Mathematics-Class-9 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. 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) 2, 8 and 4 (B) 1, 8 and 6 (C) 1, 8 and 4 (D) 1, 8 and 2 2. When a certain number N is divided by 38, the remainder is 14. When the same number N is divided by 47, the quotient is 77 with some remainder R. Find the value of R. (A) 15 (B) 10 (C) 5 (D) 20 3. In the above question, the number N is (A) 3624 (B) 3644 (C) 3524 (D) 3544 4. Which one of the following statements is not correct ? (A) Euclidean geometry is not valid for spherical geometry (B) Pythagorean numbers are in the ratio of the sides of a right-angled triangle (C) Division by zero is not allowed in mathematics (D) Mode is always greater than median [2] 5. The sides AB and AC of a triangle ABC are produced, as shown. The bisectors of exterior angles at B and C meet at D. If angles x, y and z are in the ratio 2 : 3 : 4 then the angles a, b and c will be in the ratio Rough Work (A) 4 : 3 : 2 (B) 7 : 6 : 5 (C) 9 : 8 : 7 (D) 7 : 8 : 9 6. If the letters of the word RELATION are written at random, then what is the probability that all the vowels are grouped together (A) (C) 1 (B) 1 14 70 5 (D) 3 14 35 7. In class XII of a school, 130 students appeared for the examination. 20 students got more than 90 marks out of 100 in Mathematics, as under : 93, 95, 97, 96, 98, 98, 99, 92, 99, 100, 91, 95, 99, 100, 94, 98, 95, 98, 100, 98 The mode and median of these marks are, respectively, (A) 99, 98 (B) 98, 98.5 (C) 98, 98 (D) 98, 97.5 8. In the above problem, (A) mean > mode = median (B) median = mode > mean (C) mode > mean = median (D) median > mean > mode [3] 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 ? 9. (A) 159  143  288  18 (B) 3995  17  4275  19 (C) 122  112  192  94 (D) 21  36  12  63 10. (A) 576  24  132  122 (B) 5565  15  4823  13 (C) (D) 13  17 2 172  15   183  37 3 52  3 11. (A) 54  31  253  11 (B) 289  53  2394  7 (C) 86  34  68  43 (D) 25  75  35  55 12. (A) 13  37  345  126 (B) 11700  60  15  13 (C) 210  57  1573  11 (D) 163  147  288  18 13. Find the number of zeroes on the right side of the product of the following expression. 6 × 48 × 25 × 175 × 45 × 64 × 625 (A) 6 zeroes (B) 7 zeroes (C) 8 zeroes (D) 9 zeroes Rough Work [4] 14. AB is the diameter of a circle passing through its centre O. If BOC = 120° and AOD = 80°, then the measures of ECO , OBD and EDA are, respectively, Rough Work (A) 20°, 40° and 30° (B) 30°, 40° and 30° (C) 20°, 40° and 50° (D) 20°, 30° and 30° 15. Which one of the following statements is correct ? (A)  8  6    10  8    12  10        (B)  8  6    10  8    12  10        (C)  8  6    12  10    10  8        (D)  10  8    8  6    12  10        16. Find the sum of all the even numbers from 20 to 100. (A) 2540 (B) 2440 (C) 2450 (D) 2550 17. When 94,158 and 89,879 are divided by a certain number of 3 digits, the remainder in each case is same. The divisor of 3 digits is (A) 379 (B) 389 (C) 479 (D) 489 [5] 18. The digit in the unit place of the number, obtained after the Rough Work expansion of the expression 23717  27317  , would be (A) 0 (B) 2 (C) 4 (D) 6 19. 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) 15, 18 and 23 (B) 17, 15 and 23 (C) 15, 17 and 21 (D) 15, 17 and 23 20. Two shopkeepers A and B sell the product of the same company, having same marked price. During festival season, shopkeeper A announces successive discounts of 30%, 20% and 10%; while shopkeeper B announces successive discounts of 40%, 10% and 10%. Which shopkeeper gives more discount to the customer and by what percent ? (A) Shopkeeper A gives more discount by 1.8% (B) Shopkeeper A gives more discount by 0.18% (C) Shopkeeper B gives more discount by 1.8% (D) Shopkeeper B gives more discount by 0.18% 21. Near a railway crossing, in a wedding procession two powerful crackers are exploded with an interval of 8 minutes. The driver in the train, approaching the railway crossing, heard the sound of the second cracker 7 minutes and 30 seconds after hearing the sound of the first cracker. If the speed was 360 ms–1, then the speed of the train was (A) 86.4 km/h (B) 88.0 km/h (C) 75.0 km/h (D) 78.3 km/h [6] In the following two questions, the numbers in the series follow a regular pattern (different in different series). Try to understand the pattern and find the missing number from the four alternatives given below each questions such that this number also follows the same pattern. 