Q42.Marks: +2.0UGC NET Paper 2: Computer Science 7th Dec 2023 Shift 2
Arrange the following in ascending order:
(A) Remainder of 4916 when divided by 17
(B) Remainder of 2446 when divided by 9
(C) Remainder of 15517 when divided by 17
(D) Last digits of the number 745
Choose the correct answer from the options given below:
1.(A), (B), (C), (D)
2.(A), (B), (D), (C)
3.(A), (C), (B), (D)✓ Correct
4.(D), (C), (B), (A)
Solution
The correct answer is (A), (C), (B), (D)
EXPLANATION:
(A) Remainder of 4916 when divided by 17.
Recall that if we look at powers of 49 modulo 17, we find that they alternate between 32 (equivalent to 15 mod 17) and 1. That's because 49² = 2401, which is 17 * 141 + 1. Since 16 is even, 49^16 is equivalent to 1 mod 17. So the remainder is 1.
(B) Remainder of 2446 when divided by 9.
The Remainder is 7.
(C) Remainder of 15517 when divided by 17.
Since 155 is a multiple of 17, the remainder of 155n divided by 17 will always be 2, irrespective of the value of n. So the remainder is 2.
(D) Last digits of the number 745
The cycle for the last digits of powers of 7 is 7, 9, 3, 1, repeating every 4th power. Therefore, the last digit of 745 (where 45 mod 4 = 1) will be 7.
So, the correct answer is option 3: (A), (C), (B), (D).