JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q4

MathematicsSingle correct+4 / -1Question 4 of 90

The system of equations
$-kx+3y-14z=25$
$-15x+4y-kz=3$
$-4x+y+3z=4$
is consistent for all $k$ in the set

\mathbb R

\mathbb R-\{-11,13\}

\mathbb R-\{13\}

\mathbb R-\{-11,11\}

Answer and worked solution

Official answer: D

Determinant.
$\begin{vmatrix}-k&3&-14\\-15&4&-k\\-4&1&3\end{vmatrix}=-k(12+k)-3(-45-4k)-14(1)=121-k^2.$

Unique solution (hence consistent) whenever $k\ne\pm11$ . The keyed set is $\mathbb R-\{-11,11\}$ .

(D)

JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 4