SAMPLE PAPER/MODEL TEST PAPER
SUBJECT – MATH
1. A pole 6 m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is:
(a) 30 degree (b) 45 degree (c) 60 degree (d) 90 degrees
2. Which of the following cannot be the probability of an event?
(a) 4% (b) 0. 3 (c) 1 / 5 (d) 5/4
3. If the circumference of a circle is equal to the perimeter of a square then the ratio of their areas is:
(a) 7: 11 (b) 14: 11 (c) 7 : 22 (d) 22 : 7
4. Two tangents making an angle of 120 degree with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to:
(a) 6 √ 3 cm (b) √ 2 cm (c) 2 √ 3 cm (d) √ 3 cm
5. The height of a cone is 60 cm. a small cone is cut off at the top by a plane parallel to the base and its volume is 1 / 64th the volume of original cone. The height from the base at which the section is made is:
(a) 15 cm (b) 30 cm (c) 45 cm (d) 20 cm
6. To draw a pair of tangents to a circle which is inclined to each other at an angle of 100 degree, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be:
(a) 100 degree (b) 80 degree (c) 50 degree (d) 20 degrees
7. The sum of first five multiples of 3 is:
(a) 65 (b) 75 (c) 90 (d) 45
8. Which of the following equations has he sum of its roots as 3 ?
(a) – x2 +3x + 3 = 0 (b) 3x2 – 3x – 3 = 0
(c) √2x2 – 3/√2 x – 1 (d) x2 + 3 x – 5 = 0
9. If radii of the two concentric circles are 15 cm and 17 cm, then the length of each chord of one circle which is tangent to others is:
(a) 16 cm (b) 30 cm (c) 17 cm (d) 8 cm
10. If the digit is chosen at random from the digits. 1,2,3,4,5,6,7,8,9, then the probability that it is odd, is:
(a) 5/9 (b) 1/9 (c) 2/3 (d) 4/9
Section – B
11. How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm* 11 cm * 12 cm ?
12. Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.
13. Find the roots of the following quadratic equation:
2/5 x2 – x – 3/5 = 0
14. If the numbers x – 2, 4x – 1 and 5x + 2 are in A.P. Find the value of x.
15. A coin is tossed two times. Find the probability of getting atmost one head.
16. Two dice are thrown at the sametime. Find the probability of getting different numbers on both dice.
17. Show that the point P (-4, 2) lies on the line segment joining the points A ( -4, 6).
18. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.
Section – C
19. Find the sum of the integers between 100 and 200 that are divisible by 9.
20. A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
21. A cooper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.
22. Prove that the parallelogram circumscribing a circle is a rhombus.
23. A hemispherical depression is cut out from one of a cubical wooden block such that the aiam eter t’ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining soild.
24. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and angle ABC = 60 degree. Then construct a triangle whose sides are ¾ time the corresponding sides of triangle ABC.
25. Cards with numbers 2 to 101 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 a perfect square.
26. The points A (2, 9), B (a, 5), C (5, 5) are the vertices of a triangle ABC right angled at B. Find the value of ‘a’ and hence the area of triangle ABC.
27. A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot or the tower, the angle of elevation of the top of the tower is found to be 60 degree. Find the height of the tower.
28. Prove that the points A (4, 3), B (6, 4), C (5, -6) and D (3, -7) in the order are the vertices of a parallelogram.
Section – D
29. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 degree and 60n degree respectively. Find height of the tower.
30. The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.
31. 21 glass sphere each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm * 8 cm * 8 cm and then the box is filled with water. Find the volume of water filled in the box.
A well of diameter 3 m and 14 cm deep is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
32. Prove that the lengths of tangents drawn from an external point to a circle are equal.
33. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
Find two consecutive odd positive integers, sum of whose squares is 290.
34. A sum of Rs.1400 is to be used to give seven cash prize to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.