Matrices

JEE Main 2025 (Online) 28th January Morning ShiftNumericalHard📈 Topic in 5% papers+4

Ques. 1JEE Main 2025, 28 January (Morning Shift)

Let M denote the set of all real matrices of order 3 3 and let S = \-3, -2, -1, 1, 2\. Let S1 = \A = [aij] M : A = AT and aij S, i, j\, S2 = \A = [aij] M : A = -AT and aij S, i, j\, S3 = \A = [aij] M : a11 + a22 + a33 = 0 and aij S, i, j\. If n(S1 S2 S3) = 125 , then equals .

Answer

1613

Solution

S2: a skew-symmetric matrix has aii = 0, but 0 S S2 = .

S1: a symmetric matrix is fixed by its 3 diagonal and 3 upper entries n(S1) = 56.

S3: the 6 off-diagonal entries are free 56 ways.

Diagonal triples from S with sum 0:

\-3, 1, 2\: 3! = 6; \-2, 1, 1\: 3; \-1, -1, 2\: 3 12 ways

n(S3) = 12 56

S1 S3: symmetric with trace 0 n(S1 S3) = 12 53

n(S1 S2 S3) = 56 + 12 56 - 12 53

= 53(125 + 1500 - 12) = 125 1613

= 1613

Answer: 1613

Keep practising — Matrices

Ques. 2JEE Main 2025, 28 January (Evening Shift)

Let A = bmatrix 1 2 & -2 \ 0 & 1 bmatrix and P = bmatrix & - \ & bmatrix, > 0. If B = PAP , C = P B10P and the sum of the diagonal elements of C is mn, where (m, n) = 1, then m + n is :

127
2049
258
65

Ques. 3JEE Main 2025, 24 January (Morning Shift)

Let A be a 3 3 matrix such that XTAX=O for all nonzero 3 1 matrices X= bmatrixx\ \ bmatrix. If A bmatrix1\\1\\1 bmatrix= bmatrix1\\4\\-5 bmatrix, A bmatrix1\\2\\1 bmatrix= bmatrix0\\4\\-8 bmatrix, and (adj(2(A+I)))=2 3 5 , , , N, then 2+ 2+ 2 is

Ques. 4JEE Main 2025, 24 January (Evening Shift)

Let A=[aij] 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 P(E) is :

Ques. 5JEE Main 2025, 23 January (Evening Shift)

Let A=[aij] be a 3 3 matrix such that A bmatrix0\\1\\0 bmatrix= bmatrix0\\0\\1 bmatrix, A bmatrix4\\1\\3 bmatrix= bmatrix0\\1\\0 bmatrix and A bmatrix2\\1\\2 bmatrix= bmatrix1\\0\\0 bmatrix, then a23 equals :

2
-1
1
0

All Matrices PYQs →

PDFDownload Matrices PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)