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

Determinants

JEE Main 2025 (Online) 29th January Morning ShiftMCQMedium📈 Topic in 19% papers+4−1
Ques. 1JEE 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

Answer

(1) 1280

Solution

Applying C1 C1 + C2 + C3, every entry of C1 becomes 1 + 2 x + 2 x + 4 4x = 2 + 4 4x, so

f(x) = (2 + 4 4x) vmatrix 1 & 2 x & 4 4x \ 1 & 1 + 2 x & 4 4x \ 1 & 2 x & 1 + 4 4x vmatrix

Then R2 R2 - R1, R3 R3 - R1 gives

f(x) = (2 + 4 4x) vmatrix 1 & 2 x & 4 4x \ 0 & 1 & 0 \ 0 & 0 & 1 vmatrix = 2 + 4 4x

-1 4x 1, M = 6 and m = -2.

M4 - m4 = 1296 - 16 = 1280

Answer: (1)

Keep practising — Determinants

Ques. 2JEE 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. 3JEE 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. 4JEE 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. 5JEE 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. 6JEE 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. 7JEE 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. 8JEE 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. 9JEE 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. 10JEE 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 :

  1. 12
  2. 9
  3. 22
  4. 16
Ques. 11JEE 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 :

  1. 56
  2. 132
  3. 174
  4. 280

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)