Sarvaakarshak classes Revision_Test_2 The best way to learn SECTION-A Question numbers 1 to 8 carry 2 marks each. 1. If the equation kx 2-2kx + 6 = 0 has equal roots, then find the value of k. 2. Which term of the A.P.: 120, 116, 112,... is its first negative term. 3. ABC is an isosceles triangle in which AB = AC which is circumscribed about a circle as shown in the figure. Show that BC is bisected at the point of contact. 4. If the perimeter of a protractor is 72 cm, calculate its area. (Take π =22/7) 5. A metallic sphere of total volume π is melted and recast into the shape of a right circular cylinder of radius 0.5 cm. What is the height of cylinder? 6. Find the point on the x-axis which is equidistant from the points (2, -5) and (-2, 9). 7. Prove that the points (2, -2), (-3, 8) and (-1, 4) are collinear. 8. A bag contains 6 red, 3 black and 6 white balls. A ball is selected at random from the bag. Find the probability that the selected ball is: (a) red or black (b) not black Two dice are thrown together. What is the probability of getting a doublet? SECTION-B Question numbers 9 to 18 carry 3 marks each. 9. Find the roots of the equation ax 2 + a = a 2 x + x Page 1 of 9
Solve for x: 4 3 x 2 +5x 2 3=0 10. Find the 10 th term from the end of the A.P.: 4, 9, 14, 254.: 11. Prove that the intercept of a tangent between a pair of parallel tangents to a circle subtend a right angle at the centre of the circle. Two tangents TP and TQ are drawn to a circle with centre O, from an external point T. Prove that P TQ=2 OPQ 12. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then construct another triangle whose sides are 3/5 times the corresponding sides of the first triangle. 13. ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter a semicircle is drawn. Find the area of the shaded region (take π = 22 ). 7 14. The radii of two right circular cylinders are in the ratio of 2: 3 and their heights are in the ratio of 5: 4. Calculate the ratio of their curved surface areas and ratio of their volumes. A toy is in the form of a cone mounted on a hemisphere of common base of diameter 7 cm. If the height of the toy is 15.5 cm, find the total surface area of the toy. 15. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from his eyes is 45 0 Find the height of the chimney. 16. Find the ratio in which the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3). Hence find the value of p. 17. Prove that the diagonals of a rectangle with vertices (0, 0), (a, 0), (a, b) and (0, b) bisect each other and are equal. 18. A card is drawn at random from a well shuffled deck of 52 playing cards. Find the probability that the card drawn is: (i) either a spade or an ace (ii) a black king Page 2 of 9
SECTION-C Question numbers 19 to 24 carry 4 marks each. 19. A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train. A shopkeeper buys a number of books for Rs. 1200. If he had bought 10 more books for the same amount, each book would have cost his Rs. 20 less. How many books did he buy? 20. How many terms of the A. P. 2 0, 1 9 1 / 3, 1 8 2 / 3,. should be taken so that their sum is 300. Explain the double answer. 21. Prove that the tangent to a circle is perpendicular to the radius through the point of contact. 22. A rectangular sheet of paper of dimensions 44 cm 18 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder so formed. A solid right circular cylinder has a total surface area of 462 sq. cm. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder. 23. An open container made up of a metal sheet is in the form of a frustum of a cone of height 7 cm with radii of its lower and upper circular ends as 4 cm and 10 cm respectively. Find the cost of oil which can completely fill the container at the rate of Rs.50/litre. 24. From the top of a tower the angle of depression of an object on the horizontal ground is found to be 60 0. On descending 20 m vertically downwards from the top of the tower, the angle of depression of the object is found to be 30 0. Find the height of the tower. Page 3 of 9
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