CBSE 10TH SA 2012
SAMPLE PAPER / MODEL TEST PAPER
SUBJECT – MATHEMATICS
1. The sum of first seven multiples of 5 is :
(a) 35 (b) 145 (c) 140 (d) 105
2. which of the following quadratic equations has the product of its roots as 3?
(a) 2x square -3x +6 = 0 (b) x square – 3x + 6 = 0 (c) Root 2x square – 3/root 2 x + 1 = 0 (d) 3x square – 3x +3 = 0
3. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. Then the radius of the circle is :
(a) 12 cm (b) 10 cm (c) 9 cm (d) 7 cm
4. Two concentric circles are of radii 5 cm. The length of the chord of the larger circle which touches the smaller circle is :
(a) 4 cm (b) 8 cm (c) 6 cm (d) 10
5. A hollow sphere of external and internal and internal diameters 8cm and 4 cm respectively, is melted into a cone of base radius 4 cm. Then height of the circular cone is :
(a) 15 cm (b) 10 cm (c) 14 cm (d) 16 cm
6. A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. the probability that the drawn ball is red, is :
(a) 5/15 (b) 3/15 (c) 7/15 (d) 1/15
7. If the ratio of the circumferences of two circles is 3 : 1 , then the radio of their areas is :
(a) 1: 9 (b) 9 : 1 (c) 3 : 1 (d) 1 : 3
8. The volume of the largest right circular cone that can be cut our from a cube of edge 21cm is :
(a) 1155 cm cub (b) 577.5 cm square (d) 2425.5 cm cub (d) 2400 cm cub
9. If angle between two radii of a circle is 125 degree, the angle between the tangents at the ends of the radii is :
(a) 90 degree (b) 50 degree (c) 55 degree (d) 40 degree
10. IF P (E) = 0.07, then the probability of ‘ not E’ is:
(a) 0 (b) 1 (c) 0.93 (d) 0.03
SECTION – B
11. A poorv throws two die once and computed the product of the numbers appearing on the dice. Peeehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36 ?
18 cards, numbered 1,2,3,………… , 18 are put in a box and mixed th0roughly. A card is drawn at random from the box. Find the probability that the card drawn bears :
(i) an even number (ii) a number divisible by 2 or 3.
12. Find the roots of the following quadratic equation z square – 11/4 z + 15/8 =0
13. Find the area of a ring shaped region enclosed between two concentric circles of radii 20 cm and 15 cm.
14. The seventh term of an A.P. is 34 and 15th term is 74. Determine its 40th term.
15. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
16. The volume of a cylinder is 448 PI cm cub and height 7cm. Find its lateral surface area.
17. The center O of a circle has the coordinates (4, 5) and one point on the circumference is (8, 10). Find the coordinates of the other end of the diameter of the circle through this point.
18. Show that the point P (1, 2) lies on the line segment joining the points A ( -2, 3 ) and B ( 7, 0)
19.Prove that opposite sides of a quadrilateral circumscribing a circle subtends supplementary angles at the center of the circle.
20. Draw a line segment AB of length 8 cm. Taking A as center, drawn a circle of radius 4 cm and taking B as centre, draw another another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.
21. Find the roots of the equation :
a/ax-1 + b/bx – 1 = – (a+b) ; x does not equal 1/a, 1/b
22.A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filed into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl ?
23. A man on the deck of a ship is 12 m above the water level. He observes that the angle of elevation of the top of a cliff is 45 degree and the angle of depression of the base is 30 degree Calculate the distance of the cliff from the ship and the height of the cliff.
24. If A (1, 2), B (4, 3) and C (6,6) are the three vertices of a parallelogram ABCD , find the coordinates of the fourth vertex D.
25. Point P divides the line segment joining the points A (2 ,1) and (5 , 8), such that AP : AB = 1 : 3 If P lies on the line 2x – y + k = 0, find the value of k.
26. Cards bearing numbers 1, 3, 5, ……35 are kept in a bag. A card is drawn at random from the bag . Find the probability of getting a card bearing :
(i) a prime number less than 15 (ii) a number divisible by 3 and 5
27. Find the 31st tern of an A.P. whose 11th term is 38 and the 16th term is 73.
28. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and angle =90 degree . BD is the perpendicular from B on AC. The circle through B,C,D, is drawn. Construct the tangents from A to this circle.
29. Find two consecutive odd positive integers sum of whose square is 970.
30. A train travelling at a uniform speed for 360 km/h would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
31. Solve the equation :
– 4 + ( -1) + 2 + …..+ x = 437
32. A bucket is in the form of frustum of cone. Its depth is 24 cm and the diameters of the top and the bottom ends are 30 cm 10 cm respectively. Find the capacity of bucket.
33. In a right triangle ABC, right angled at B, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.
34. An aeroplane left 30minutes later than its schedule time, and in order to reach its destination 1500 km aways in time, it has to increase its speed by 250 km/h from its usual speed. Determine its usual speed.
SAMPLE PAPER / MODEL TEST PAPER