The remainder left out when 8²ⁿ –(62)²ⁿ⁺¹ is divided by 9 is 

• 0

• 2

• 7

• 7

B.

2

8²ⁿ – (62)^{2n + 1}
⇒ (9 – 1)²ⁿ – (63 – 1)^{2n + 1}
⇒ (²ⁿC₀ 9²ⁿ–²ⁿC₁ 9^{2n – 1} + ….. + ²ⁿC_2n)
– (2n + ¹C₀ 63^{2n + 1}–2n + ¹C₁ 63²ⁿ + ….
–^{2n +1}C_2n + 1
Clearly remainder is ‘2’.