SECTION A / Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided, of which only one is correct. You have to select the correct choice. 1 8 1 1. Any point where graph of linear equation in two variables cuts x-axis is of the form (a) (x, y) (b) (0, y) (c) (x, 0) (d) (y, x) x (a) (x, y) (b) (0, y) (c) (x, 0) (d) (y, x) 2. If a rectangle and a square stand on the same base and between the same parallels, then the ratio of their areas is (A) 1 : 2 (B) 1 : 4 (C) 1 : 1 (D) 2 : 1 (A) 1 : 2 (B) 1 : 4 (C) 1 : 1 (D) 2 : 1 3. In Fig, O is the centre of the circle and ABC 40, then AOC is (A) 140 (B) 40 (C) 20 (D) 80 O ABC 40 AOC (A) 140 (B) 40 (C) 20 (D) 80 4. The graph of y = a, is a (A) straight line parallel to x-axis (B) straight line parallel to y-axis (C) straight line passing through origin (D) straight line that intersects both x-axis and y-axis y = a (A) (B) y (C) x Page 3 of 9
(D), x y 5. The mean of x 1, x 3, x 4, x 8 is (A) x 1 (B) x 3 (C) x 4 (D) x 8 x 1, x 3, x 4, x 8 (A) x 1 (B) x 3 (C) x 4 (D) x 8 6. In a cylinder, if radius is halved and height is doubled, the volume will be : (A) Same (B) Doubled (C) Halved (D) Four times (A) (B) (C) (D) 7. An experiment has two outcomes E and F. P(E) P(F) is equal to (A) 1 (B) 0 (C) 2 (D) ½ E F P(E) P(F) (A) 1 (B) 0 (C) 2 (D) ½ 8. If A, B and C denote the areas of three adjacent faces of a cuboid, then its volume is (A) ABC (B) 2 ABC (C) ABC (D) A+B+C A, B C (A) ABC (B) 2 ABC (C) ABC (D) A+B+C SECTION-B / Question number 9 to 14 carry two marks each. 9 14 2 9. In Fig, ABC is a triangle. E is the mid-point of median AD. Show that ar (BED) = ar (ABC)/4 ABC AD E ar (BED) = 1 4 ar (ABC) 10. The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding. 7m Page 4 of 9
11. Find the median of the following data 15, 28, 72, 56, 44, 32, 31, 43 and 51. If 32 is replaced by 23, find the new median. 15, 28, 72, 56, 44, 32, 31, 43 51. 32 23 12. A coin is tossed 600 times. The outcomes are : Number of heads = 248, Number of tails = 352 It is tossed once more. Find the probability of getting, (i) a tail (ii) a head 600 = 248, = 352. (i) (ii) 13. PQRS is a cyclic quadrilateral, in which P 2x, Q y, R 3x and S 2y. Find the values of x and y. PQRS P 2x, Q y, R 3x S 2y x y ABCD is a cyclic quadrilateral, in which AD BC. If B 70, then find A and C? ABCD AD BC B 70 A C 14. The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number. 27 25 SECTION-C / Question numbers 15 to 24 carry three marks each. 15 24 3 15. Find the value of k, if x 2, y 1 is a solution of the equation 2x 3y k. Hence find two more solutions of the equation. 2x 3y k x 2, y 1 k 16. P is a point in the interior of a parallelogram ABCD. Show that ar (APB) ar (PCD) 1 2 ar(abc) P ar (APB) ar (PCD) 1 ar (ABCD). 2 17. Construct angle 75 using ruler and compass only. 75 18. A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6m, find the cost of painting it, if the cost of painting is Rs. 5 per 100cm 2. (Take 22/7) Page 5 of 9
