All Types of Questions Asked in GATE Exam for All Branches.
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Typel 1) 2) 3) 4) 5) 6) 7) 8) 9) Chapterl - Number System Useful for - Gate/ESE/PSUs/other competitive Exams - Questions based on types of number system The sum of all the natural numbers from 51 to 100 is a. 5050 b. 4275 c. 4025 d. 3775 The sum of first 20 odd natural numbers is equal to b. 300 c. 400 d. 420 a. 210 Out of six consecutive natural numbers, if the sum of first three is 27, what is the sum of the other three? b. 35 c. 25 d. 24 a. 36 Which one of the following is a factor of the sum of first 25 natural numbers? a. 26 b. 24 c. 13 d. 12 The sum of three consecutive odd natural number is 87. The smallest of these numbers is b. 31 a. 29 c. 23 d. 27 In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the sum of the last 5 numbers in the sequence? b. 495 c. 400 d. 535 a. 485 GATE, 2014 The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even numbers? b. 153 d. 94 163 c. 190 a. GATE, 2014 The sum of all natural numbers between 100 and 200 which are multiples of three is a. 5000 b. 4950 d. 4900 c. 4980 in the form p/q is equal to The number 0.121212 a. 4/11 b. 2/11 c. 4/33 d. 2/33 10) 0.001 is equal to 1/1000 b. 1/999 c. 1/99 d. 1/9 a. 11) If a and b are integers and a— b is even, which of the following must always be even? ab b. a2 + b2+1 c. a2+b+1 d. ab—b GATE, 2017 a. Type2-Questions based on unit digits 754 12) The unit digit in the expansion of (2137) is a. 13) The unit digit in the sum of (124)372 + (124)373 is 6521 + 36528 + 7354 is 14) The unit digit of the expression 25 1793 x (615)317 x (131)491 15) The digit in the unit place of the product (2464) is 16) The last digit of (2171)7 + (2172)9 + (2173)11 + (2174)13 is GATE, 2017 17) The numerals in the unit position of 211870 + 146127 x 3424 is GATE, 2017 Type3- No. of zeros, Factors based problems 18) The maximum power of 5 in 60! a. 14 b. 15 c. 16 d. 17 19) How many zero's are there at the end of 100! a. 24 b. 25 c. 26 d. 23 20) Find the smallest number y such that y x 162 is a perfect cube a. 24 b. 27 c. 32 d. 36 GATE, 2017
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21) If f(x) = 3x -5, which of the following is a factor of f(x) ? GATE , 2016 Type4- Questions based on divisibility 22) If the number 48326*8 is divisible by 11, then the missing digit is 23) If a number is divisible by both 11 and 13, then it must be necessarily a. Divisible by (11 + 13) b. divisible by (11 - 13) c. divisible by (11 x 13) 24) How many 3-digit numbers, in all, are divisible by 6? 140 b. 150 c. 160 d. 170 a. 25) The smallest 6 digit number exactly divisible by 111 is: d. 429 b. 110011 c. 100011 d. 110101 26) If the number 653 xy is divisible by 90, then (x + y) = ? 27) What least number, of 5 digits is divisible by 41? 10045 b. 10004 c. 10041 d. 41000 a. 16 — 1 is divisible by 28) 2 11 b. 13 c. 17 d. 19 a. 29) A common factor of 137 + 117 and 135 + 115 is a. 24 b. 135+11 5 c. 132 + 112 d. None of these 30) Both the ends of digits of a 99 digits number N are 2. N is divisible by 11, then all the middle digit are a. Type4- Questions based on Remainder 31) When 233 is divided by 10 , the remainder will be 32) The remainder when 321 is divided by 5 is? a. 33) If 17200 is divided by 18, the remainder is 17 b. 16 c.i d. 2 a. 34) What is the remainder when (13100 + 17100) is divided by 25? D. 11 35) What will be remainder when (6767 + 67) is divided by 68 ? B. 63 c. 66 36) Find the reminder when 1! + 2! +3! + A. 783 B. 873 37) Find the remainder when 10099 is divided by 11 A. 10 D. 67 99! + 100! is divided by the product of first 7 natural numbers D. 11 38) In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 40, then the dividend is a. 240 b. 440 c. 4040 d. 4000 39) A number when divided by 280 leaves 115 as remainder. When the same number is divided by 35, the remainder is 15 b. 10 c. 20 d. 17 a. 40) A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is a. 220030 b. 22030 c. 1220 d. 1250 41) When n is divided by 5 the remainder is 2. What is the remainder when re is divided by 5? 42) What is the remainder when + 3x- 7 is divided by x +9 ? A. 439 B. 425 c. 385 D. 371
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Miscellaneous 43) The sum of squares of three consecutive natural numbers is 2030, then what is the middle number? a. 25 b. 26 c. 27 d. 28 44) If a and b are odd numbers, then which of the following is even? a-kb4-ab b. a+b-l c. a-kb+l d. a-kb+2ab a. 45) Which of the following numbers is the greatest of all? 0.9, 0.5, 0.05, 0.09 a. 0.9 b. 0.9 c. 0.05 d. 0.09 46) A number divided by 13 leaves a remainder 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65? a. 28 b. 16 c. 18 d. 40 47) The numbers 2272 and 875 are divided by 3-digits number N, giving the same remainders. The sum of the digits of N is 10 b. 11 c. 12 d. 13 a. 48) Which of the following numbers will always divide a six digit number of the form xy xy xy (where 1 x 9, 1 y 9 ) ? 1010 b. 10101 c. 11011 d. 11010 a. 49) A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is: 50) How many 3-digit numbers are completely divisible 6 ? 10. B 12. B 16. B 11. D 13. D 14. D 17. B 20. D 21. B 22. D 23. c 24. B 25. c 26. c 27. B 28. c 30. D 32. c 33. c 34. B 36. B 35. c 37. B 38. c 39. B 42. D 43. B 41. D 44. D 45. B 46. D 50. B 52. B 53. c 48. B 49. D 54. D B. 150 A. 149 c. 151 D. 166 15 51) Which of the following numbers will completely divide (49 B. 14 c. 46 D. 50 52) What is the remainder when (13100 + 17100) is divided by 25? D. 11 53) Find the unit digit of the expression 1781+2781+3781+4781+ ... 54) Which of the following number is divisible by 24 ? A. 35718 Answer Key B. 63810 C. 537804 D. 3125736 c 3. 781 B 1. 19. D 2. 29. 47. 4. 40. c 5. D 6. 15. 51. 7. 8. B 9. 18. c
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