List of top Questions asked in CBSE CLASS XII- 2024

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: 
 
If \( A \) and \( B \) are two skew-symmetric matrices, then \( AB + BA \) is:
Anisole reacts with HI to give:
Which of the following alkyl halides will undergo S$_N$1 reaction most readily?
Write the stepwise mechanism of nucleophilic addition reactions in the carbonyl compounds.
Let \( \mathbb{Z} \) denote the set of integers. Then, the function \( f : \mathbb{Z} \to \mathbb{Z} \) defined as \( f(x) = x^3 - 1 \) is:
The following initial rate data were obtained for the reaction: \[ 2\text{NO (g)} + \text{Br}_2 \text{(g)} \rightarrow 2 \text{NOBr (g)} \] initial rate data were obtained for the reaction
A 1% solution of solute ‘X’ is isotonic with a 6% solution of sucrose (molar mass = \( 342 \) g mol\(^{-1}\)). The molar mass of solute ‘X’ is:
An azeotropic solution of two liquids has a boiling point lower than either of them when it:
The relative lowering of vapor pressure of an aqueous solution containing a non-volatile solute is 0.0225. The mole fraction of the non-volatile solute is:
Phenol dimerises in benzene having van’t Hoff factor 0.54. Its degree of association is: