[B].
[C].
[D].
Answer: Option D
Explanation:
(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40
= 324 x 3 x 4 x 10
= (324 x 4 x 30), which is divisible by30.
[B].
[C].
[D].
Answer: Option B
Explanation:
(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10.
[B].
[C].
[D].
Answer: Option D
Explanation:
Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 – x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
[B].
[C].
[D].
Answer: Option B
Explanation:
When n is odd, (xn + an) is always divisible by (x + a).
Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).
[B].
[C].
[D].
Answer: Option C
Explanation:
7429 Let 8597 – x = 3071
-4358 Then, x = 8597 – 3071
—- = 5526
3071
—-
[B].
[C].
[D].
Answer: Option C
Explanation:
When n is even. (xn – an) is completely divisibly by (x + a)
(17200 – 1200) is completely divisible by (17 + 1), i.e., 18.
(17200 – 1) is completely divisible by 18.
On dividing 17200 by 18, we get 1 as remainder.
[B].
[C].
[D].
Answer: Option A
Explanation:
For every natural number n, (xn – an) is completely divisible by (x – a).
[B].
[C].
[D].
Answer: Option A
Explanation:
(xn – 1) will be divisibly by (x + 1) only when n is even.
(4915 – 1) = {(72)15 – 1} = (730 – 1), which is divisible by (7 +1), i.e., 8.
[B].
[C].
[D].
Answer: Option C
Explanation:
(xn + 1) will be divisible by (x + 1) only when n is odd.
(6767 + 1) will be divisible by (67 + 1)
(6767 + 1) + 66, when divided by 68 will give 66 as remainder.
[B].
[C].
[D].
Answer: Option B
Explanation:
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.