Question

If f(x) = \(\begin{vmatrix}x^n & x^{n+2} & x^{2n} \\1 & x^p & p \\x^{n+5} & x^{p+6} & x^{2n+5} \end {vmatrix}\) = 0,then what will be the value of p?

(a) x^n

(b) (n + 1)

(c) Either x^n or (n + 1)

(d) Both x^n and (n + 1)

I had been asked this question during an interview for a job.

I need to ask this question from Application of Determinants in division Determinants of Mathematics – Class 12

Answer 1

Correct option is (d) Both x^n and (n + 1)

To explain I would say: Here, C1 and C3 becomes equal when we put p = x^n

And R1 and R3 becomes equal when we put p = n + 1

As both of the conditions are satisfied so d is the correct one.