The number formed from the last two digits (ones and tens) of the expression 2¹²ⁿ - 6⁴ⁿ , where n is any positive integer is :

A. 10

B. 00

C. 30

D. 02

Answer: Option B

Solution(By Examveda Team)

We have : (2¹²ⁿ - 6⁴ⁿ)
= (2¹²ⁿ - 2⁴ⁿ × 3⁴ⁿ)
= 2⁴ⁿ (2⁸ⁿ - 3⁴ⁿ)
Putting n = 1, we get the number 2⁴ (2⁸ - 3⁴)
= 16 (256 - 81)
= (16 × 175)
= 2800
Hence, the number formed by last two digits is 00