Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20257 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Matrices

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Matrices

The number of singular matrices of order 2 , whose elements are...

The number of singular matrices of order 2 , whose elements are from the set {2,3,6,9}\{2,3,6,9\} is

Correct answer

36

Step-by-step solution

\left|<br/>a d bc<br/>\begin{array}{ll}<br/>\mathrm{a} & \mathrm{~d} \\ \mathrm{~b} & \mathrm{c}<br/>\end{array}\right|=$\mathrm{ad}-\mathrm{bc}$ \Rightarrow $\mathrm{ad}=\mathrm{bc}$<br/>Case-I Exactly 1 no. is used<br/>$\Rightarrow \text{ All singular }={ }^4 \mathrm{C}_1<br/>Case-II$ Exactly 2 no. is used<br/>$\Rightarrow{ }^4 \mathrm{C}_2 \times 2 \times 2$<br/>Case-III Exactly 3 no. is used<br/>None will be singular<br/>Case-IV Exactly 4 No. is used<br/>ad=bc<br/>\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}$<br/>Total<br/>Total=36$
Practice Matrices on Quantrex Academy →

More from Matrices

Which one of the following matrices can be obtained by performing elementary row… JEE Advanced 2026Consider the matrix M = bmatrix 2 & -1 1 & 0 bmatrix . Let p, q, r, s, a, b, c and d be… JEE Advanced 2026For real numbers α, β, γ, δ and μ , consider the matrix M = bmatrix α & 1 2 & - 1 2 1 3 &… JEE Advanced 2026Let ℝ denote the set of all real numbers and let i = -1 . Consider the matrices S =… JEE Advanced 2026Let A = bmatrix α & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5α &… JEE Main 2026Let A = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and B = [b_ ij ] , 1 ≤ i, j ≤ 3 .… JEE Main 2026Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + α(adj(adj(A))) +… JEE Main 2026Let M be a 3 × 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M… JEE Main 2026Let A be a 3 × 3 matrix such that A^T bmatrix 1 0 1 bmatrix = bmatrix 5 2 2 bmatrix , A^T… JEE Main 2026Let A= bmatrix 1 & 2 & 7 4 & -2 & 8 3 & 8 & -7 bmatrix and (A-α I)=0 , where α is a real… JEE Main 2026Let S = \ A = bmatrix a & b c & d bmatrix : a, b, c, d ∈ \ 0, 1, 2, 3, 4\ and A^2 - 4A +… JEE Main 2026Let A = bmatrix 1 & 1 & 2 -2 & 0 & 1 1 & 3 & 5 bmatrix . Then the sum of all elements of… JEE Main 2026Consider the matrices A = bmatrix 2 & -2 4 & -2 bmatrix and B = bmatrix 3 & 9 1 & 3… JEE Main 2026Let A = bmatrix 1 & 2 1 & α bmatrix and B = bmatrix 3 & 3 β & 2 bmatrix . If A^2 - 4A + I… JEE Main 2026Let A=[ array ll 3 & -4 1 & -1 array ] and B be two matrices such that A^ 100 =100 B+I .… JEE Main 2026Let A, B and C be three 2 × 2 matrices with real entries such that B=(I+A)^ -1 and A+C=I… JEE Main 2026 Full Matrices list Matrices JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs