Expression = (2⁷¹ + 2⁷² + 2⁷³ + 2⁷⁴)
Expression = 2⁷¹ (1 +2 + 4 + 8)

Correct Option: B

Expression = (2⁷¹ + 2⁷² + 2⁷³ + 2⁷⁴)
Expression = 2⁷¹ (1 +2 + 4 + 8)
= 2⁷¹ × 15 = 2⁷¹ × 3 × 5 , Which is exactly divisible by 10.
Therefore required answer is 10 .

Let required number be p.
According to question ,
∴  0.022 × p = 66

Correct Option: A

Let required number be p.
According to question ,
∴  0.022 × p = 66

Expression = 3²⁵ + 3²⁶ + 3²⁷ + 3²⁸
= 3²⁵ (1 + 3 + 3² + 3³)

Correct Option: D

Expression = 3²⁵ + 3²⁶ + 3²⁷ + 3²⁸
= 3²⁵ (1 + 3 + 3² + 3³)
= 3²⁵ (1 + 3 + 9 + 27)
= 3²⁵ × 40, which is clearly divisible by 30.
Hence the given expression is divisible by 30.

A number is divisible by 11 if the difference of the sum of digits at odd and even places be either zero or multiple of 11.

Correct Option: D

A number is divisible by 11 if the difference of the sum of digits at odd and even places be either zero or multiple of 11. If the middle digit be 4, then 24442 or 244442 etc are divisible by 11.

Let the unit digit be p and ten’s digit be q.
∴ Number = 1000q + 100p + 10q + p
Number = 1010q + 101p = 101(10q + p)

Correct Option: D

Let the unit digit be p and ten’s digit be q.
∴ Number = 1000q + 100p + 10q + p
Number = 1010q + 101p = 101(10q + p)
Clearly, this number is divisible by 101, which is the smallest three-digit prime number.