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Determinants

JEE Main 2024 (Online) 6th April Evening ShiftMCQMedium📈 Topic in 38% papers+4−1
Ques. 1JEE Main 2024, 6 April (Evening Shift)

If A is a square matrix of order 3 such that (A) = 3 and (adj(-4 adj(-3 adj(3 adj((2A)-1))))) = 2m3n, then m + 2n is equal to :

  1. 2
  2. 4
  3. 3
  4. 6

Answer

(2) 4

Solution

For order 3: |adj M| = |M|2, |kM| = k3|M|, |M-1| = 1|M|

Determinants from the innermost bracket outwards:

|(2A)-1| = 123 3 = 2-33-1, its adj: 2-63-2

Times 3: 33 2-63-2 = 2-631, its adj: 2-1232

Times (-3): -27 2-1232 = -2-1235, its adj: 2-24310

Times (-4): -64 2-24310 = -2-18310, its adj: 2-36320

∴ m = -36, n = 20 ⇒ m + 2n = -36 + 40 = 4

Answer: (2)

Keep practising — Determinants

Ques. 2JEE Main 2024, 6 April (Evening Shift)

If the system of equations 2x + 7y + z = 3 3x + 2y + 5z = 4 x + y + 32z = -1 has infinitely many solutions, then ( - ) is equal to :

Ques. 3JEE Main 2024, 5 April (Morning Shift)

Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |ATA(adj(2 A))-1(adj(4 B))(adj(AB))-1AAT| is equal to :

  1. 32
  2. 81
  3. 64
  4. 108
Ques. 4JEE Main 2024, 5 April (Morning Shift)

If the system of equations 11x + y + z = -5 2x + 3y + 5z = 3 8x - 19y - 39z = has infinitely many solutions, then 4 - is equal to :

  1. 51
  2. 45
  3. 47
  4. 49
Ques. 5JEE Main 2024, 5 April (Evening Shift)

The values of m, n, for which the system of equations x + y + z = 4, 2x + 5y + 5z = 17, x + 2y + mz = n has infinitely many solutions, satisfy the equation :

  1. m2 + n2 - m - n = 46
  2. m2 + n2 + mn = 68
  3. m2 + n2 - mn = 39
  4. m2 + n2 + m + n = 64
Ques. 6JEE Main 2024, 5 April (Evening Shift)

Let 0 and A = bmatrix & & 3 \ & & \ - & & 2 bmatrix. If B = bmatrix 3 & -9 & 3 \ - & 7 & -2 \ -2 & 5 & -2 bmatrix is the matrix of cofactors of the elements of A, then (AB) is equal to :

  1. 64
  2. 343
  3. 125
  4. 216
Ques. 7JEE Main 2024, 4 April (Morning Shift)

Let (0, ) and A= bmatrix1 & 2 & \ 1 & 0 & 1 \ 0 & 1 & 2 bmatrix. If det ( adj (2A-AT ) adj (A-2AT ) )=28, then ( det(A))2 is equal to:

  1. 16
  2. 36
  3. 49
  4. 1
Ques. 8JEE Main 2024, 4 April (Morning Shift)

If the system of equations x+( 2 )y+( 2 )z=0 x+( )y+( )z=0 x+( )y-( )z=0 has a non-trivial solution, then (0, 2 ) is equal to :

  1. 5 24
  2. 11 24
  3. 7 24
  4. 3 4
Ques. 9JEE Main 2024, 4 April (Morning Shift)

Let A be a 3 3 matrix of non-negative real elements such that A bmatrix1\\1\\1 bmatrix=3 bmatrix1\\1\\1 bmatrix. Then the maximum value of (A) is .

Ques. 10JEE Main 2024, 1 February (Morning Shift)

If A= bmatrix 2 & 1\ -1 & 2 bmatrix, B= bmatrix1 & 0\ 1 & 1 bmatrix, C=ABAT and X=ATC2A, then is equal to :

  1. 243
  2. 729
  3. 27
  4. 891
Ques. 11JEE Main 2024, 1 February (Morning Shift)

If the system of equations 2x+3y-z=5 x+ y+3z=-4 3x-y+ z=7 has infinitely many solutions, then 13 is equal to :

  1. 1110
  2. 1120
  3. 1210
  4. 1220

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