List of top Mathematics Questions asked in CBSE CLASS XII

If \( x = e^{\frac{x}{y}} \), then prove that \( \frac{dy}{dx} = \frac{x - y}{x \log x} \).
Find: \( \int 2x^3 e^{x^2} \,dx \).
If \( |\mathbf{a}| = 2 \), \( |\mathbf{b}| = 3 \) and \( \mathbf{a} \cdot \mathbf{b} = 4 \), then evaluate \( |\mathbf{a} + 2\mathbf{b}| \).
If \( A \) and \( B \) are square matrices of order \( m \) such that \( A^2 - B^2 = (A - B)(A + B) \), then which of the following is always correct?
If \( A \) denotes the set of continuous functions and \( B \) denotes the set of differentiable functions, then which of the following depicts the correct relation between set \( A \) and \( B \)?
If a line makes angles of \( \frac{3\pi}{4} \) and \( \frac{\pi}{3} \) with the positive directions of \( x \), \( y \), and \( z \)-axes respectively, then \( \theta \) is:
A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \( Z = 5x + 7y \), where \( x \) and \( y \) are the number of units of X and Y respectively sold. Which of the following statements is correct?
The function \( f(x) = x^2 - 4x + 6 \) is increasing in the interval:
If \( E \) and \( F \) are two events such that \( P(E)>0 \) and \( P(F) \neq 1 \), then \( P(E \,|\, F) \) is:
The line \( x = 1 + 5\mu, y = -5 + \mu, z = -6 - 3\mu \) passes through which of the following points?
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
The area of the shaded region
The probability distribution of a random variable \( X \) is given by:
probability distribution of a random variable X
Then \( E(X) \) of distribution is:
If the projection of \( \mathbf{a} = \alpha \hat{i} + \hat{j} + 4 \hat{k} \) on \( \mathbf{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} \) is 4 units, then \( \alpha \) is:
The equation of a line parallel to the vector \( 3 \hat{i} + \hat{j} + 2 \hat{k} \) and passing through the point \( (4, -3, 7) \) is:
If \( \int_0^a x \, dx \leq \frac{a}{2} + 6 \), then which of the following holds for \( a \)?
If \( A \) and \( B \) are square matrices of the same order, then \( (A B^T - B A^T) \) is a:
Which of the following can be both a symmetric and skew-symmetric matrix?
If \( p \) and \( q \) are respectively the order and degree of the differential equation \( \frac{d}{dx} \left( \frac{dy}{dx} \right)^3 = 0 \), then \( (p - q) \) is:
The value of \( \cos \left( \frac{\pi}{6} + \cot^{-1}(-\sqrt{3}) \right) \) is:
If \( \mathbf{p} \) and \( \mathbf{q} \) are unit vectors, then which of the following values of \( \mathbf{p} \cdot \mathbf{q} \) is not possible?

Given that $ A^{-1} = \frac{1}{7} \begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix} $, matrix $ A $ is:

If $$ \int_{0}^{a} \frac{1}{4 + x^2} \, dx = \frac{\pi}{6}, $$ then the value of \( a \) is: 

If \( A \) and \( B \) are two non-zero square matrices of the same order such that: $$ (A + B)^2 = A^2 + B^2, $$ then: 

Using integration, find the area of the ellipse: \[ \frac{x^2}{16} + \frac{y^2}{4} = 1, \] included between the lines \(x = -2\) and \(x = 2\).
If \( P(A|B) = P(A'|B) \), then which of the following statements is true?