Number System
कुल प्रश्न: 77 | पेज 6
51. Find the remainder when (17^200) is divided by 18.
सही उत्तर: [C]
हल (Solution):
Using the format (x-1)^n / x.
Here (18-1)^200 / 18. Since the power (200) is even, the remainder will always be 1.
Using the format (x-1)^n / x.
Here (18-1)^200 / 18. Since the power (200) is even, the remainder will always be 1.
52. The sum of the first 50 odd natural numbers is:
सही उत्तर: [A]
हल (Solution):
Correct Answer: A) 2500
Solution:
The sum of the first 'n' odd natural numbers is n^2.
Here n = 50. Sum = 50^2 = 2500.
Correct Answer: A) 2500
Solution:
The sum of the first 'n' odd natural numbers is n^2.
Here n = 50. Sum = 50^2 = 2500.
53. What is the largest 4-digit number exactly divisible by 88?
सही उत्तर: [A]
हल (Solution):
Correct Answer: A) 9944
Solution:
Largest 4-digit number = 9999.
9999 / 88 gives a remainder of 55.
Required number = 9999 - 55 = 9944.
Correct Answer: A) 9944
Solution:
Largest 4-digit number = 9999.
9999 / 88 gives a remainder of 55.
Required number = 9999 - 55 = 9944.
54. A number when divided by 899 gives a remainder 63. If the same number is divided by 29, the remainder will be:
सही उत्तर: [B]
हल (Solution):
Since 899 is perfectly divisible by 29 (29 x 31 = 899), we just need to divide the first remainder (63) by 29.
63 / 29 = Quotient 2, Remainder 5.
Since 899 is perfectly divisible by 29 (29 x 31 = 899), we just need to divide the first remainder (63) by 29.
63 / 29 = Quotient 2, Remainder 5.
55. The difference between the local value (place value) and the face value of 7 in the numeral 32675149 is:
सही उत्तर: [C]
हल (Solution):
Correct Answer: C) 69993
Solution:
Place value of 7 is 70000.
Face value of 7 is 7.
Difference = 70000 - 7 = 69993.
Correct Answer: C) 69993
Solution:
Place value of 7 is 70000.
Face value of 7 is 7.
Difference = 70000 - 7 = 69993.
56. Which of the following is a prime number?
सही उत्तर: [C]
हल (Solution):
Correct Answer: C) 373
Solution:
Check divisibility by prime numbers up to the square root of the number.
373 is not divisible by 2, 3, 5, 7, 11, 13, 17, or 19. Hence, it is prime.
Correct Answer: C) 373
Solution:
Check divisibility by prime numbers up to the square root of the number.
373 is not divisible by 2, 3, 5, 7, 11, 13, 17, or 19. Hence, it is prime.
57. How many factors does the number 120 have?
सही उत्तर: [B]
हल (Solution):
Correct Answer: B) 16
Solution:
Prime factorization of 120 = 2^3 x 3^1 x 5^1.
Number of factors = (3+1) * (1+1) * (1+1) = 4 * 2 * 2 = 16.
Correct Answer: B) 16
Solution:
Prime factorization of 120 = 2^3 x 3^1 x 5^1.
Number of factors = (3+1) * (1+1) * (1+1) = 4 * 2 * 2 = 16.
58. The sum of three consecutive even numbers is 252. Find the largest number.
सही उत्तर: [C]
हल (Solution):
Correct Answer: C) 86
Solution:
Average (middle number) = 252 / 3 = 84.
The numbers are 82, 84, 86. The largest is 86.
Correct Answer: C) 86
Solution:
Average (middle number) = 252 / 3 = 84.
The numbers are 82, 84, 86. The largest is 86.
59. What least number must be added to 1056 to get a number exactly divisible by 23?
सही उत्तर: [A]
हल (Solution):
Correct Answer: A) 2
Solution:
1056 / 23 gives a remainder of 21.
Number to be added = Divisor - Remainder = 23 - 21 = 2.
Correct Answer: A) 2
Solution:
1056 / 23 gives a remainder of 21.
Number to be added = Divisor - Remainder = 23 - 21 = 2.
60. 1/0.04 is equal to:
सही उत्तर: [D]
हल (Solution):
Correct Answer: D) 25
Solution:
1 / 0.04 = 1 / (4/100) = 100 / 4 = 25.
Correct Answer: D) 25
Solution:
1 / 0.04 = 1 / (4/100) = 100 / 4 = 25.