Matrices

JEE Main 2025 (Online) 28th January Evening ShiftMCQMedium📈 Topic in 8% papers+4−1

Ques. 1JEE 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

Answer

(4) 65

Solution

P P = bmatrix & \ - & bmatrix bmatrix & - \ & bmatrix = I, so P is orthogonal.

B2 = PAP PAP = PA2P

B10 = PA10P

C = P (PA10P )P = A10

A is upper triangular, so A10 is upper triangular with diagonal elements ( 1 2 )10 and 110.

sum of diagonal elements of C = 132 + 1 = 3332

m = 33, n = 32 (coprime)

m + n = 65

Answer: (4)

Keep practising — Matrices

Ques. 2JEE 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. 3JEE 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. 4JEE 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

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