As we know that ,
3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243
i.e. unit’s digit is repeated after index 4.
Remainder after dividing 21 by 4 = 1

Correct Option: C

As we know that ,
3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243
i.e. unit’s digit is repeated after index 4.
Remainder after dividing 21 by 4 = 1
∴  Unit’s digit in the expansion of (3)²¹ = 3
∴  Remainder after dividing by 5 = 3

If n is divisible by 5 then remainder = 2.
Required remainder = Remainder obtained by dividing 2² by 5.

Correct Option: D

If n is divisible by 5 then remainder = 2.
Required remainder = Remainder obtained by dividing 2² by 5.
Hence Remainder = 4

Here, the first divisor (221) is a multiple of second divisor (13)

Correct Option: D

Here, the first divisor (221) is a multiple of second divisor (13)
Hence, required remainder = remainder obtained on dividing 64 by 13 = 12

Let two numbers are P and Q.
According to question ,
First number (P) = 17p + 13
Second number (Q) = 17q + 11

Correct Option: C

Let two numbers are P and Q.
According to question ,
First number (P) = 17p + 13
Second number (Q) = 17q + 11

If the first divisor be a multiple of the second divisor, then
Required remainder = remainder obtained by dividing the first remainder (36) by the second divisor (17)

Correct Option: D

If the first divisor be a multiple of the second divisor, then
Required remainder = remainder obtained by dividing the first remainder (36) by the second divisor (17)
⇒ 36 = ( 17 × 2 ) + 2
Hence , Required remainder = 2