Atomos Test Generator Free PYQs ExamsMy practice Log in / Sign up free

Determinants

JEE Main 2025 (Online) 2nd April Evening ShiftMCQEasy📈 Topic in 50% papers+4−1
Ques. 1JEE Main 2025, 2 April (Evening Shift)

If the system of equations 2x + y + 3z = 5 3x + 2y - z = 7 4x + 5y + z = 9 has infinitely many solutions, then ( 2 + 2) is equal to :

  1. 30
  2. 26
  3. 22
  4. 18

Answer

(2) 26

Solution

The 2nd equation is not a multiple of the 1st (x and z coefficients 3, −1 against 2, 3), so for infinitely many solutions the 3rd equation must be a combination of the first two:

(4x + 5y + z - 9) = p(2x + y + 3z - 5) + q(3x + 2y - z - 7)

x: 2p + 3q = 4

constant: 5p + 7q = 9

p = -1, q = 2

y: p + 2q = 5 - + 4 = 5 = -1

z: 3p - q = = -3 - 2 = -5

Check: with = -1, = -5, = vmatrix 2 & -1 & 3 \ 3 & 2 & -1 \ 4 & 5 & -5 vmatrix = 2(-5) + 1(-11) + 3(7) = 0

2 + 2 = 1 + 25 = 26

Answer: (2)

Keep practising — Determinants

Ques. 2JEE Main 2025, 29 January (Morning Shift)

Let A = [aij] = bmatrix 5 128 & 4 5 \ 5 8 & 4 25 bmatrix. If Aij is the cofactor of aij, Cij = k=12 aikAjk, 1 i, j 2, and C = [Cij], then 8|C| is equal to :

  1. 288
  2. 262
  3. 222
  4. 242
Ques. 3JEE Main 2025, 29 January (Morning Shift)

Let M and m respectively be the maximum and the minimum values of f(x) = vmatrix 1 + 2 x & 2 x & 4 4x \ 2 x & 1 + 2 x & 4 4x \ 2 x & 2 x & 1 + 4 4x vmatrix, x R Then M4 - m4 is equal to :

  1. 1280
  2. 1040
  3. 1215
  4. 1295
Ques. 4JEE Main 2025, 29 January (Evening Shift)

Let , ( ) be the values of m, for which the equations x + y + z = 1, x + 2y + 4z = m and x + 4y + 10z = m2 have infinitely many solutions. Then the value of n=110(n + n ) is equal to :

  1. 3410
  2. 560
  3. 3080
  4. 440
Ques. 5JEE Main 2025, 24 January (Morning Shift)

If the system of equations 2x-y+z=4 5x+ y+3z=12 100x-47y+ z=212 has infinitely many solutions, then -2 is equal to

  1. 56
  2. 59
  3. 57
  4. 55
Ques. 6JEE Main 2025, 24 January (Evening Shift)

For some a,b, let f(x)= vmatrixa+ xx&1&b\ &1+ xx&b\ &1&b+ xx vmatrix, x 0, x 0f(x)= + a+ b. Then ( + + )2 is equal to :

  1. 25
  2. 16
  3. 9
  4. 36
Ques. 7JEE Main 2025, 24 January (Evening Shift)

If the system of equations x+2y-3z=2 2x+ y+5z=5 14x+3y+ z=33 has infinitely many solutions, then + is equal to :

  1. 13
  2. 10
  3. 12
  4. 11
Ques. 8JEE Main 2025, 23 January (Morning Shift)

If the system of equations ( -1)x+( -4)y+ z=5 x+( -1)y+( -4)z=7 ( +1)x+( +2)y-( +2)z=9 has infinitely many solutions, then 2+ is equal to

  1. 20
  2. 10
  3. 6
  4. 12
Ques. 9JEE Main 2025, 23 January (Morning Shift)

If A, B, and (adj (A-1 )+adj (B-1 ) ) are non-singular matrices of same order, then the inverse of A (adj (A-1 )+adj (B-1 ) )-1B, is equal to

  1. AB-1|A|+ BA-1|B|
  2. adj (B-1 )+adj (A-1 )
  3. AB-1+A-1B
  4. 1|AB| (adj(B)+adj(A) )
Ques. 10JEE 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

  1. =17, =18
  2. =17, 18
  3. =15, 17
  4. 17, 18
Ques. 11JEE 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 .

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 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)