Mathematics-Class-10 DPP Talent Search Examinations

Each question has four alternatives marked (A), (B), (C) and (D), but only one of these alternatives is the correct answer. Find the correct answer. 1. An aeroplane is flying along a horizontal direction at a constant height of 450 3 m. If from the point of observation, the angle of elevation changes from 60° to 30° in 6 seconds, then the speed of the aeroplane is Rough Work (A) 630 km/hr (B) 600 km/hr (C) 540 km/hr (D) 500 km/hr 2. A cube of side 2 cm is converted into a sphere by adding plasticine around it. The minimum volume of the plasticine required for the purpose would be (A) 8  3   cm3 (B) 8 4 3  1 cm3  2 1     8  2 3   3   3 (C)  2 1 cm (D) 8  3  1 cm   3. From the bottom and the top of a building of height h, the angles of elevation of the top of a tower are, respectively,  and . If H is the height of the tower, then H and h are related by the relation (A) H  h tan  (B) H  h tan  tan   tan  tan   tan  (C) H  h tan  (D) H  h tan  tan   tan  tan   tan  [2] 4. Fill in single digits in each of the following squares such that the sum of these digits is equal to the number written either above or on the left side of the row of the squares. No digit is to be repeated along any line. In the duplicate figure on the right side, letters A, B and C have been written in some squares Rough Work The letters A, B and C are, respectively, (A) 7, 8 and 8 (B) 8, 4 and 9 (C) 8, 2 and 9 (D) 7, 2 and 9 5. When a certain number N is divided by 78, the remainder is 35. When the same number N is divided by 87, the quotient is 40 with some remainder R. Find the value of R. (A) 45 (B) 55 (C) 65 (D) 75 6. In the above question, the number N is (A) 4535 (B) 3545 (C) 4635 (D) 3645 7. If (x – y)2/3 + 15 (x + y)2/3 = 8 (x2 – y2)1/3, then the value x  y of x  y (A) lies between 27 and 125 (B) is greater than 125 or less than 27 (C) is either 27 or 125 (D) is either –27 or 125 8. Find the remainder when [710 + 2] is divided by 6. (A) 1 (B) 2 (C) 3 (D) 5 [3] Number of condidates appeared, qualified and selected in a competitive examination from the four States A, B, C and D, over the years 1994 to 1998 are given in the following table. Study the above table carefully and answer the following three questions given below : 9. What is the average percentage of students qualified over the given five years for the State C. (A) 8.78% (B) 7.88% (C) 9.16% (D) 9.38% 10. In which year, the percentage of students selected is minimum for the State B ? (A) 1994 (B) 1995 (C) 1997 (D) 1998 11. Find the percentage of the total students selected over the given five years from State A. (A) 27.48% (B) 26.54% (C) 25.44% (D) 24.25% 12. The area of the quadrilateral formed by the four points P(– 6, – 6), Q(2, – 2), R(6, 6) and S(–2, 2) is equal to (A) 36 units (B) 48 units (C) 64 units (D) 72 units Rough Work [4] In each of the following three questions, there is some relationship between the first two terms. The same relationship exists between the second set of terms of which the missing terms is representative by ..?.. and is one of the four alternatives given below each question. Find the correct alternative. 13. CFED : GJIH : : QTSR : ..?.. (A) UWXV (B) XZVY (C) UXWV (D) YXAZ 14. ZXYW : ACBD : : ..?.. : IGHF (A) RTSU (B) RQSU (C) USTR (D) RQSP 15. YWZX : RPSQ : : MKNL : ..?.. (A) TRSU (B) PRQS (C) FDGE (D) ECDF 16. ABC and DBC are two triangles on the same base BC. AD is joined, meeting BC at O. AE and DF are perpendiculars to the line BC. If areas of triangles ABC and DBC are in the ratio 2 : 3, then the areas of triangles AEO and DFO are in the ratio Rough Work (A) 2 : 3 (B) 4 : 9 (C) 8 : 27 (D) none of these 17. The points A(1, – 4), B(10, – 1), C(5, 7) and D(– 4, 4) enclose (A) a rhombus (B) a square (C) a rectangle (D) a parallelogram [5] If + is written as α, – as γ, × as δ,  as λ, = as μ, > as β and < as θ, then in the following four questions which one of the four relations is not correct ? Rough Work 18. (A) 34  86  43  68 (B) (C) 13  17  83  137 253  11  54  31 (D) 15  21  143  159 19. (A) 159  143  288  18 (B) 112  122  192  94 (C) (D) 345  126  37  13 63  12  36  21 20. (A) 1573  11  200  57 (B) 576  24  132  122 (C) 172    2 52  3 (D) 2394  7  289  53 21. (A) 75  25  55  35 (B) 4275  19  3995  17 (C) 15  13  11700  60 (D) 4823  13  5565  15 22. How many numbers of 7 different digits are possible, each number having 7 digits ? (A) 181,440 (B) 544,320 (C) 535,320 (D) 454,320 [6] In the following two questions, the problem figure is rotated along the direction of the