Mathematics · Matrices

JEE Main 2025 — 24 January, Evening Shift — Question 17

Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $\mathrm{P}(\mathrm{E})$ is :

Option A:
$\frac{5}{8}$
Option B:
$\frac{3}{16}$
Option C:
$\frac{1}{8}$
Option D:
$\frac{3}{8}$
Correct

Answer: D

Step-by-step solution

C-I $\left|\begin{array}{ll}1 & 1\\ 0 & 1\end{array}\right| \rightarrow 4$ ways

C-II $\left|\begin{array}{ll}1 & 0 \\0 & 1\end{array}\right| \&\left|\begin{array}{ll}0 & 1 \\1 & 0\end{array}\right| \rightarrow 2$ ways

$\mathrm{P}=\frac{\text { favourable }}{\text { total }}=\frac{6}{16}=\frac{3}{8}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 24 January, Evening Shift
Subject: Mathematics
Chapter: Matrices
Topic: Inverse of a Matrix

If the system of equations x+2 y-3 z=2 2 x+lambda y+5 z=5 14 x+3 y+mu z=33 has infinitely many solutions, then lambda+mu is equal to:

Answer: D

Step-by-step solution

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