908

6. For a given data with 35 observations the less than ogive and more than ogive intersect at(28.5, 30). The median of the data is :

(A) 28.5 (B) 30 (C) 1.5 (D) 35

7. If sin 3u 5 cos (u - 26o) where 3u and (0 - 268) are acute angles, then value of u is :

(A) 308 (B) 298 (C) 278 (D) 268

8. According to Euclids division algorithm using Euclids division lemma for any two positiveintegers a and b with a > b enables us to find :

(A) HCF (B) LCM

(C) Decimal expansion (D) Probability


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9. In figure 2, the graph of a polynomial p (x) is shown. The number of zeroes of p (x) is :

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

10. In figure 3, if DE ?? BC then x equals :

(A) 6 cm (B) 7 cm (C) 3 cm (D) 4 cm

SECTION - B

Question numbers 11 to 18 carry two marks each :

11 . Can (x27) be the remainder on division of a polynomial p(x) by (7x12) ? Justify youranswer.

12. Is 8373635343314 a composite number ? Justify your answer.


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13. In Fig. 4 ABCD is a rectangle. Find the values of x and y.

14. Find the mode of the following distribution

Family size 13 35 57 79 911

No. of families 7 8 2 2 1

15. If sin (A 1 B) 5 cos (A 2 B) 53

2and A, B (A > B) are acute angles, find the values of A

and B .

OR

If tan u 55

12find the value of :

cos sin

cos sin

M M

M M

16. The marks obtained by 60 students, out of 50 in a Mathematics examination, are given

below.

Marks 0 10 1020 20 30 30 40 40 50

No. of students 5 13 12 20 10

Write the above distribution as less than type cumulative frequency distribution.


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17. In figure 5, if PQ ?? CB and PR ?? CD , prove thatAR AQ

AD AB

18. In fig 6, PM 5 6 cm, MR 5 8 cm and QR 5 26 cm, find the length of PQ.

SECTION - C

Question numbers 19 to 28 carry 3 marks each :

19 Prove that3

2 5is an irrational number.

OR

Prove that 3 5 is an irrational number.

20 A lending library has a fixed charge for first three days and an additional charge for eachday there after. Bhavya paid Rs. 27 for a book kept for seven days, while Vrinda paid Rs 21for a book kept for five days. Find the fixed charge and the charge for ecah extra day.

OR

The sum of the digits of a two digit number is 5. On reversing the digits of the number, itexceeds the original number, by 9. Find the original number.


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21. If a , b are zeroes of the polynomial 2x 2 4 3x then form a quadratic polynomial whose

zeroes are 3a and 3 b.

22. ABC is an isosceles triangle, right angled at C. Prove that 2AB = 22BC .

23. Show that any positive odd integer is of the form 4q11 or 4q13 where q is a positiveinteger.

24. Prove that (cosec u 2 cot u)2 51 cos

1 cos

25. In a trapezium ABCD, AB ?? DC . Its diagonals AC and BD intersect at O. Show that

OA

OC5

OB

OD

26. If m sin u 1 n cos u 5 p and m cos u 2n sin u 5q then prove that m21 n25 p21q2

27 Find the median of the following data.

Classes 500 600 600 700 700 800 800 900 900 1000

Frequency 40 28 35 22 25

28 Find the mean of the following frequency distribution, using step deviation method.

Classes 100 150 150 200 200 250 250 300 300 350

Frequency 4 5 12 2 2

OR

The mean of the following frequency distribution is 25. Determine the value of p

Classes 0 10 10 20 20 30 30 40 40 50

Frequency 5 18 15 p 6


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SECTION - D

Question numbers 29 to 34 carry 4 marks each :

29 . Solve graphically the pair of linear equations 3 5 0x y

and 2 5 0x y

shade the triangulararea formed by two lines with y axis.

30. Find other zeroes of the polynomial 4 3 29 3 18x x x x if it is given that two of its zeroes

are 3 and 3 .

31. Prove that sec4u2sec2u5tan4u1tan2u.

32. Prove thatsin FRV

2cosec1 cos VLQ

OR

Evaluatecos70 cos55 cosec35

sin20 tan5 tan25 tan45 tan65 tan85

33. The following distribution gives the annual profit earned by 30 shops of a shopping complex.

Profit (inLakh Rs.)

0 5 5 10 10 15 15 20 20 25

No. of shops3 14 5 6 2

Change the above distribution to more than type distribution and draw its ogive.

34. If a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points,then prove that the line drawn, divides the two sides in the same ratio.

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

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U- 1 10

1. tan u5cot u sec u

(A) 2 (B) 1 (C)23 (D) 2

2. 1,DABC B 90 cot A53

4AC510 AB

(A) 3 (B) 4 (C) 6 (D) 8

3.7

125 , S

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

4. 5x14y520 10x18y516 (A) (B) (C) (D)

5. sec A5cosec B55

3 A1B

(A) (B) 908 (C) < 908 (D) > 908

6. 35 (28.5, 30)U U

(A) 28.5 (B) 30 (C) 1.5 (D) 35

7. sin 3u 5 cos (u2268)3u u2268 u (A) 308 (B) 298 (C) 278 (D) 268

8. Za ba > b (A) .. (B) .. (C) (D)


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9. (2) p (x) p (x)

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

10. (3) DE ?? BC x

(A) 6 (B) 7 (C) 3 (D) 4

U-

11 18 2

11. p(x) (7x12) (x27) ? SC

12. 8373635343314 ? SC


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13. 4, ABCD xy

14. 18.

5 13 35 57 79 911

7c 7 8 2 2 1

15. sin (A1B)5cos (A2B)53

2A, B (A > B) A B

tan u 55

12

cos sin

cos sin

M M

M M

16. 60l m ( 50)

0 10 1020 20 30 30 40 40 50

7zc 5 13 12 20 10

17. 5, PQ ?? CB PR ?? CD h AR AQ

AD AB


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18. 6, PM56, MR58. QR526. PQ

U- 19 28 3

19. h 3

2 5

h 3 5

20. 3 , S , S 27L S 21L

5 # , S , 9 ,S

21. a, b 2x 2 4 6x 3a 3b

22. ABC m , C h 2AB 5 22BC

23. Z M4q114q13 q Z

24. h (cosec u 2 cot u)2 51 cos

1 cos

25. ABCDAB ?? DC, AC BDS O

OA

OC5

OB

OD


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26. m sinu1n cosu5p m cosu2n sinu5q h m21 n25 p21q2

27 7 500 - 600 600 - 700 700 - 800 800 - 900 900 - 1000

777 40 28 35 22 25

28 - m

100 150 150 200 200 250 250 300 300 350

7 4 5 12 2 2

25 p

7 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50

777 5 18 15 p 6

U-

29 34 4 29. 3 5 0x y 2 5 0x y m y-

30. 4 3 29 3 18x x x x 3 3

31. h sec4 u2sec2 u5tan4 u1tan2 u.

32. h sin FRV

2cosec1 cos VLQ

cos70 cos55 cosec35

sin20 tan5 tan25 tan45 tan65 tan85


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33. $ 30

7. 0 5 5 10 10 15 15 20 20 25

c 3 14 5 6 2

34. , h ,

h Z

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10th 1040125_C2 Mathematics QP.pdf

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