10th Maths sample papers

                     Section - A
1. Which of the following equations has the same roots ?

a) x2 -6x+6=0 

b) x2 + 8x + 16 = 0 

c) 3x2+2x + 6 = 0 

b) x2 + 2x + 1 = 0

2. If a, a – 2 and 3a are in AP, then the value of a is

a) – 3   b) -2   c) 3   d) 2

3. A quadrilateral MNOP is drawn to circumscribe a circle. If MN=6cm, ON=7.5cm, OP=7cm, then MP is equal to

a) 6cm      b) 5cm 

c) 5.5cm  d) 6.5cm

4. If the area of quadrant of a circle is 9.625cm2. Find the circumference of circle.

a) 24cm      b)22cm. 

c) 35cm      d) 25cm

5. If TP and TQ are two tangents to a circle with centre O so that <POQ=110, then <PTQ is equal to :
a) 60   b) 90   c) 70   d) 80

6. Tangents TP and TQ are drawn to a circle with centre O from anexternal point M. <OPQ= 35. Find PMQ.

a) 65   b) 80   c) 70   d) 65.5

7. The ratio between the volumes of two spheres is 8:27. What is theratio between their surface areas?

a) 4:9   b) 5:6   c) 4:5   d) 2:3

8. The difference between the circumference and radius of a circle is 37cm. The area of the circle is

a) 111cm2      b) 184cm2 

c) 154cm2      d) 259cm2.

9. The ratio of the height of a man and its shadow is 3 : √3 . The angle of elevation of sun is :

a) 45.   b) 30    c) 60   d) 90.

10. Find the probability of black or red 10 from well suffled 52 cards.

a) 2/13    b) 2/52   

c) 4/52    d) 4/13

Section – B

11. Find the roots of the following quadratic equations: 5x – (35/x) = 18

12. The 10th term of an arithmetic progression(A.P.) is 44 and its 15th term is 64. Find the A.P.

13. Find he area of the shaded region in the given figure. Take П=3.14.

14. The incircle of triangle ABC touches the sides BC, CA and AB at D, E and F respectively. Prove that AB+BD+CE = AE+CD+BF

15. How many spherical lead shots each having diameter 3cm can be made from a cuboidal  lead solid of dimensions 9cm×11cm×12cm.

16. Determine the ratio in which the point P(– 6,a) divides the join of A( - 3 , - 1) and B( - 8,9) . Also find the value of a.

17. Show that the points A(-1,0) , B(3,1) , C(2,2) and D(-2,2) are vertices of parallelogram.

18. A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Or    A coin is tossed three times. Find the probability of getting atmost one head.

Section – C

19. If the roots of the equation (a-b)x2 + (b-c)x + (c-a)=0 are equal, prove that b+c = 2a.

Or,

Find the values of k for which the given equation has real and equal roots. (k-12)x2 + 2(k-12)x + 2 = 0

20 Find the sum of the integers between 50 and 250 that are divisible by 13.

21. ABC is a right triangle, right angled at B.A circle is inscribed in it. lengths of the two sides containing  the right angle are 6cm and 8cm. Find the radius of the incircle.

22. Draw a circle of radius 3cm. Take two points P and Q on one of its extended diameter each at a distance of 7cm from its centre. Draw tangents to the circle from these two points P and

Q.23. A racetrack is in the form of a ring whose inner and outer circumferences are 437m and 503m respectively. Find the width of the track and also its area.

24. From a solid cylinder whose height is 12cm and diameter 10cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.

Or

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter ‘l’ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

25. A person standing on the bank of a river observes that angle of elevation of the top of a tree standing on the opposite bank is 60 deg.  When he moves 40m away from the bank, he finds the angle of elevation to be 30 deg.. Find the height of the tree and the width of the river.

26. Find the area of Δ formed by vertices (a, b+c) (b, c+a) and (c, a+b).

27. Prove that (2, -2), (-2,1) and (5,2) are vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.

28. Cards with numbers 5 to 125 are placed in a box. A card is selected at random from the box. Find the probability that the card which is selected has a number which is perfect square                                       

Section – D

29. Had Ravinder scored 10 more marks in his mathematics test out of 30 marks, 9 times these marks would have been the square of his actual marks. How many marks did he get in this test?

Or,

Out of a number of Saras birds, one forth the number are moving about in lotus plants, 1/9 th coupled(along) with ¼ as well as 7 times the square root of the number move on a hill; 56 birds remain in vakula trees. What is the total number of birds.

30. The spiral is made up of successive semi-circles, with centres alternately at A and B, starting with    centre at A, of radii 0.5cm, 1.0cm, 2.0cm,…. 

What is the total length of such a spiral made up of thirteen consecutive semi- circles ? (π= 22/7)

31. L and M are two parallel tangents at A and B. The tangent at C makes an intercept DE betweenl and m. Prove that <DFE = 90 deg..

32. The height of a cone s 30cm. A small cone is cut off at the top bya plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section mode?

33. 21 glass spheres each of radius 2cm are packed in a cuboidal box of internal dimensions 16cm×8cm×8cm and then the box is filled with water. Find the volume of water filled in the box.

34. A man on a cliff observes a boat at an angle of depression of 30deg which is approaching the shore to the point  immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be 60deg. Find the time taken by the boat to reach the shore.