Match List-I with List-II
|
List-I |
List-II |
|
(A) Unit's digit of $2^{11}$ |
(I) 2 |
|
(B) Unit's digits of $11^{132}$ |
(II) 1 |
|
(C) Remainder when 71 × 73 × 75 is divided by 23 |
(III) 4 |
|
(D) Remainder when $7^{30}$ is divided by 5 |
(IV) 8 |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(II), (C)-(II), (D)-(III) **
|
List-I |
List-II |
|
(A) Unit's digit of $2^{11}$ |
(IV) 8 |
|
(B) Unit's digits of $11^{132}$ |
(II) 1 |
|
(C) Remainder when 71 × 73 × 75 is divided by 23 |
(I) 2 |
|
(D) Remainder when $7^{30}$ is divided by 5 |
(III) 4 |
Compute each value:
(A) Unit digit of $2^{11}$ Cycle of 2: $2,4,8,6$ (length 4) $11 \bmod 4 = 3$ → 3rd term = 8 → (IV)
(B) Unit digit of $11^{132}$ Unit digit of 11 is 1 → $1^{132}=1$ → (II)
(C) Remainder of $71 \times 73 \times 75$ mod 23
$71 \equiv 2$, $73 \equiv 4$, $75 \equiv 6$ (mod 23)
Product = $2 \cdot 4 \cdot 6 = 48$
$48 \bmod 23 = 2$ → (I)
(D) Remainder of $7^{30}$ mod 5 $7 \equiv 2$ mod 5 → $2^{30}$
Cycle of 2 mod 5: $2,4,3,1$ (length 4)
$30 \bmod 4 = 2$ → 2nd term = 4 → (III)