JEE Main 2025 — Matrices Question with Solution
JEE Main 2025 (7 Apr Shift 1)
Question
The number of singular matrices of order 2 , whose elements are from the set is
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Show full solutionCorrect answer: 36
Correct answer
36
Step-by-step explanation
$\left|\begin{array}{ll}
\mathrm{a} & \mathrm{~d} \\ \mathrm{~b} & \mathrm{c}
\end{array}\right|=\mathrm{ad}-\mathrm{bc} \Rightarrow \mathrm{ad}=\mathrm{bc}\Rightarrow \text { All singular }={ }^4 \mathrm{C}_1\Rightarrow{ }^4 \mathrm{C}_2 \times 2 \times 2\begin{aligned} & \Rightarrow 2 \times 9=3 \times 6 \\ & \left|\begin{array}{ll}9 & - \\ - & 2\end{array}\right| \Rightarrow{ }^4 \mathrm{C}_1 \times 21\end{aligned}=36$
\mathrm{a} & \mathrm{~d} \\ \mathrm{~b} & \mathrm{c}
\end{array}\right|=\mathrm{ad}-\mathrm{bc} \Rightarrow \mathrm{ad}=\mathrm{bc}\Rightarrow \text { All singular }={ }^4 \mathrm{C}_1\Rightarrow{ }^4 \mathrm{C}_2 \times 2 \times 2\begin{aligned} & \Rightarrow 2 \times 9=3 \times 6 \\ & \left|\begin{array}{ll}9 & - \\ - & 2\end{array}\right| \Rightarrow{ }^4 \mathrm{C}_1 \times 21\end{aligned}=36$
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This is a previous-year question from JEE Main 2025, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.