Determinants

JEE Main 2025 (Online) 23rd January Evening ShiftMCQMedium📈 Topic in 50% papers+4−1

Ques. 1JEE Main 2025, 23 January (Evening Shift)

The system of equations x+y+z=6, x+2y+5z=9, x+5y+ z= , has no solution if

=17, =18
=17, 18
=15, 17
17, 18

Answer

(2) =17, 18

Solution

= vmatrix1&1&1\\1&2&5\\1&5& vmatrix= -17=0 =17 (no unique solution).

Reduce: R2-R1: y+4z=3; R3-R1: 4y+( -1)z= -6; R3-4(R2-R1): ( -17)z= -18.

For =17: 0 z= -18, which is impossible when 18.

=17, 18

Answer: (2)

Keep practising — Determinants

Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let A be a square matrix of order 3 such that (A)=-2 and (3 adj (-6 adj(3A) ) )=2m+n 3mn, m>n. Then 4m+2n is equal to .

Ques. 3JEE Main 2025, 22 January (Evening Shift)

If the system of linear equations : x+y+2z=6 2x+3y+az=a+1 -x-3y+bz=2b where a,b , has infinitely many solutions, then 7a+3b is equal to :

Ques. 4JEE Main 2025, 22 January (Evening Shift)

For a 3 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 3 matrix such that |A|= 12 and trace (A)=3. If B=adj(adj(2A)), then the value of |B|+ trace (B) equals :

All Determinants PYQs →

PDFDownload Determinants 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)