PrepWiser › Learn › Mathematics › DeterminantsDeterminants — JEE Main PYQs & Practice Questions Determinants is a Mathematics chapter in the JEE Main syllabus. This page brings together 196 previous-year and practice questions on Determinants, organised into 5 topics: Properties of Determinants, Minors and Cofactors, Adjoint and Inverse, Cramer's Rule and Consistency of Linear Equations. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Properties of Determinants Let A = [aᵢⱼ] be a 3 × 3 matrix, where aᵢⱼ = { 1, ,, if i = j; - x, ,, if | i - j | = 1… The determinant of an upper triangular matrix is the x of its diagonal elements. If x, y, z are in arithmetic progression with common difference d, x ≠ 3d, and the… The number of singular matrices of order 2 , whose elements are from the set {2,3,6,9}… If α ≠ a, β ≠ b, γ ≠ c and |α, b, c; a, β, c; a, b, γ|=0, then a/(α-a)+b/(β-b)+γ/(γ-c)… Let A = [ 1, - 2, α; α, 2, - 1 ] and B = [ 2, α; - 1, 2; 4, - 5 ], α ∈ C. Then the… The maximum value of f(x) = | sin ²x, 1 + cos ²x, cos 2x; 1 + sin ²x, cos ²x, cos 2x… The value of | (a + 1)(a + 2), a + 2, 1; (a + 2)(a + 3), a + 3, 1; (a + 3)(a + 4), a +… Let A be a matrix of order 3 × 3 and |A|=5. If |2 adj(3 A adj(2 A))|=2^α · 3^β · 5^γ, α… Let M and m respectively be the maximum and the minimum values of f(x)=|1+sin ² x, cos ²… If A is a 3 × 3 matrix and |A| = 2, then |3 adj (|3A|A²)| is equal to : If A is a square matrix of order 3 such that det(A)=3 and det(adj(-4 adj(-3 adj(3 adj((2… Let a ∈ R and A be a matrix of order 3 × 3 such that det(A)=-4 and A+I=[1, a, 1; 2, 1… Let A be a square matrix of order 3 such that det(A)=-2 and det(3 adj(-6 adj(3 A)))=2ᵐ⁺ⁿ… Let A be a 3 × 3 matrix with det(A) = 4. Let Rᵢ denote the iᵗʰ row of A. If a matrix B… Let A and B be two square matrices of order 2. If det (A) = 2, det (B) = 3 and det (… Let A = [ a, b; c, d ] and B = [ α; β ] ≠ [ 0; 0 ] such that AB = B and a + d = 2021… Let f(x) = | sin ²x, - 2 + cos ²x, cos 2x; 2 + sin ²x, cos ²x, cos 2x; sin ²x, cos ²x, 1… The solutions of the equation | 1 + sin ²x, sin ²x, sin ²x; cos ²x, 1 + cos ²x, cos ²x… If A=[√2, 1; -1, √2], B=[1, 0; 1, 1], C=ABAᵀ and X=Aᵀ C² A, then det X is equal to : Minors and Cofactors Let A = [aᵢⱼ] = [log₅ 128, log₄ 5; log₅ 8, log₄ 25] . If Aᵢⱼ is the cofactor of aᵢⱼ… Let α β ≠ 0 and A=[β, α, 3; α, α, β; -β, α, 2 α]. If B=[3 α, -9, 3 α; -α, 7, -2 α; -2 α… Adjoint and Inverse Let A be a matrix of order 3 × 3 and det (A) = 2. Then det (det (A) adj (5 adj (A³))) is… Let A = [2, 2+p, 2+p+q; 4, 6+2p, 8+3p+2q; 6, 12+3p, 20+6p+3q] . If det(adj(adj(3A))) =… Let A be a 3 × 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|² is… Let S = √n : 1 ≤ n ≤ 50 and n is odd. Let a ∈ S and A = [ 1, 0, a; - 1, 1, 0; - a, 0, 1… Let A be a 3 × 3 matrix such that Xᵀ AX=O for all nonzero 3 × 1 matrices X=[x; y; z]. If… Let A be a 3 × 3 matrix such that |adj(adj(adj A))|=81. If S={n ∈ ℤ:(|adj(adj… Let P=[pᵢⱼ] and Q=[qᵢⱼ] be two square matrices of order 3 such that qᵢⱼ=2⁽ⁱ⁺ʲ⁻¹⁾pᵢⱼ and… Let A be a 3× 3 matrix such that A+Aᵀ=O. If A[1; -1; 0]=[3; 3; 2],A²[1; -1; 0]=[-3; 19… Let the matrix A=[0, 1, 0; 0, 0, 1; 