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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Determinants

The values of m, n , for which the system of equations aligned &...

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

Options

  1. Am2+n2−mn=39m^2+n^2-m n=39
  2. Bm2+n2−m−n=46m^2+n^2-m-n=46
  3. Cm2+n2+m+n=64m^2+n^2+m+n=64
  4. Dm2+n2+mn=68m^2+n^2+m n=68

Correct answer

A. m2+n2−mn=39m^2+n^2-m n=39

Step-by-step solution

D=∣11125512 m∣=0⇒m=2D3=∣114251712n∣=0⇒n=7\begin{aligned} & \mathrm{D}=\left|\begin{array}{lll}1 & 1 & 1 \\ 2 & 5 & 5 \\ 1 & 2 & \mathrm{~m}\end{array}\right|=0 \Rightarrow \mathrm{m}=2 \\ & \mathrm{D}_3=\left|\begin{array}{ccc}1 & 1 & 4 \\ 2 & 5 & 17 \\ 1 & 2 & \mathrm{n}\end{array}\right|=0 \Rightarrow \mathrm{n}=7\end{aligned}
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