KENDRIYA VIDYALAYA ASHOK NAGAR, CHENNAI – 83

X – MATHS : PRACTICE PAPER – 8 (GROUP – B ): 31 – 12 – 17

Time allowed : 3 Hours Max. Marks: 80

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SECTION – A ( 6× 1 = 6 )

1. Two friends were born in the year 2000. What is the probability that they have the same birthday.

2. Write the value of sin (65˚ + ) – cos (25˚ – ).

3. For the A.P.: , , , , ………., write the first term a and the common difference d.

4. Find the values of K form which the equation x2 + 5Kx + 16 = 0 has no real roots.

5. What is the sum and product of zeroes of quadratic polynomial 2x2 – 3x – 5.

6. DE || BC and = . If AC = 4.8 cm, find the length of AE. $C:\Users\User\Desktop\1.PNG$

SECTION – B ( 6× 2 = 1 2 )

7. The sum of first n terms of an AP is 3n² + 6n. Find the 15th term of this AP.

8. A bag contains 15 white and some black balls .If the probability of the drawing a black ball from the bag is thrice that of drawing a white ball find the number of black ball In the bag.

9. Two different dice are thrown together .Find the probability that the numbers obtained have even sum and

even product.

10. Find the roots of the quadratic equation – 7x+5

11. For what values of a and b does the following pairs of linear equations have infinite number of solutions:

2 x +3 y = 7, (a – b ) x + (a + b) y = 3a + b -2

12. Find the relation between x and y such that point (x, y) is equidistant from the points (6, – 1 ) and (2, 3 ).

SECTION – C ( 10×3 = 30 )

13. Find all the zeroes of the polynomial p(x)= 2 x4 – 2 x3 – 7 x2 + 3 x + 6 if its two zeroes are

14. In an AP, the first term is 8 and the common difference is 7. If the last term of the AP is 218, find its

middle term.

15. D is a point on the side BC of a triangle ABC such that . Show that CA2 = CB.CD.

16. In fig. , a quadrilateral ABCD is drawn to circumscribe a circle , with centre O , in such a way that the sides

AB, BC, CD and DA touch the circle at the points P,Q,R and S respectively . Prove that AB + CD = BC + DA.

D R C

A P B

17. Using Euclid’s algorithm , find the HCF of 117 and 65.

18. Solve for x and y :

19. Prove that : – = –

20. Find the ratio in which the line segment joining A ( 1, – 5 ) and B ( – 4 , 5 ) is divided by the x axis.

Also, find the coordinates of the point of division.

21. Find the values of y for which the distance between the points P ( 2 , – 3 ) and Q ( 10 , y ) is 10 units.

22. The volume of a hemisphere is . Find the curved surface area.

SECTION – D ( 8×4 = 32 )

23. Draw a triangle ABC with side BC =6 cm ,AB=5 cm and ABC =600 .Then construct a triangle whose

sides are of the corresponding sides of the triangle ABC.

24. In fig., the line segment XY is parallel to side AC of ABC and it divides the triangle into two parts of equal

areas. Find the ratio . A

B Y C

25. The sum of first six terms of an AP is 42. The ratio of its 10th term to its 30th term is 1:3. Find the first term

of the AP.

26. Solve for x :

27. The sum of the squares of two consecutive even numbers is 340 .Find the numbers.

28. Solve the following equations graphically;

4 x – 3 y + 4 = 0, 4 x + 3 y – 20 = 0. Also find the vertices of the triangle formed by lines and y axis.

29. The angle of elevation of an aero plane from a point A on the ground is 60˚. After a flight of 15 seconds,

the angle of elevation changes to 30˚. If the aero plane is flying at a constant height of

1500

30. The following table gives the production yield per hectare of wheat of 100 farms of a village.

Production yield in kg/hectare	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80
Number of farms	2	8	12	24	38	16

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

median from the graph.