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Model Question Paper - Xth Mathematics Time : 2½ hrs. Max.marks 100 I. Choose the best answer 1. In a G.P. r<1 then the s is ____ a. a 1-r b. a r-1 c. d. None 2. The sum of 2+3+4+...................+10 is ____ a. 50 b. 54 c. 55 d. 10 3. The volume of the two spheres is in the ratio 64 : 125, then their radius ratio is ____ a. 4 : 5 b. 8 : 25 c. 4 : 25 d. 8 : 5 4. If A = {3, 8, 9}, then A∩A is = ____ a. {3} b. 3 c. {9} d. {3, 8, 9} 5. f(x)=x2, g(x)=3x then fog (2) is ____ a. 36 b. 9 c. 18 d. 2 6. The quadratic equation with roots (2+3), (2-3) is ____ a. x2 + 4x - 1 = 0 b. x2 - 4x - 1 = 0 c. x2 - 4x + 1 = 0 d. x2 + 4x + 1 = 0 7. x2-25 is ____ x-5 a. (x-5) b. (x+5) c. 0 d. 1 8. A point 4x + 4y < 5 is a. (1,1) b. (2,0) c. (0,7) d. None 9. In a rt. angled LB = 90; AB=8 cm, BC=15 cm then AC is a. 13 cm b. 10 cm c. 17 cm d. 20 cm 10. Angle is the major segment is ____ a. Acute angle b. Obtuse angle c. Right angle d. Reflexive angle 11. Two similar triangles have corresponding sides proportional to 3 : 4 then their areas are proportional to ____ a. 3 : 4 b. 4 : 3 c. 9 : 16 d. 16 : 9 12. The centroid G of the triangle whole vertices are (1, 10), (-7, 2), (-3, -9) is a. (3, 7) b. (-3, -7) c. (3, 7) d. (-3, 7) 13. The given st. lines 3x + 5y = 10, 6x + 8y = 15 are a. Parallel b. Not Parallel c. Perpendicular d. None 14. The x intercept of the line 3x + 5y = 15 is a. 5 b. 3 c. 15 d. None 15. 3tanθ = 4 then cosθ is ____ a. 3/4 b. 3 c. 4 d. 4 3 II. Answer any TEN questions only 10 x 2 = 20 16. Find the 10th term of the A.P. 10, 10.5, 11, ..... 17. Find the sum 17+19+21+.........+30 upto 30 terms. 18. Find the volume of a cylinder of diameter 8 cm and height 10 cm. 19. If A = {1,2,3,4}, B = {3,4,5,6} find A-B 20. Find the quotient and remainder : x3 - 3x2 - 6x - 5 x - 2 21. Factorise : x3 + 2x2 + 2x + 1 22. Determine the nature of the roots of the equation 4x2 - 28x + 49 = 0 23. If θ = 45 Evaluate 2tan2 θ - sin2 θ - 1 24. A 6 3 In triangle ABC DE II BC D E Find the value of AD = 6 10 X DB = 10 AE = 3 B C EC = x 25. Find the point p which divides the line joining the points (3, 4) and (-6, 2) internally in the ratio 1 : 3 26. An integer is chosen from 1 to 50. Find the probability that it is a multiple of 9. 27. Find the equation of st. line whose slope is 3/4 and 'y' intercept is - 4. C 28. In the figure O is the centre mOAC = 35 35O 45 mOBC = 45 then find mAOB A B 29. A chord of 12 cm from the centre of the circle of radius 10 cm. Find the distance between the centre and the chord. 30. Draw the graph of 2x + 4 ≥ 4 III. Answer any nine questions only, choosing either of the alternatives. 9 x 5 = 45 31. In a G.P. the sixth term is 63 and tenth term is 5103 find the G.P. (OR) Find the sum of all the integers divisible by 9 lying between 400 and 600. 32. The total volume of a cone and a sphere is equal to the volume of a cylinder whose radius is 4 cm and height is 8 cm. The radius of the cone is 4 cm and height is 22 cm. Find the radius of the sphere. (OR) The noon meal is kept in 3 cylindrical vessels. The diameter of the vessels is 1.4 mts and the height is 54 cm. The meal is served twice in a hemispherical bowl of radius 14 cm. Find the number of students who got the meal. 33. Among the girls studying in a class, 28 speak tamil, 24 speak telugu, 18 speak malayalam, 10 speak both tamil and telugu, 6 speak tamil and malayalam whole 7 speak telugu and malayalam. If 3 can speak all the three languages find the number of girls. (OR) 2 f(x) = 4x - 1, g(x) = 1 + x Prove that fog ≠ go f 34. Solve 2x - 2y + 4z = -12 3x + 2y + 2z = 19 -x + y - z = 3 (OR) (x-7), (x-4) are the factors of px3 + qx2 - 5x + 84 find the values of P, Q 35. Find the square root of 16x4 - 24x3 - 31x2 + 30x + 25 (OR) The perimeter of the rectangle is 36 cm. Its area is 80 cm2. Then find its length and breadth. 36. Solve the L.P.P. Minimize z = 5x + 4y subject to 4x + 4 ≥ 40; 2x + 3y ≥ 90. (x ≥ 0) (y ≥ 0) (OR) The following table gives the activities in a construction project and relevant information Activity 1-2 1-3 2-3 3-4 3-5 4-6 5-6 6-7 Duration days 5 10 3 4 6 6 5 5 Draw the network for the project and find the critical path. Compute the project duration. 37. Prove : The sum of the opposite angles of a cyclic quadrilateral is 180 (OR) In the given diagram prove that PQ+RS=PS+QR. P D S A O C Q B R 38. Find the area of the Triangle whose vertices are (5, 6), (2,4), (1,-3) (OR) Find the equation of the straight line joining the point (4,5) and the point of intersection of the st. lines 5x - 3y = 8 and 2x - 3y = 5. 39. Find the area of an isosceles triangle with base 20cm and vertical angle 48 40'. (OR) Two men are on the opposite side of a tower. They measure the angles of elevation of the top of the tower as 30 and 45 respectively if the height of the tower is 150 m. find the distance between the men. 40. When two dice are thrown at a time. Find the probability of getting the sum of numbers that appear on the two dice (i) to be 9 (ii) to be less than 9. (OR) The following are the marks scored out of 50 in five tests by two students. Arun : 45 35 17 40 23 Ramesh : 30 47 32 41 28 find who is more consistent is scoring marks. IV. Answer both the questions choosing either of the alternatives 2 x 10 = 20 41. Draw a circle of radius 3 cm. Mark a point which is at a distance of 8 cm from its centre. Draw two tangents through the point and measure its length. (OR) Draw a triangle ABC such that AB = 4.5 cm, MC = 70 the altitude drawn from C to AB is 3.5 cm. 42. Solve Graphically y = x2 + 2x - 8 = 0 (OR) A man takes 10 days to complete a work by working 8 hrs a day. Draw the graph showing the relation and from the graph find our how many days he will take if he works 5 hrs a day.