NUMBER SYSTEM (CDS)

Total Questions: 101

91. Solve the following equation [2014 (II) Evening Shift ]

Correct Answer: (b)
Solution:

92. How many pairs of X and Y are possible in the number 763X4Y 2, if the number is divisible by 9? [2014 (II) Evening Shift ]

Correct Answer: (d) 11
Solution:We know that, any number is divisible by 9, if sum of all the digits is divisible by 9. Given number is 763X 4Y2.

93. What is the remainder when 4¹⁰¹² is divided by 7? [2014 (II) Evening Shift ]

Correct Answer: (d) 4
Solution:

94. What is the remainder when (1235 × 4523 × 2451) is divided by 12? [2014 (II) Evening Shift ]

Correct Answer: (b) 3
Solution:Let E = (1235 × 4523 × 2451)

95. p, q and r are prime numbers such that p < q < r < 13. In how many cases would (p + q + r) also be a prime number? [2014 (II) Evening Shift ]

Correct Answer: (b) 2
Solution:The prime numbers less than 13 are 2, 3, 5, 7, 11.

96. What is the remainder when (17²³ + 23²³ + 29²³) is divided by 23? [2014 (II) Evening Shift ]

Correct Answer: (a) 0
Solution:

97. If n is a whole number greater than 1, then n² (n²− 1) is always divisible by [2014 (I) Morning Shift ]

Correct Answer: (a) 12
Solution:If n is greater than 1, then (n² − 1) is always divisible by 12.

98. Consider the following statements [2014 (I) Morning Shift ]

I. No integer of the form 4k + 3, where k an integer, can be expressed as the sum of two squares.
II. Square of an odd integer can expressed in the form 8k + 1, where k is an integer.

Which of the above statement(s) is/are correct?

Correct Answer: (a) Only I
Solution:I. f (k) = 4k + 3

99. The difference of two consecutive cubes [2014 (I) Morning Shift ]

Correct Answer: (b) is never divisible by 2
Solution:The difference of two consecutive cubes is never divisible by 2.

100. The product of four consecutive natural numbers plus one is [2014 (I) Morning Shift ]

Correct Answer: (c) a square
Solution:Product of four consecutive numbers plus one is always a square.