[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.
[B].
[C].
[D].
Answer: Option B
Explanation:
(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
[B].
[C].
[D].
Answer: Option D
Explanation:
Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,
(2n + 3)2 – (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 – 2n – 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8.
[B].
[C].
[D].
Answer: Option B
Explanation:
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 – 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.