Here is a question paper for class 10 Mathematic .those student was preparing the board examination see this question paper this was very help full to you. In this time you were work very hard because time and tide wait for none so start the preparing.

*ALL THE BEST FOR YOUR EXAM*

### SECTION – A

** Question numbers 1 to 10 carry one mark each.**

1. Find the value of k so that the following system of equations has no solution:

3x – y – 5 = 0; 6x – 2y – k = 0.

2. The nth term of an A.P. is 6n + 2. Find its common difference.

3. In fig. 1, AD = 4 cm, BD = 3 cm and CB = 12 cm, find cot q . Fig.1

4. Write the zeroes of the polynomial x2 – x – 6.

5. If p q is a rational number (q ¹ 0), what is condition on q so that the decimal representation of p q is termination?

6. From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.

7. Which measure of central tendency is giving by the x-coordinate of the point of intersection of the “more than o give” and “less than o give”?

8. In Fig. 2, O is the centre of a circle. The area of sector OAPB is 5 18

of the area of the circle. Find x. Fig. 2

9. In. Fig. 3, PQ = 24 cm, QR = 26 cm, ÐPAR = 900, PA = 6 cm and AR = 8 cmFindÐQPR. Fig. 3.

10. In Fig. 4, P and Q are points on the sides AB and AC respectively of △ ABC such that AP = 3.5 cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm, find BC.

Fig.4

SECTION – B

Question numbers 11 to 15 carry 2 marks each.

11. For what value of p, are points (2, 1), (p, -1) and (-1, 3) collinear?

12. Without using trigonometrically tables, evaluate the following:

sin18

3[tan10 tan 30 tan 40 tan 50 tan 80 ]

cos72

13. Find the zeroes of the quadratic polynomial 6×2 – 3 – 7x and verify the relationship between the zeros and the co-efficients of the polynomial.

14. A die is thrown once. Find the probability of getting

(i) An even prime number

(ii) A multiple of 3

15. ABC is an isosceles triangle, in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contract.

OR

In Fig. 5, a circle is inscribed in a quadrilateral ABCD in which ÐB = 900. If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius (r ) of the circle.

Fig.5

### SECTION – C

Question numbers 16 to 25 carry 3 marks each.

16. Prove that:

cot cos cos 1

cot cos cos 1

A A ecA

A A ecA

- = –

+ +

OR

Prove that: (1 + cot A – cosec A) (1 + tan A + sec A) = 2

17. Find the 10th term from the end of the A.P. 8, 10, 12,…………….,126.

18. Represent the following system of linear equations graphically. From the graph. Find the points where the lines intersect y-axis: 3x + y – 5 = 0; 2x – y – 5 = 0.

19. Find the roots of the following equation:

1 1 11

; 4,7

4 7 30

x

x x

- = ¹ –

+ –

20. Show that 2 – 3 is an irrational number.

21. In Fig. 6, find the perimeter of shaded region where ADC, AEB and BFC are semi – circles on

diameters AC, AB and BC respectively.

Fig. 6

OR

Find the area of the shaded region in Fig. 7, where ABCD is square of side 14 cm.

Fig. 7

22. If the distances of P(x, y) from the points A(3, 6) and B(-3, 4) are equal, prove that 3x +y = 5.

23. If the diagonals of a quadrilateral divided each other proportionally, prove that it is a trapezium.

OR

Two s△ ABC and DBC are on the same base BC and on the same side of BC in which ÐA =

ÐD = 900. If CA and BD meet each other at E, show that AE.EC = BE.ED

24. Construct a △ABC in which AB = 6.5 cm, ÐB = 600 cm, and BC = 5.5 cm. Also construct a triangle. AB’C’ similar to △ABC , whose each side is 3 2

times the corresponding side of the △ABC.

25. Determine the ratio in which the line 3x + 4y – 9 = 0 divides the line-segment joining the points (1, 3) and (2, 7).

### SECTION – D

Question numbers 26 to 30 carry 6 marks each.

26. A state 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 600 and from the same point, the angle of elevation of the top of the pedestal is 450. Find the height of the pedestal (use 3 = 1.73)

27. In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.

OR

The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m,

find the sides of the two squares.

28. 100 surnames were randomly picked up from a local telephone directory and the distribution of

number of letters of the English alphabet in the surnames was obtained as follows:

No. of

letters

1 – 4 4 – 7 7 – 10 10 – 13 13 – 16 16 – 19

Numbers

of

surnames

6 30 40 16 4 4

Determine the median and mean number of letters in the surnames. Also find the modal size of

surnames.

29. Prove that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

Using the above result, prove the following:

In a △ ABC, XY is parallel to BC and it divides △ ABC into two parts of equal area.

Prove that

bx/ab and=2 –1 /2

30. A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also find the cost of the bucket it the cost of metal sheet used is Rs 20 per 100 cm2. (use p = 3.14)

OR

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his

field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 6 km/h., in how much time will the tank be filled?