The value of ​|(5^2,5^3,5^4)(5^3,5^4,5^5)(5^4,5^5,5^6)| is

Question

Mark the correct alternative in the following :

The value of \(\begin{vmatrix} 5^2 & 5^3& 5^4 \\[0.3em] 5^3 & 5^4 &5^5\\[0.3em] 5^4 & 5^5 &5^6 \end{vmatrix}\) is

A. 5² 

B. 0 

C. 5¹³ 

D. 5⁹

Answer 1

Correct answer is B.

Δ =\(\begin{vmatrix} 5^2 & 5^3& 5^4 \\[0.3em] 5^3 & 5^4 &5^5\\[0.3em] 5^4 & 5^5 &5^6 \end{vmatrix}\)

Δ = \(5^9\begin{vmatrix} 1 & 5& 5^2 \\[0.3em] 1 & 5 &5^2\\[0.3em] 1 & 5 &5^2 \end{vmatrix}\)

Δ = \(5^95^3\begin{vmatrix} 1 & 1& 1 \\[0.3em] 1 & 1 &1\\[0.3em] 1 & 1 &1 \end{vmatrix}\)

∆ = 0