Determinants

JEE Main 2025 (Online) 22nd January Evening ShiftMCQMedium📈 Topic in 50% papers+4−1

Ques. 1JEE 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 :

Answer

(4) 16

Solution

R2-2R1: y+(a-4)z=a-11

R3+R1: -2y+(b+2)z=2b+6

Eliminate y: (2a+b-6) z=2a+2b-16

Infinitely many solutions both sides =0

2a+b=6, 2a+2b=16

b=10, a=-2

7a+3b=-14+30=16

Answer: (4)

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Ques. 2JEE 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 :

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