List of top Questions asked in CBSE CLASS XII

Let \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] be a square matrix such that \[ \text{adj } A = A. \] Then, \( (a + b + c + d) \) is equal to:
If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix}, \] then \( A^{-1} \) is:
If \[ \begin{bmatrix} 1 & 3 & 1 \\ k & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \] has a determinant of \( \pm 6 \), then the value of \( k \) is:
If \( A = [a_{ij}] \) is an identity matrix, then which of the following is true?
The value of \[ \begin{vmatrix} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{vmatrix} \textbf{is:} \]
If \( A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix} \), then \( A^{-1} \) is:
If \( A = [a_{ij}] \) is an identity matrix, then which of the following is true?
Let \( \Delta = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) be a square matrix such that \( \text{adj} A = A \). Then, \( (a + b + c + d) \) is equal to:
If \[ \begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix} \] is a scalar matrix, then the value of \[ a + 2b + 3c + 4d \] is:
If \( A = \begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix} \), then the value of \( I - A + A^2 - A^3 + \dots \) is:
Given that \[ \begin{bmatrix} 1 & x \end{bmatrix} \begin{bmatrix} 4 & 0 \\ -2 & 0 \end{bmatrix} = 0 \] then the value of \( x \) is:
If X, Y and XY are matrices of order 2 × 3, m × n, and 2 × 5 respectively, then the number of elements in matrix Y is:
The order and degree of the differential equation: \[ \left[ 1 + \left(\frac{dy}{dx}\right)^2 \right]^3 = \frac{d^2y}{dx^2} \] respectively are:
The integrating factor of the differential equation \( x \frac{dy}{dx} - y = x^4 - 3x \) is:
The order and degree of the differential equation: \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^3 = \frac{d^2y}{dx^2}, \] respectively, are:
The number of arbitrary constants in the particular solution of the differential equation \[ \log \left( \frac{dy}{dx} \right) = 3x + 4y; \quad y(0) = 0 \] is/are:
The integrating factor of the differential equation \( (x + 2y^2) \frac{dy}{dx} = y \, (y>0) \) is:} 
 
The general solution of the differential equation \( x \, dy + y \, dx = 0 \) is:
The integrating factor of the differential equation \[ (x + 2y^2) \frac{dy}{dx} = y, \quad (y > 0) \] is:
If \( A \) and \( B \) are two skew-symmetric matrices, then \( AB + BA \) is:
If \( g(x) \) is a continuous function satisfying \( g(-x) = -g(x) \), then \( \int_{0}^{2a} g(x) \, dx \) is equal to: {5pt}
If \(A = [a_{ij}] = \begin{bmatrix} 2 & -1 & 5 \\ 1 & 3 & 2 \\ 5 & 0 & 4 \end{bmatrix}\) 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:
If \(A = \begin{bmatrix} 1 & 3 \\ 3 & 4 \end{bmatrix}\) and \( A^2 - kA - 5I = 0 \), then the value of \( k \) is:
If \(\begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix}\)is a scalar matrix, then the value of \( a + 2b + 3c + 4d \) is: 
 
If \(A = \begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix}\), then the value of \( I - A + A^2 - A^3 + \ldots \) is: