Question

Assertion (A): The digit in the unit place of $183! + 3^{183}$ is $7$.
Reason (R) : $183!$ have unit place $0$ and $3^{4k +3}$ ends with $7$.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true

Answer 1

Answer: (A)

For every $n! \forall n \ge 5$ ends with $0$ and $3^{4n}$ ends with $1$.
$\therefore 3^{4n + 3} = 3^{4n}3^{3}$ ,whose unit place is $7$. ($\because$ ends at $7$)