If n is a natural number then what is the of all distinct remainders of 4n 6n 9n 11n ...........

Quantitative Aptitude (CDS) Number System

If n is a natural number, then what is the of all distinct remainders of 4ⁿ + 6ⁿ + 9ⁿ + 11ⁿwhen divided by 10 for various values of n ?

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2024 CDS -1 MATH

- Breakdown by Numbers:

- 4ⁿ: The remainder cycle when divided by 10 is 4, 6.

- 6ⁿ: The remainder when divided by 10 is consistently 6.

- 9ⁿ: The cycle is 9, 1.

- 11ⁿ: The cycle is 1, 1 (since 11 is the same as 1 mod 10).

- Evaluating Cycles:

- For even n: The expression results in 6.

- For odd n: The expression results in 0.

- Distinct Remainders:

- The distinct remainders possible are 0 and 6.

- Options:

- Option:1, 3

- Option:2, 4

- Option:3, 6

- Option:4, 7

- Correct Option:

- The correct number of distinct remainders is 2 and matches Option:3, 6.

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