Here, the first divisor (91) is a multiple of second divisor (13).

Correct Option: B

Here, the first divisor (91) is a multiple of second divisor (13).
∴ Required remainder = Remainder obtained on dividing 17 by 13
⇒ 17 = ( 13 × 1 ) + 4
Hence Required remainder = 4

Of the given alternatives,
When 64 is divided by 3, remainder = 1

Correct Option: C

Of the given alternatives,
When 64 is divided by 3, remainder = 1
When 65 is divided by 5, remainder = 0

Let the unknown number be p.
∴  71 × p + 47 = 98 × 7
⇒   71p = 686 – 47 = 639

Correct Option: D

Let the unknown number be p.
∴  71 × p + 47 = 98 × 7
⇒   71p = 686 – 47 = 639

The Expression 4⁶¹ + 4⁶² + 4⁶³ = 4⁶¹ (1 + 4 + 4²)

Correct Option: A

The Expression 4⁶¹ + 4⁶² + 4⁶³ = 4⁶¹ (1 + 4 + 4²)
= 4⁶¹ × 21 which is divisible by 3.
Hence , the given expression is divisible by 3 .

The given expression 2⁶ⁿ − 4²ⁿ = (2⁶)ⁿ − (4²)ⁿ

Correct Option: D

The expression 2⁶ⁿ − 4²ⁿ = (2⁶)ⁿ − (4²)ⁿ
= 64ⁿ − 16ⁿ
which is divisible by 64 –16= 48
Therefore required answer is 48 .