∴  The required number
= 11 – 4 = 7
Method 2 :
Sum of digits at odd places = 2 +
6 + 0 = 8, sum of digits at even
places = 4 + 3 + 8 = 15. For divisibility by 11, difference i.e.,
(15 – 8) = 0 or mutiple of 11.
∴  The required number = 7

Correct Option: C

∴  The required number
= 11 – 4 = 7
Method 2 :
Sum of digits at odd places = 2 +
6 + 0 = 8, sum of digits at even
places = 4 + 3 + 8 = 15. For divisibility by 11, difference i.e.,
(15 – 8) = 0 or mutiple of 11.
∴  The required number = 7

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

Correct Option: C

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

Divisor = 6 × 2 = 12
Again, Divisor = 3 × quotient

Correct Option: A

Divisor = 6 × 2 = 12
Again, Divisor = 3 × quotient

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

Correct Option: D

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

n = 6q + 4
2n = 12q + 8
Dividing 8 by 6 the remainder = 2

Correct Option: A

n = 6q + 4
2n = 12q + 8
Dividing 8 by 6 the remainder = 2