List of top Mathematics Questions asked in CBSE CLASS XII

If \( P(A \mid B) = P(A' \mid B) \), then which of the following statements is true?
A linear programming problem deals with the optimization of a/an:
The derivative of \( \sin(x^2) \) w.r.t. \( x \), at \( x = \sqrt{\pi} \), is:
The integrating factor of the differential equation \( x \frac{dy}{dx} - y = x^4 - 3x \) is:
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
Let \( \theta \) be the angle between two unit vectors \( \hat{a} \) and \( \hat{b} \) such that \( \sin \theta = \frac{3}{5} \).
Then, \( \hat{a} \cdot \hat{b} \) is equal to:
\( \int_a^b f(x) \, dx \) is equal to:
Let \( \theta \) be the angle between two unit vectors \( \mathbf{\hat{a}} \) and \( \mathbf{\hat{b}} \) such that \( \sin \theta = \frac{3}{5} \). Then, \( \mathbf{\hat{a}} \cdot \mathbf{\hat{b}} \) is equal to:
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
A linear programming problem deals with the optimization of a/an:
The determinant \(\begin{vmatrix} x+1 & x-1 \\ x^2+x+1 & x^2-x+1 \end{vmatrix}\) is equal to:
The derivative of \( \sin(x^2) \) w.r.t. \( x \), at \( x = \sqrt{\pi} \), 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 vector with terminal point \( A(2, -3, 5) \) and initial point \( B(3, -4, 7) \) is:
The distance of point P(a, b, c) from the y-axis is:
The number of corner points of the feasible region determined by constraints \(x \geq 0\), \(y \geq 0\), \(x + y \geq 4\) 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:
Assertion (A): For the matrix \[ A = \begin{bmatrix} 1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1 \end{bmatrix}, \quad \text{where } \theta \in [0, 2\pi], \] \(|A| \in [2, 4]\).
Reason (R): \(\cos \theta \in [-1, 1], \ \forall \ \theta \in [0, 2\pi].\)

Assertion (A): A line in space cannot be drawn perpendicular to \( x \), \( y \), and \( z \) axes simultaneously. 

Reason (R): For any line making angles \( \alpha, \beta, \gamma \) with the positive directions of \( x \), \( y \), and \( z \) axes respectively, \[ \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1. \] 

Check whether the function \( f(x) = x^2 |x| \) is differentiable at \( x = 0 \) or not.
Answer: \( f(x) \) is differentiable at \( x = 0 \).
If \( y = \sqrt{\tan\sqrt{x}} \), prove that: \[ \sqrt{x} \frac{dy}{dx} = \frac{1 + y^4}{4y}. \]
Find: \[ \int x \sqrt{1 + 2x} \, dx \]
Evaluate: \[ \int_0^{\frac{\pi^2}{4}} \frac{\sin\sqrt{x}}{\sqrt{x}} \, dx \]
In the given figure, ABCD is a parallelogram. If \( \vec{AB} = 2\hat{i} - 4\hat{j} + 5\hat{k} \) and \( \vec{DB} = 3\hat{i} - 6\hat{j} + 2\hat{k} \), then find \( \vec{AD} \) and hence find the area of parallelogram ABCD.
A function \( f \) is defined from \( R \to R \) as \( f(x) = ax + b \), such that \( f(1) = 1 \) and \( f(2) = 3 \). Find the function \( f(x) \). Hence, check whether the function \( f(x) \) is one-one and onto.