1, 0, 0] and the matrix B₀=A⁴⁹+2 A⁹⁸. If Bₙ=A d… The positive value of the determinant of the matrix A, whose Adj(Adj(A)) = ( 14, 28, -… Let A be a 3 × 3 matrix such that adj A = [ 2, - 1, 1; - 1, 0, 2; 1, - 2, - 1 ] and B =… Let I be the identity matrix of order 3 × 3 and for the matrix A=[λ, 2, 3; 4, 5, 6; 7… Let A and B be two 3 × 3 matrices such that AB = I and |A| = 1/8. Then |adj (B adj(2A))|… If X=[x; y; z] is a solution of the system of equations AX=B, where adjA=[4, 2, 2; -5… Let A=[2, 1, 0; 1, 2, -1; 0, -1, 2]. If |adj(adj(adj 2 A))|=(16)ⁿ, then n is equal to : Let A=[1, 1, 2; -2, 0, 1; 1, 3, 5]. Then the sum of all elements of the matrix… If A = [ 2, 3; 0, - 1 ], then the value of det(A⁴) + det(A¹⁰ - (Adj(2A))¹⁰) is equal to… For a 3 × 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M… Let x,y,z > 1 and A = [ 1, log ₓy, log ₓz; log _yx, 2, log _yz; log _zx, log _zy, 3 ]… Let |A|=6, where A is a 3× 3 matrix. If |adj(3adj(A²· adj(2 A)))|=2ᵐ· 3ⁿ,m,n∈ N, then… Cramer's Rule Consistency of Linear Equations If the system of equations x+2y+3z=3 4x+3y-4z=4 8x+4y-λ z=9+μ has infinitely many… The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is… Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is… Let α, β (α ≠ β) be the values of m , for which the equations x+y+z=1 , x+2y+4z=m and… If the system of equations kx + y + 2z = 1 3x - y - 2z = 2 -2x -2y -4z = 3 has… If the system of linear equations x-2 y+z=-4 ; 2 x+α y+3 z=5 ; 3 x-y+β z=3 has… Let n be the number obtained on rolling a fair die. If the probability that the system… Let α,β∈ ℝ be such that the system of linear equations x+2y+z, =5; 2x+y+α z, =5; 8x+4y+β… The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no… The values of m, n, for which the system of equations x+y+z=4, ; 2 x+5 y+5 z=17, ; x+2… For the system of linear equations α x+y+z=1,x+α y+z=1,x+y+α z=β, which one of the… The number of values of α for which the system of equations : x + y + z = α αx + 2αy +… Let S be the set of values of λ, for which the system of equations 6 λ x-3 y+3 z=4 λ², 2… Let the system of linear equations x+y+kz=2 2x+3y-z=1 3x+4y+2z=k have infinitely many… Let the system of equations : 2 x+3 y+5 z=9 ; 7 x+3 y-2 z=8 ; 12 x+3 y-(4+λ) z=16-μ have… Let S be the set of all integer solutions, (x, y, z), of the system of equations x – 2y… If the system of equations 2 x-y+z=4 ; 5 x+λ y+3 z=12 ; 100 x-47 y+μ z=212 has… Let S be the set of all λ ∈ R for which the system of linear equations 2x – y + 2z = 2 x… If the system of linear equations : x+y+2 z=6 ; 2 x+3 y+az=a+1 ; -x-3 y+b z=2 b where a… If the system of equations (λ-1) x+(λ-4) y+λ z=5 ; λ x+(λ-1) y+(λ-4) z=7 ; (λ+1) x+(λ+2)… More Mathematics chapters Frequently asked questions How many Determinants questions are there for JEE Main? PrepWiser has 196 Determinants questions for JEE Main, grouped into 5 topics such as Properties of Determinants, Minors and Cofactors and Adjoint and Inverse.
Are these Determinants questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Determinants questions? Open any Determinants question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.