arrow. Only one of the four alternative figures (A, B, C and D) is the correct position after it has been rotated to a new position. Identify the correct figure 23. Problem figure : Rough Work (A) (B) (C) (D) 24. Problem figure : (A) (B) (C) (D) 25. A bag contains 10 green balls and 15 red balls. Two balls are drawn in succession at random. What is the probability that one of the balls is green and the other is red ? (A) 1 (B) 2 2 5 (C) 3 4 10 (D) 15 [7] The following graph shows the percentage net profit of a certain company during the given period. Study it carefully and answer the questions given below. Rough Work 26. During which year the ratio of percentage net profit earned to that in the previous year is the maximum (A) 1996 (B) 1994 (C) 1993 (D) same in all these years 27. In the above problem, if the income in 1994 was Rs 25 lakhs, what was the expenditure in the year ? (A) 16 lakhs (B) 16.33 lakhs (C) 16.67 lakhs (D) 15.67 lakhs 28. AB, CD, EF and GH are, respectively, the chords of circles of radii 5 cm, 6 cm, 7 cm and 10 cm, subtending angles 180°, 120°, 90° and 60° respectively, at the centres of their corresponding circles. Which one of the following statements is correct, regarding their lengths ? (A) AB > GH > CD > EF (B) CD > GH > AB > EF (C) CD > AB = GH > EF (D) CD > EF > AB = GH [8] 29. Fill in single digits in each of the following squares such that the sum of these digits is equal to the number written either above or on the left side of the row of the squares. No digit is to be repeated along any line. In the duplicate figure on the right side, letters A, B and C have been written in some squares Rough Work The letters A, B and C are, respectively, (A) 7, 9 and 8 (B) 9, 7 and 8 (C) 8, 9 and 9 (D) 7, 7 and 8 30. When 94,158 and 89,879 are divided by a certain number of 3 digits, the remainder in each case is same. The remainder in each case would be (A) 20 (B) 35 (C) 40 (D) 45 31. How many more four-digit numbers are divisible by 7 than by 14 ? (A) 640 (B) 642 (C) 643 (D) None of these 32. Out of 15 foreign students in a section, studying at Paris, 7 are from India, 5 from China and 3 from Japan. Four students are selected at random for advisory committee. What is the probability that at least one student is from China ? (A) (C) 13 11 15 (B) 14 14 11 15 (D) 13 [9] 33. A field is in the shape of an isosceles trapezium. Parallel sides of the field are of lengths 780 m and 600 m and are separated by a distance of 120 m each. Water pipe is to be laid for watering the field along the boundary of the field as well as parallel to the parallel sides of the field such that distance between each parallel pipe is 20 m. Find the total length of the pipe to be laid. Rough Work (A) 5.31 km (B) 5.23 km (C) 4.98 km (D) 5.18 km 34. The following three figures are alike in some way : Look at the following four alternative figures and find the one which is alike the above three figures (A) (B) (C) (D) 35. Find the sum of all the positive terms in the following series: 127, 123, 119, 115, .......... (A) 2079 (B) 2080 (C) 2084 (D) 2075 [10] 36. The numbers 15 to 23 are to be written in small squares in the following figure such that the sum of the numbers along each row, along each column and along each diagonal of the grid is 57. The numbers given by A, B and C may be, respectively, (A) 16, 15 and 21 (B) 18, 15 and 23 (C) 18, 15 and 21 (D) 18, 17 and 21 37. The digit in the unit place of the number, obtained after the Rough Work expansion of the expression be 27326  37226  , would (A) 2 (B) 3 (C) 5 (D) 6 38. Three cubes of steel whose edges are of the lengths 6 cm, 8 cm and 10 cm, respectively, are melted in a furnace and recast another single cube. Find the decrease in surface area, resulting in saving for polishing the surface. (A) 360 cm2 (B) 336 cm2 (C) 372 cm2 (D) 396 cm2 39. Distance between two stations is 300 km. The express train, running 15 km/hr faster than goods train, takes 1 hour less than goods train. Time taken by goods train to reach from one station to the other would be (assume that trains travel non-stop) (A) 4 hours (B) 4 hours, 30 minutes (C) 5 hours (D) 6 hours [11] 40. The following three figures are alike in some way : Rough Work Look at the following four alternative figures and find the one which is alike the above three figures (A) (B) (C) (D) [12] ANSWERS : CLASS X MATHS 1 C 2 A 3 C 4 D 5 C 6 B 7 C 8 C 9 B 10 A 11 C 12 B 13 C 14 A 15 C 16 B 17 D 18 D 19 C 20 A 21 B 22 B 23 C 24 B 25 A 26 C 27 C 28 C 29 D 30 A 31 C 32 D 33 A 34 A 35 B 36 C 37 B 38 B 39 C 40 D