Assertion (A): The digit in the unit place of 183! + 3183 is 7. Reason (R): 183! have unit place 0 and 34k +3 ends with 7.

Question

Assertion (A): The digit in the unit place of 183! + 3183 is 7. Reason (R): 183! have unit place 0 and 34k +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

Tardigrade Admin · Accepted Answer

For every n! ∀ n ge 5 ends with 0 and 34n ends with 1. ∴ 34n + 3 = 34n33 ,whose unit place is 7. (∵ ends at 7)

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

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

(A) is true but (R) is false.

(A) is false but (R) is true

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

Q. Assertion (A): The digit in the unit place of 183!+3183 is 7. Reason (R) : 183! have unit place 0 and 34k+3 ends with 7.