Determinants

CBSE Class 12 Mathematics · every board question from this chapter, 2023–2026 · 23 of them repeated across years

• If Δ 1= and Δ 2=, then2026asked 3×
• If points (2, 3), (0, 4) and (p, 2) are collinear, then the value of p is:2026asked 3×
• One of the values of x for which =1 is2026asked 3×
• If =-86, then the sum of all possible values of a is2026asked 3×
• If B(adj B)=[ ], 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:2026asked 3×
• If A(adj A)=[ ], then the value of 2 A is:2026
• If A(adj A)=[ ], then the value of adj A is equal to:2026
• If =, then the value of x is:2025asked 3×
• If A and B are two square matrices each of order 3 with A =3 and B =5, then 2 AB is:2025asked 3×
• 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:2025asked 3×
• If A is a square matrix of order 2 such that det =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:2025asked 3×
• If =-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 =3 and det =-4. Find the value of det(-6 A B).2025
• The value of is:2024
• If =kabc, then the value of k is:2024asked 3×
• Let A=[ ] be a square matrix such that adj A=A. Then, (a+b+c+d) is equal to:2024asked 3×
• If A=[a ij]=[ ] and c ij is the cofactor of element a ij, then the value of a 21 · c 11+a 22 · c 12+a 23 · c 13 is:2024
• If A=[ ], then the value of A (adj. A) is:2024
• If a ij and A ij represent the (ij)th element and its cofactor of [ ] respectively, then the value of a 11 A 21+a 12 A 22+a 13 A…2024
• Let f(x)=, 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:2024asked 3×
• is equal to:2024asked 2×
• If = ± 6, then the value of k is:2024asked 2×
• Assertion: For matrix A=[ ], where θ ∈[0,2 π], A ∈[2,4]. Reason (R): cos θ ∈[-1,1], θ ∈[0,2 π].2024asked 3×
• If A=[ ], then find A^-1 and hence solve the following system of equations: OR Find the product of the matrices [ ][ ] and hence…2024asked 3×
• Find A^-1, if A=[ ]. Hence, solve the following system of equations:2024
• If A=[ ], 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 y-z=82024
• If A =2, where A is a 2 × 2 matrix, then 4 A^-1 equals:2023
• If A ·(adj A)=[ ], then the value of A + adj A is equal to:2023asked 3×
• 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:2023asked 3×
• If [ ] is non-singular matrix and a ∈ A, then the set A is2023asked 3×
• If A = kA, where A is a square matrix of order 2, then sum of all possible values of k is2023asked 3×
• The value of is2023
• The value of the determinant is2023
• The value of the determinant 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?2023asked 2×
• If =0, then the value of α is2023asked 2×
• If (a, b), (c, d) and (e, f) are the vertices of ABC and Δ denotes the area of ABC, then ^2 is equal to2023asked 3×
• 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 is independent of θ.2023

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