cm 2 22 7 17.6 m 5 100 The internal and external diameters of a hollow hemispherical vessel are 24cm and 25cm respectively. The cost to paint 1 sq. cm of surface is Rs. 1.75. Find the total cost to the nearest rupee to paint the vessel allover. Ignore the area of the edge. (Take 3.14) 24cm 25cm 1 cm 3 1.75 19. Find the mean of the following distribution X 4 6 9 10 15 f 5 10 10 7 8. x 4 6 9 10 15 f 5 10 10 7 8 If the mean of the following data is 15, find p. x 5 10 15 20 25 f 6 p 6 10 5. 15 p x 5 10 15 20 25 f 6 p 6 10 5 20. Draw the graphs of y x and y x in the same axes. Also, find the coordinates of the point where the two lines intersect. y x y x Express y in terms of x in the equation 2x 3y 12. Draw the graph and find the points where the line represented by this equation cuts x axis and y axis. 2x 3y 12 y x x y 21. A rectangular piece of paper is 22cm long and 12cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder (Use 22/7) 22 cm 12 cm 22 7 22. If the non parallel sides of trapezium are equal, prove that sum of each pair of opposite angles is supplementary. Page 6 of 9
23. In quadrilateral ABCD, B 90, C D 60 and A C D 10. Find A, C and D. ABCD B 90, C D 60 A C D 10 A, C D 24. The weekly pocket expenses of students are given below. Find the probability that the weekly pocket expenses of a student are (i) Rs. 59 (ii) more than Rs. 59 (iii) less than Rs. 59 Pocket Expenses (in Rs) 45 40 59 71 58 63 65 No. of Students 7 4 10 6 3 8 1 (i) 59 (ii) 59 (iii) 59 45 40 59 71 58 63 65 7 4 10 6 3 8 1 SECTION-D / Question numbers 25 to 34 carry four marks each. 25 34 4 25. Prove that a diagonal of a parallelogram divides it into two congruent triangles. 26. Construct a triangle XYZ, in which Y 30, Z 90 and XY YZ ZX 11 cm. XYZ Y 30, Z 90 XY YZ ZX 11 cm Construct a triangle PQR in which QR = 7cm, Q 45 and PQ PR 4 cm. PQR QR=7cm, Q 45 PQ PR 4 cm 27. Solve the equation 3(x 2) 2(2x 1) and represent the solution on : (i) the number line (ii) the Cartesian plane 3(x 2) 2 (2x 1) (i) (ii) 28. Twenty seven solid iron spheres, each of radius r and surface area s are melted to form a sphere with surface area s 1. Find the (i) radius r 1 of the new sphere (ii) ratio of s and s 1. 27 r s s 1 (i) r 1 (ii) s s 1 Page 7 of 9
29. In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If DBC 55 and BAC 45, find BCD. BCD ABCD AC BD DBC 55 BAC 45 30. ABCD is a rhombus and P, Q, R, S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. ABCD AB, BC, CD DA P, Q, R S PQRS ABC is a triangle, right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD AC (iii) CM MA ½ AB ABC C AB M BC AC D : (i) AC D (ii) MD AC (iii) CM MA ½ AB 31. Yamini and Fathima, two students of Class IX, together contributed Rs. 100 towards the Prime Minister s relief fund to help the earthquake victims. Write a linear equation which satisfies this information. Draw the graph of the same by taking their contributions as Rs.x and Rs.Y). IX y 100 x 32. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any other point on the remaining part of the circle. Page 8 of 9
33. Madhu has a piece of canvas, whose area is 550 m 2. He uses it to have a conical tent made, with a base radius of 7m. Assuming the stitching wastage is negligible, find the volume of the tent that can be made with the canvas. 7 m 550 m 2 34. The distribution of weekly wages of 40 casual labourers in a factory is given below. Draw a frequency polygon for the data. Weekly 210-230 230-250 250-270 270-290 290-310 310-330 330-350 Wages (in Rs) No. of labourers 4 7 5 9 5 6 4 40 210-230 230-250 250-270 270-290 290-310 310-330 330-350. 4 7 5 9 5 6 4 - o O o - Page 9 of 9