If (-1)ⁿ + (-1)⁴ⁿ = 0, then n is

A. Any positive integer

B. Any negative integer

C. Any odd natural number

D. Any even natural number

Answer: Option C

Solution(By Examveda Team)

Putting n = 1, 2, 3, 4, 5 . . . .
n = 1 in the given equation
(-1)¹ + (-1)^{4 × 1} = 0
Or, -1 + 1 = 0

n = 2
(-1)² + (-1)^{4 × 2} = 0
Or, 1 + 1 ≠ 0

n = 3,
-1 + 1 = 0
We will see that the given condition will be satisfy only for ANY ODD NATURAL NUMBER.