# Sample Paper – Math 10th CBSE SA 2

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**SAMPLE PAPER/MODEL TEST PAPER**

**SUBJECT – MATH 10 ^{TH} CBSE SA 2 2011**

**Section** -** A**

1. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 300 with horizontal, then the length of the wire is:

(a) 8 m (b) 6 cm (c) 10 m (d) 12 m

2. If the equation 9×2 + 6kx + 4 = 0 has equal, then the roots are both equal to:

(a) ±3 (b) ±3/2 (c) ± 2/3 (d)0

3. If three coins are tossed simultaneously, then the probability of getting at least two heads, is:

(a) ¼ (b) ½ (c) 3/8 (d) 1/3

4. If in an A.P., S_{n} = n^{2}p and S_{m} = m^{2}p, where S_{r} , denotes the sum of r terms of the A.P., then S_{p} is equal to:

(a) mnp (b) p^{3} (c) ½ p^{3} (d) (m + n) p^{2}

5. From the point Q the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of circle is:

(a) 15 cm (b) 24.5 cm (c) 7 cm (d) 24.5 cm

6. In a single throw of a die, the probability of getting a multiple of 3 is:

(a) 2/3 (b) 1/3 (c) ½ (d) 1/6

7. If the sun of n terms of an A.P. is 3n^{2} + 5n, then which of its terms is 164?

(a) 27^{th} (b) 28^{th} (c) 26^{th} (d) none of these

8. If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these is 273, then the third term is:

(a) 9 (b) 17 (c) 13 (d) 21

9. If TP and TQ are two tangents to a circle with centre O, so that ∟POQ = 1100, then ∟PTQ is equal to:

(a) 90^{0} (b) 70^{0 } (c) 60^{0 } (d) 80^{0}

10. The length of the tangent from point A at a circle, of radius 3 cm. The distance of a from the centre of circle is:

(a) 25 cm (b) 7 cm (c) 5 cm (d) √7 cm

Selection – B

11. A car has wheels which are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km/h.

12. A dice that the points (4, 3), (5, 1) and (1, 9) are collinder.

(a) a multiple of there

(b) an even prime number

13. In an A.P., the sum of first n terms is 3n^{2}/2 + 5n/2. Find its 25^{th} term.

14. A right circular cone of height 8.4 cm and the radius of its base is 2.1 cm. It melted and recast.

15. Solve for x:

1/x + 1 + 2/ x + 2 = 4 / x + 4

16. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

17. If the point C ( -1, 2) divides the line segment AB in the ration 3 : 4, where the co – ordinates of A are (2, 5). Find the co – ordinates of B.

18. The 5^{th} term of an Arithmetic Progression (A .P.) is 26 and the 10^{th} term is 51. Determne the 15^{th} term of A.P.

18. Find the area of the quadrilateral whose vertices taken in order are A( -5, -3), B( -4, -6), C( 2, – 1) and D (1, 2)

Section – C

19. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag. Find the probability of getting.

(a) neither a green ball nor a red ball.

(b) a white ball or a green ball.

20. How many times will the wheel of a car rotate in a journey of 88 km if it is known that the diameter of the wheel is 56 cm ? [Take π = 22/7]

21.A gulabjamun when completely ready for eating contains sugar syrup to about 30% of its volume. Find approximately how much syrup would be found in 45 gulabjaImun shaped like a cylinder with two hemispherical ends, if the complete length of each of gulabjamuns is 5 cm and its diameter is 2.8 cm.

22. A square park has each side of 100 m. At each corner of the park, there is a flowerbed in the form of a quadrant of radius 14 m as shown in the figure given below. Find the area of the remaining.

23. A train covers a distance of 90 km at a uniform speed. Had if the speed been 15 km/hour more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

24. Construct a triangle with side 5 cm and 7 cm and then another triangle whose sides are 7/5 times of corresponding sides of first triangle.

25. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height m. From a point on the plane the angle of elevation of the bottom and top of the flagstaff are respectively 30_{0} and 60^{0} find the height of the tower.

26. From a point P outside a circle with centre O, tangents PA and PB are drawn. Prove that

(a) OP is the perpendicular bisector of AB.

(b) ∟AOP = ∟BOP

27. If the points (10, 5), (8, 4) and (6, 6) are mid points of the side of a triangle. Find its vertices.

28. Cards being numbers 3 to 19 are put in a box and mixed thoroughly. A card is drawn from the box at random, find the probability that the number on the card drawn is:

(a) divisible by 2 and 3 both.

(b) even.

Section – D

29. A horse is tied to a peg at one corner to a square shaped grass field of side 15 m by means of a 5 m long rope. Find:

(a) the increases in grazing area if a rope were 10 m long instead of 5 m. (Use π = 3.14)

(b) the area of the field in which the horse can graze.

30. Marbles of diameter 1.4 cm are dropped into a cylinder beaker, of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beakers so that the water level rises by 5.6 cm.

31. From the top of a building 60 m high, the angles of depression of the top and bottom of a vertical lamp post are observed to be 30_{0} and 60^{0} respectively. Find.

(a) The height of lamp post.

(b) The horizontal distance between the building and the lamp post.

32. A manufacturer of T.V. sets produced 6,000 units in third year and 7,000 units in the seventh year. Assuming the production uniformly increases by a fixed number every year. Find:

(a) the production in 10^{th} year.

(b) the production in first year.

(c) the total production in 7 years.

33. A container made up of a metal sheet is the form of a frustum of a cone of height 16 cm from of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs. 20 per litre and the cost of the metal used if it costs. Rs. 10 per 100 cm^{2}.

34. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

20. How many times will the wheel of a car rotate in a journey of 88 km if it is known that the diameter of the wheel is 56 cm ? [Take π = 22/7]

r=28cm no.of rotation=(8800000)/2*π*28 =8800000*7/2*22*28 =61600000/1232 =50000

hey first see the area of the wheel then multiply this area with 88km.ie 22/7*28*28=2464 ie=2464*88=216832 times

what is the answer for 20th question?

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.

First find out the radii of the inner circle and the outer circle with the help of the given circumferences. The width of the track = R1 – R2 [where are is the radius] Area of the track = Area of bigger circle – Area of the smaller circle.

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

Solve 10ax2 – 6x + 15ax – 9 = 0, a ≠ 0.

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

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?

33. A container made up of a metal sheet is the form of a frustum of a cone of height 16 cm from of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs. 20 per litre and the cost of the metal used if it costs. Rs. 10 per 100 cm2 plz rply the answer………..

name the various in which sulphate products which people living near to itmay use