22. 14, 35, 77, 161, ..?.., 665 (A) 413 (B) 343 (C) 329 (D) 309 23. 1, 3, 4, 9, 9, 27, 16, ..?.., 25 (A) 54 (B) 48 (C) 64 (D) 81 24. Try to understand the changing patterns in the following three figures. Rough Work Which one of the following four figures should replace the sign ..?.. so that the same changing patterns are followed. (A) (B) (C) (D) 25. How many different numbers of 6 digits are possible ? (A) 999,999 (B) 900,000 (C) 899,999 (D) None of these 26. The bisectors of angles of a parallelogram enclose (A) a parallelogram (B) a rhombus (C) a square (D) a rectangle [7] 27. 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, 1 and 9 (B) 7, 2 and 9 (C) 7, 1 and 8 (D) 7, 2 and 8 28. Find the numerical values of A, B and C, respectively in the following product (A) 5, 9, 4 (B) 5, 7, 3 (C) 4, 6, 3 (D) 6, 4, 2 29. Which one of the following is not a factor of the expression : x4 – 6x3 + 11x2 – 6x ? (A) x – 1 (B) x – 2 (C) x – 3 (D) x – 4 30. 133 + 183 – 29791 + 3 × 31 × 234, after simplification, is found to be (A) a positive integer (B) a negative integer (C) 0 (D) none of these 31. A hollow cylindrical tube, open at both its ends, is made of an alloy 2 cm thick. The external diameter of the tube is 40 cm and the length of the tube is 70 cm. If 1 cm3 of the alloy weighs 7.5 g, then the total weight of the cylindrical tube is (A) 64.35 kg (B) 118.8 kg (C) 128.7 kg (D) 125.4 kg [8] 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 32. During which year the ratio of percentage net profit earned to that in the previous year is the maximum ? (A) 1993 (B) 1994 (C) 1996 (D) Same in all these years 33. In the above problem, if the income in 1994 was Rs 30 lakhs, what was the expenditure in the year ? (A) 18 lakhs (B) 24 lakhs (C) 20 lakhs (D) 25 lakhs 34. The radius of a solid metallic sphere is decreased by 30%. The cost of the material and the cost of polishing its surface will decrease, respectively, by (A) 65.7% and 49% (B) 65.7% and 51% (C) 67.5% and 51% (D) 67.5% and 49% 35. A thin circular wire of radius 21 cm is cut and bent in the form a rectangle whose sides are in the ratio 6 : 5. The ratio of the area of the circular wire and that of the rectangular wire would be (A) 35 : 27 (B) 21 : 16 (C) 77 : 60 (D) 56 : 45 [9] 36. In the following figure, AB = AD, AC = AE and BAD = CAE . Rough Work Which one of the following relations is not correct ? (A) (C) AED  DAC  ACB DEC (B) (D) ADE  ACE  ABC CEA 37. In an advisory committee of 15 persons, 7 are technocrats, 5 are politicians and 3 are bureaucrats. A select committee of 4 persons is to be formed from these 15 persons. What is the probability that this select committee has no politician ? (A) (C) 3 2 26 (B) 39 2 3 13 (D) 13 38. CD  the diameter AB of the semicircle shown. If AD = 7 cm, then the magnitude of CD, upto 3 places of decimals, is (A) 2.646 cm (B) 2.645 cm (C) 2.828 cm (D) 2.829 cm [10] 39. Select the diagram, from the following, that best represents doctors, patients and males. (A) (B) Rough Work (C) (D) 40. Which one of the following statements is correct ? (A) [125% of 300] = [93.50% of 400] (B)  1  1 is greater than  1    4 9   (C) Area of a circle of radius 7 cm is same as area of a square of perimeter 48 cm ( = 22/7) (D) 0.9  0.9 [11] ANSWERS : CLASS IX MATHS 1 C 2 C 3 A 4 D 5 B 6 A 7 C 8 B 9 A 10 D 11 B 12 C 13 D 14 A 15 A 16 B 17 B 18 A 19 D 20 C 21 A 22 C 23 D 24 B 25 B 26 D 27 B 28 A 29 D 30 C 31 D 32 A 33 C 34 B 35 C 36 C 37 C 38 A 39 C 40 D 1. ABCD is a quadrilateral in which AD = BC and DAB  CBA , as shown under. AC and BD are joined, intersecting at point O. Rough Work D C = O = A B Which one of the following statements is wrong ? (A) AOB is an isosceles triangle (B) AOB and DOC are not similar triangles (C) ACD and ABD are equal in magnitude (D) Quadrilateral ABCD is a trapezium 2. The angles A, B, C of a triangle are such that A : B = 3 : 5 and C : B = 2 : 1. Which one of the following statements is not correct ? (A) Angle A is one-fifth of the sum of the angles B and C (B) The angles A, B, C are in the ratio 3 : 5 : 10 (C) Angle B is 80% of the sum of angles A and C (D) ABC is an obtuse-angled triangle 3. A bag contains 5 white and 3 black balls. Four balls are drawn out one by one and not replaced. What is the probability that the balls drawn out are alternately of different colours ? (A) 1 (B) 1 14 7 (C) 2 3 7 (D) 14 [13]