JEE Advanced Determinants — previous year questions
33 questions from 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2008.
- Consider the matrix M = 2 -1 1 0 Let p, q, r, s, a, b, c and d be integers such that M²⁶ = p q r s and ∑ₖ₌₁²⁶…
- Let I = 1 0 0 1 and P = 2 0 0 3 . Let Q = x y z 4 for some non-zero real numbers x, y and z, for which there…
- Let S = { A = 0 1 c 1 a d 1 b e : a, b, c, d, e ∈ {0,1} and |A| ∈ {-1,1} } where |A| denotes the determinant…
- Let α and β be the distinct roots of the equation x²+x-1=0. Consider the set T = {1, α, β} For a 3 × 3 matrix…
- Let M = (aᵢⱼ), i, j ∈ {1, 2, 3}, be the 3 × 3 matrix such that aᵢⱼ = 1 if j + 1 is divisible by i, otherwise…
- Let α, β and γ be real numbers. Consider the following system of linear equations x + 2y + z = 7 x + α z = 11…
- Let |M| denote the determinant of a square matrix M. Let g:[0,π/2]→R be the function defined by where…
- Let p, q, r be nonzero real numbers that are, respectively, the 10ᵗʰ, 100ᵗʰ and 1000ᵗʰ terms of a harmonic…
- For any 3 × 3 matrix M, let |M| denote the determinant of M. Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0…
- For any 3 × 3 matrix M, let |M| denote the determinant of M. Let I be the 3 × 3 identity matrix. Let E and F…
- The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 × 2 matrix such…
- Let M be a 3 × 3 invertible matrix with real entries and let I denote the 3 × 3 identity matrix. If M⁻¹ = adj…
- Let P₁ = I = 1 0 0 0 1 0 0 0 1 , P₂ = 1 0 0 0 0 1 0 1 1 , P₃ = 0 1 0 1 0 0 0 0 1 , P₄ = 0 1 0 0 0 1 1 0 0 ,…
- Let M = 0 1 a 1 2 3 3 b 1 and (adj M) = -1 1 -1 8 -6 2 -5 3 -1 where a and b are real numbers. Which of the…
- Let x ∈ R and let P = 1 1 1 0 2 2 0 0 3 , Q = 2 x x 0 4 0 x x 6 and R = PQP⁻¹. Then which of the following…
- Let P be a matrix of order 3 x 3 such that all the entries in P are from the set {-1, 0, 1}. Then, the…
- Let S be the set of all column matrices b₁ b₂ b₃ such that b₁, b₂, b₃ ∈ R and the system of equations (in…
- Which of the following is(are) not the square of a 3 × 3 matrix with real entries?
- For a real number α, if the system 1 α α² α 1 α α² α 1 x y z = 1 -1 1 of linear equations, has infinitely…
- Let z = (-1 + √3i)/2, where i = √(-1), and r, s ∈ {1, 2, 3}. Let P = (-z)ʳ z²ˢ z²ˢ zʳ and I be the identity…
- Let a, λ, μ ∈ R. Consider the system of linear equations ax + 2y = λ 3x - 2y = μ Which of the following…
- Which of the following values of α satisfy the equation (1+α)² (1+2α)² (1+3α)² (2+α)² (2+2α)² (2+3α)² (3+α)²…
- Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠ N² and M² = N⁴, then
- Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if
- For 3 × 3 matrices M and N, which of the following statement(s) is (are) NOT correct?
- Let P = [aᵢⱼ] be a 3 × 3 matrix and let Q = [bᵢⱼ], where bᵢⱼ = 2ⁱ⁺ʲ aᵢⱼ for 1 ≤ i, j ≤ 3. If the determinant…
- Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form 1 a b ω 1 c ω² ω…
- Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If P^T denotes the…
- Let ω be the complex number cos 2π/3+isin 2π/3. Then the number of distinct complex numbers z satisfying z+1…
- Let k be a positive real number and let A = 2k-1 2√k 2√k 2√k 1 -2k -2√k 2k -1 and B = 0 2k-1 √k 1-2k 0 2√k…
- The number of 3 × 3 matrices A whose entries are either 0 or 1 and for which the system A x y z = 1 0 0 has…
- Consider three points P = (-sin(β-α), -cosβ), Q = (cos(β-α), sinβ) and R = (cos(β-α+θ), sin(β-θ)), where 0 <…
- Consider the system of equations x - 2y + 3z = -1; -x + y - 2z = k; x - 3y + 4z = 1 \ Statement-I : The…