Determinants

JEE Main 2025 (Online) 22nd January Morning ShiftNumericalMedium📈 Topic in 42% papers+4

Ques. 1JEE 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 .

Answer

Solution

For order 3: (kM)=k3 M and ( adjM)=( M)2.

(3A)=-54; for N=-6 adj(3A): N=(-6)3 542

(3 adjN)=27( N)2=27 2162 544=210 321

m+n=10, mn=21, m>n m=7, n=3

4m+2n=34

Answer: 34

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Ques. 2JEE 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. 3JEE 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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