Let P= [p_ i j ] and Q= [q_ i j ] be two square matrices of order 3 such that q_ ij =2^ ( i + j -1) p _ ij and det ( Q )=2^ 10 . Then the value of det ( adj ( adj P )) is:

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Quantrex Academy · Accepted Answer

Correct answer: B. 16

vmatrix 2p_ 11 & 2^2p_ 12 & 2^3p_ 13 \ 2^2p_ 21 & 2^3p_ 22 & 2^4p_ 23 \ 2^3p_ 31 & 2^4p_ 32 & 2^5p_ 33 vmatrix = 2^ 10 2^2 2 2^3 vmatrix p_ 11 & p_ 12 & p_ 13 \ 2p_ 21 & 2p_ 22 & 2p_ 23 \ 2^2p_ 31 & 2^2p_ 32 & 2^2p_ 33 vmatrix = 2^ 10 2^9 vmatrix p_ 11 & p_ 12 & p_ 13 \ p_ 21 & p_ 22 & p_ 23 \ p_ 31 & p_ 32 & p_ 33 vmatrix = 2^ 10 |P| = 2 | adj ( adj (P))| = |P|^ (n-1)^2 = |P|^4 = 2^4 = 16

JEE Main Mathematics Question (2026) — Solution

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