5⁷¹ + 5⁷² + 5⁷³ = 5⁷¹ (1 + 5 + 5²)

Correct Option: C

5⁷¹ + 5⁷² + 5⁷³ = 5⁷¹ (1 + 5 + 5²)
⇒ 5⁷¹ + 5⁷² + ⇒ 5⁷³ = 5⁷¹ × which is exactly divisible by 155.
Hence required answer is 155 .

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 .

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.

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

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