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

Determinants

JEE Main 2025 (Online) 7th April Evening ShiftMCQHard📈 Topic in 59% papers+4−1
Ques. 1JEE Main 2025, 7 April (Evening Shift)

Let the system of equations x + 5y - z = 1 4x + 3y - 3z = 7 24x + y + z = , R, have infinitely many solutions. Then the number of the solutions of this system, if x, y, z are integers and satisfy 7 x + y + z 77, is :

  1. 4
  2. 5
  3. 3
  4. 6

Answer

(3) 3

Solution

For infinitely many solutions, = 0:

vmatrix 1 & 5 & -1 \ 4 & 3 & -3 \ 24 & 1 & vmatrix = (3 + 3) - 5(4 + 72) - (4 - 72) = 0

-17 - 289 = 0 = -17

The third equation must then be a combination a(I) + b(II):

a + 4b = 24, 5a + 3b = 1 b = 7, a = -4 (z-coefficient: -a - 3b = -17 ✓)

= a(1) + b(7) = -4 + 49 = 45

Solving the first two equations with z = t:

x + 5y = 1 + t, 4x + 3y = 7 + 3t

y = t - 317, x = 12t + 3217

For integer y put t = 17k + 3 (k Z), so x = 12k + 4, y = k, z = 17k + 3 are all integers and

x + y + z = 30k + 7

7 30k + 7 77 0 k 73 k = 0, 1, 2

number of integer solutions = 3

Answer: (3)

Keep practising — Determinants

Ques. 2JEE Main 2025, 3 April (Morning Shift)

If y(x) = vmatrix x & x & x+ x+1 \ 27 & 28 & 27 \ 1 & 1 & 1 vmatrix, x R, then d2ydx2 + y is equal to

  1. 28
  2. 27
  3. -1
  4. 1
Ques. 3JEE Main 2025, 3 April (Morning Shift)

Let A be a matrix of order 3 3 and |A| = 5. If |2 adj(3A adj(2A))| = 2 3 5 , , , N, then + + is equal to

  1. 26
  2. 27
  3. 25
  4. 28
Ques. 4JEE Main 2025, 3 April (Evening Shift)

Let I be the identity matrix of order 3 3 and for the matrix A = bmatrix & 2 & 3 \ 4 & 5 & 6 \ 7 & -1 & 2 bmatrix, |A| = -1. Let B be the inverse of the matrix adj (A adj (A2 ) ). Then |( B + I)| is equal to

Ques. 5JEE Main 2025, 2 April (Morning Shift)

Let a R and A be a matrix of order 3 3 such that (A) = -4 and A + I = bmatrix 1 & a & 1 \ 2 & 1 & 0 \ a & 1 & 2 bmatrix, where I is the identity matrix of order 3 3. If ((a + 1) adj((a - 1)A)) is 2m 3n, m, n \0, 1, 2, , 20\, then m + n is equal to :

  1. 14
  2. 17
  3. 15
  4. 16
Ques. 6JEE Main 2025, 2 April (Morning Shift)

If the system of linear equations 3x + y + z = 3 2x + y - z = -3 x + 2y + z = 4 has infinitely many solutions, then the value of 22 - 9 is :

  1. 31
  2. 37
  3. 43
  4. 49
Ques. 7JEE 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
Ques. 8JEE 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. 9JEE 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. 10JEE 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. 11JEE 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

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)