The values of m, n , for which the system of equations x + y + z =4 2 x+5 y+5 z=17 x+2 y+m z=n has infinitely many solutions, satisfy the equation :

Mathematics · Determinants

JEE Main 2024 — 5 April, Shift 2 — Question 14

The values of $m, n$ , for which the system of equations $\mathrm{x}+\mathrm{y}+\mathrm{z}=4$ $2 x+5 y+5 z=17$ $x+2 y+m z=n$ has infinitely many solutions, satisfy the equation :

Option A:
$m^{2}+n^{2}-m-n=46$
Option B:
$m^{2}+n^{2}+m+n=64$
Option C:
$\mathrm{m}^{2}+\mathrm{n}^{2}+\mathrm{mn}=68$
Option D:
$m^{2}+n^{2}-m n=39$
Correct

Answer: D

Step-by-step solution

$D=\left|\begin{matrix}1&1&1\\2&5&5\\1&2&\text{}\!\!~\!\!\text{m}\\\end{matrix} \right|=0\Rightarrow \text{ }\!\!~\!\!\text{ m}=2$

$D=\left|\begin{matrix}1&1&1\\2&5&17\\1&2&\text{}\!\!~\!\!\text{n}\\\end{matrix} \right|=0\Rightarrow \text{ }\!\!~\!\!\text{ n}=7$

Answer key and solution verified before publishing.

Practise Determinants

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Mathematics
Chapter: Determinants
Topic: Consistency of Non-homogeneous system