SAMPLE PAPER/MODEL TEST PAPER
SUBJECT – MATH CBSE 10TH SA 2 2011
1. If the radius of a circle is diminished by 10%, then its area is diminished by:
(a) 20 % (b) 19 % (c) 36% (d) 10 %
2. The volumes of two spheres one is the ratio 64: 27. The ratio of their surface areas is:
(a) 1 : 2 (b) 9 : 16 (c) 16 : 9 (d) 2 : 3
3. The number of quadratic equation having real roots and which do not change by squaring their roots is:
(a) 2 (b) 1 (c) 3 (d) 4
4. If points (1, 2), (-5, 6) and (α, 2) are collinear, then α =
(a) 7 (b) 2 (c) -2 (d) -3
5. The area of the in circle of an equilateral triangle of sides 42 cm is:
(a) 321 cm2 (b) 924 cm2 (c) 472 cm2 (d) 22√3 cm2
6. If four sides of a quadrilateral ABCD are tangential to a circle, then:
(a) AB +CD = BC + AD (b) AC + AD+ = BC +DB
(c) AC + AD = AC + CD (d) AB + CD = AC + BC
7. The length of the tangent drawn from a point 8 cm away from the centre of a circle radius 6 cm is:
(a) 10 cm (b) 5 cm (c) √7 cm (d) 2 √7 cm
8. The number of quadratic equations having real roots and which do not change by squaring their roots is:
(a) 1 (b) 2 (c) 3 (d) 4
9. If 7th terms of an A.P. be 34 and 64, respectively, then its 18th term is:
(a) 88 (b) 89 (c) 87 (d) 90
10. The ratio of the length of a rod and its shadow is 1: √ 3. The angle of elevation of the sum is:
(a) 30 degree (b) 60 degree (c) 90 degree (d) 45 degree
Section – B
11. Find the area of a quadrant of a circle whose circumference is 22 is.
12. A pair of dice thrown once. Find the probability of getting the same number of each dice.
13. Find the circumference and area of a circle of radius 8.4 cm.
14. Two cube each of 10n cm edge are joined end to end. Find the surface area of resulting cuboid.
15. If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2, 3), find the value of x.
16. Find the common difference and write the next three terms of the A.P. 3, -2, -7, -12.
17. Find the value of (α – 12) x2 + 2 (α – 12) x + 2 = 0 has equal roots.
18. A point P is 13 cm from the centre of the circle. The length of the tangent drawn to the circle is 12.
Section – C
19. An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45 degree. What is the height of the tower?
20. The base radius and height of a right of a right circular solid cone are 2 cm and 8 cm respectively. It is melted and recast into spheres of diameter 2 cm each. Find the number of spheres so formed.
21. One card is drawn from a well shuffeled deck of 52 playing cards. Find the probability of getting:
(a) a black king or a red queen
(b) a non – face card
22. The co – ordinates of the mid – point of the line joining the points (2p +1, 4) and
(5, q – 1) are (2p, q), Find the values of p and q.
23. A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of the major and minor segments. (Take PI = 3.14)
24. In an A.P. the first term is 8, nth term is 33 and sum to first n terms is 123, find n and d.
25. Construct a triangle ABC in which CA = 6 cm, AB = 5 cm and angle BAC = 45 degree then construct a triangle similar to the given triangle whose are 6/5 of the corresponding side of the triangle.
26. The vertices of a triangle are (-1, 3), (1, 1); and (5, 1). Find the length of medians through vertices (-1, 3) and (5, 1).
27. The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/6 times the base. Find the area of the triangle.
28. The sum of 5th and 9th term of an A.P. is 72 and the sum of 7th and 12th terms is 97.
Find the A.P.
Section – D
29. A gulabjamun when completely ready for eating contains sugar syrup up to about 30 % of its volume. Find approximately how much syrup would be found is 45 gulabjamuns shaped like a cylinder with two hemispherical ends, if the complete length of each of gulabjamun is 5cm and its diameter is 2.8 cm.
30. Two tangents TP or TQ are drawn to a circle with centre O from an external point T.
∟PTQ = 2∟OPQ
31. The sum of n, 2n, 3n terms of an AP are S1, S2, S3 respectively. Prove that
S3 = 3 (S2 – S1).
32. The angle of depression of the top and bottom of an 8 m tall building from the top of a multistoreyed building are 30 degree and 45 degree respectively. Find the height of the multi storeyed building and the distance between the two buildings.
33. In a flight of 600 km, a air craft slowed donor due to bad weather, its average speed of the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. Find the duration of flight.
34. A chord of circle of radius 12 cm subtends an angle of 120 degree at the centre. Find the area of the corresponding segment of circle. (PI = 3.14 and √3 = 1.73)