If is the number of positive integral solutions of x1 x2 x3 x4 = 210. Then which is incorrect

Since 210 = 2 . 3 . 5 . 7 the number of solution must be same as number of ways of distributing  distinct object (given prime 2,3,5,7 ) is  boxes x₁,x₂,x₃,x₄.

Thus the number of solution = 4 x 4 x 4 x 4 = 4⁴ = 2⁸

Hence,  must be a perfect square of an integer or a perfect  4^th power of an integer or a perfect  8^th power of an integer. Option (B), (C) and (D) follows.

And (A) is false since  can't be divisible by more than one prime.

Final Answer: The correct option is (A) n  must be divisible by 3 distinct primes.