Determinants

CBSE Class 12 Mathematics · every board question from this chapter, 2023–2026

• If Δ_1= |1, 0, 0; 0, 2, 0; 0, 0, 3| and Δ_2= |0, 2, 0; 1, 0, 0; 0, 0, 6|, then2026
• If points (2, 3), (0, 4) and (p, 2) are collinear, then the value of p is:2026
• One of the values of x for which |cos x, sin x; - cos x, sin x| =1 is2026
• If |-1, -2, 5; -2, a, -1; 0, 4, 2 a| =-86, then the sum of all possible values of a is2026
• If B(adj B)= [1/3, 0, 0; 0, 1/3, 0; 0, 0, 1/3], then the value of det(B^-1)=2026
• If the area of Δ ABC with vertices A(3, 1), B(-2,1) and C(0, k) is 5 sq. units, then values of k are:2026
• If A(adj A)= [3, 0, 0; 0, 3, 0; 0, 0, 3], then the value of |2 A| is:2026
• If A(adj A)= [2026, 0, 0; 0, 2026, 0; 0, 0, 2026], then the value of |adj A| is equal to:2026
• If |2 x, 5; 12, x| = |6, -5; 4, 3|, then the value of x is:2025
• If A and B are two square matrices each of order 3 with |A|=3 and |B|=5, then |2 AB| is:2025
• If A=[a_ij] is a 3 × 3 diagonal matrix such that a_11=1, a_22=5 and a_33=-2, then |A| is:2025
• If A is a square matrix of order 2 such that det(A)=4, then det(4 adj A) is equal to:2025
• Let A be a square matrix of order 3. If |A|=5, then |adj A| is:2025
• If |-1, 2, 4; 1, x, 1; 0, 3, 3 x| =-57, the product of the possible values of x is:2025
• Using matrices and determinants, find the value(s) of k for which the pair of equations 5 x-ky=2; 7 x-5 y=3 has a unique solution.2025
• Let A and B be two square matrices of order 3 such that det(A)=3 and det(B)=-4. Find the value of det(-6 A B).2025
• The value of |8, 2, 7; 12, 3, 5; 16, 4, 3| is:2024
• If |-a, b, c; a, -b, c; a, b, -c| =kabc, then the value of k is:2024
• Let A= [a, b; c, d] be a square matrix such that adj A=A. Then, (a+b+c+d) is equal to:2024
• If A=[a_ij]= [2, -1, 5; 1, 3, 2; 5, 0, 4] and c_ij is the cofactor of element a_ij, then the value of a_21 · c_11+a_22 ·…2024
• If A= [-2, 0, 0; 1, 2, 3; 5, 1, -1], then the value of ∣ A (adj. A) is:2024
• If a_ij and A_ij represent the (ij)th element and its cofactor of [2, -3, 5; 6, 0, 4; 1, 5, -7] respectively, then the value of…2024
• Let f(x)= |x^2, sin x; p, -1|, where p is a constant. The value of p for which f^′(0)=1 is:2024
• If A is a square matrix of order 3 such that the value of |adj · A|=8, then the value of |A^T| is:2024
• |x+1, x-1; x^2+x+1, x^2-x+1| is equal to:2024
• If |1, 3, 1; k, 0, 1; 0, 0, 1| = ± 6, then the value of k is:2024
• Assertion: For matrix A= [1, cos θ, 1; - cos θ, 1, cos θ; -1, - cos θ, 1], where θ ∈[0,2 π], |A| ∈[2,4]. Reason (R): cos θ…2024
• If A= [1, 2, -3; 2, 0, -3; 1, 2, 0], then find A^-1 and hence solve the following system of equations: x+2 y-3 z=1; 2 x-3 z=2;…2024
• Find A^-1, if A= [1, 2, 1; 2, 3, -1; 1, 0, 1]. Hence, solve the following system of equations: x+2 y+z=5; 2 x+3 y=1; x-y+z=82024
• If A= [2, 1, -3; 3, 2, 1; 1, 2, -1], find A^-1 and hence solve the following system of equations: 2 x+y-3 z=13 3 x+2 y+z=4 x+2…2024
• If |A|=2, where A is a 2 × 2 matrix, then |4 A^-1| equals:2023
• If A ·(adj A)= [3, 0, 0; 0, 3, 0; 0, 0, 3], then the value of |A|+|adj A| is equal to:2023
• If the area of a triangle with vertices ( 2,-6 ), ( 5,4 ) and ( k, 4 ) is 35 sq units, then k is2023
• Let A be a 3 × 3 matrix such that |adj A|=64. Then |A| is equal to:2023
• If [1, 2, 1; 2, 3, 1; 3, a, 1] is non-singular matrix and a ∈ A, then the set A is2023
• If |A|=|kA|, where A is a square matrix of order 2, then sum of all possible values of k is2023
• The value of |x+y, y+z, z+x; z, x, y; 1, 1, 1| is2023
• The value of the determinant |6, 0, -1; 2, 1, 4; 1, 1, 3| is2023
• The value of the determinant |2, 7, 1; 1, 1, 1; 10, 8, 1| is:2023
• Let A be the area of a triangle having vertices (x_1, y_1),(x_2, y_2) and (x_3, y_3). Which of the following is correct?2023
• If |α, 3, 4; 1, 2, 1; 1, 4, 1| =0, then the value of α is2023
• If (a, b), (c, d) and (e, f) are the vertices of ABC and Δ denotes the area of ABC, then |a, c, e; b, d, f; 1, 1, 1|^2 is equal to2023
• If |(A^-1)/2|=1/(k|A|), where A is a 3 × 3 matrix, then the value of k is:2023
• Using determinants, find the area of PQR with vertices P(3,1), Q(9,3) and R(5,7). Also, find the equation of line PQ using…2023
• Show that the determinant |x, sin θ, cos θ; - sin θ, -x, 1; cos θ, 1, x| is independent of θ.2023

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