∵ 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.

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 .

∴ The required number = 11 – 4 = 7
2nd Method to solve this question :
Sum of digits at odd places = 2 + 6 + 0 = 8

Correct Option: C

∴ The required number = 11 – 4 = 7
2nd Method to solve this question :
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

[n] < n (integer); (n) > n (integer)
∴ Expression

	1	1		×		1	1		−		1	1		÷		1	1		+ (1.5) = 2 × 1 – 2 ÷ 1 + 2
		5					5					5					5

Correct Option: B

[n] < n (integer); (n) > n (integer)
∴ Expression

	1	1		×		1	1		−		1	1		÷		1	1		+ (1.5) = 2 × 1 – 2 ÷ 1 + 2 = 2
		5					5					5					5

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