CSATNumber System & SeriesDivisibility Divisors and Remainder2025

If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4 ?

A

0

B

1

C

2

D

3

Correct Answer: Option C

Explanation

To find the number of distinct remainders for $(1^n + 2^n)$ divided by 4, we use the 'Small Number Simulation' strategy learned from previous yea

More Number System & Series PYQs

What is the unit digit in the multiplication of 1 x 3 x 5 x 7 x 9 x ... x 999?
Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR – PS = PPT . If Q = 3 and T < 6, then what is the number of possible values of (R, S) ?
What is the 489th digit in the number 123456789101112...?
The 5-digit number PQRST (all distinct digits) is such that T ≠ 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible ?
A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?
A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N ?

View all Number System & Series questions →

Master UPSC Revision

Get 10,000+ topic-wise MCQs, spaced repetition, daily CSAT challenges, and detailed performance analytics.

Coming Soon to Play Store

Coming Soon to Play Store