∵ 2¹⁶ – 1 = (2⁸)²–1
= (2⁸+1) (2⁸–1)

Correct Option: C

∵ 2¹⁶ – 1 = (2⁸)²–1
= (2⁸+1) (2⁸–1)
= (256 + 1) (256 – 1)
2¹⁶ – 1 = 257 × 255 which is exactly divisible by 17.

According to question ,
Divisor = 6 × Remainder
Divisor = 6 × 2 = 12
Again, Divisor = 3 × quotient

Correct Option: A

According to question ,
Divisor = 6 × Remainder
Divisor = 6 × 2 = 12
Again, Divisor = 3 × quotient

If the remainder be p, then (11284 – p ) and (7655 – p ) are divisible by three digit number.
i.e. (11284 – p ) – (7655 – p ) = 3629 is divisible by that number.
3629 = 19 × 191

Correct Option: D

If the remainder be p, then (11284 – p ) and (7655 – p ) are divisible by three digit number.
i.e. (11284 – p ) – (7655 – p ) = 3629 is divisible by that number.
3629 = 19 × 191
Hence, required number = 191
Sum of digits = 1 + 9 + 1 = 11

According to question ,
n = 6q + 4
And 2n = 12q + 8

Correct Option: A

According to question ,
n = 6q + 4
And 2n = 12q + 8
Dividing 8 by 6 the remainder = 2
Hence required remainder = 2

Here, the first divisor (289) is a multiple of second divisor (17).
∴ Required remainder = Remainder obtained on dividing 18 by 17

Correct Option: D

Here, the first divisor (289) is a multiple of second divisor (17).
∴ Required remainder = Remainder obtained on dividing 18 by 17 = 1
Therefore required answer is 1.