List of top Questions asked in CBSE CLASS XII- 2026

Solve the differential equation $y \, dx + (x - y^3) \, dy = 0$.

Find the indefinite integral:
\[ \int \frac{x - \sin x}{1 - \cos x} \, dx \]

If $y = P \cos(ux) + Q \sin(ux)$, where $P, Q,$ and $u$ are constants, show that $\frac{d^2y}{dx^2} + u^2y = 0$.

Differentiate the function $x^x$ with respect to the function $x \log x$.

Determine the exact mathematical interval(s) in which the function defined by $f(x) = 5x^{3/2} - 3x^{5/2}$ for all $x > 0$ is strictly increasing.

Find the exact angular measurement $\theta$ between the following pair of spatial lines in three-dimensional space: \[ \frac{x-2}{3} = \frac{y+5}{2} = \frac{1-z}{-6} \quad \text{and} \quad \frac{x-7}{1} = \frac{y}{2} = \frac{6-z}{-2} \]

If $A$, $B$ and $C$ are three non-collinear points in a plane such that their relative position vectors form the directed sides $\vec{AB} = \hat{i} + 2\hat{j} - \hat{k}$ and $\vec{AC} = 2\hat{i} - 3\hat{j}$, then compute the exact geometric area of the triangle $\Delta ABC$.

Three honey bees were found flying along the vectors $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$, $\vec{b} = 4\hat{j} - 2\hat{k}$ and $\vec{c} = 3\hat{i} + 2\hat{k}$ respectively. Find the scalar value of $\lambda$ such that the path represented by the vector $\vec{a} + \lambda \vec{b}$ is perfectly perpendicular to the vector $\vec{c}$.

Evaluate the exact numerical value of the given inverse trigonometric expression: $\sin\left[\cos^{-1} \cos\left(\frac{7\pi}{6}\right)\right]$.

Two statements are provided: an Assertion (A) and a Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) given below: Assertion (A): Consider a Linear Programming Problem with minimise $Z = x + 2y$ subject to constraints $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$ which gives minimum $Z$ at infinitely many points. The corner points of feasible region are $(0, 3)$ and $(6, 0)$.
Reason (R): If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

A relation $R$ on the set $\{1, 2, 3\}$ defined as $R = \{(1, 1), (1, 2), (2, 1), (2, 2), (3, 3)\}$ is given. Two statements are provided: an Assertion (A) and a Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) given below: Assertion (A): A relation $R$ on the set $\{1, 2, 3\}$ defined as $R = \{(1, 1), (1, 2), (2, 1), (2, 2), (3, 3)\}$ is an equivalence relation.
Reason (R): A relation that is reflexive, symmetric and transitive is an equivalence relation.

If vectors \( \vec{a} = 3\hat{i} + 2\hat{j} + \lambda\hat{k} \) and \( \vec{b} = 2\hat{i} - 4\hat{j} + 5\hat{k} \) represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of \( \lambda \) is :

The general solution for the differential equation \( \frac{dy}{dx} = e^{3x - y} \) is :

An ant is observed crawling on a sheet of paper along a straight line given by equation \( y = 2x - 4 \). Area of the surface covered by the ant bounded by y-axis, x-axis and \( x = 1 \) is :

The order and degree of differential equation \( \frac{d^2y}{dx^2} = 1 - \left( \frac{d^3y}{dx^3} \right)^2 \) is :

The corner points of the feasible region determined by the system of linear constraints are \( (0, 0), (0, 40), (20, 40), (60, 20) \) and \( (60, 0) \). If the objective function of an LPP is \( Z = 4x + 3y \), then the maximum value is :

If position vector \( \vec{p} \) of a point \( (24, n) \) is such that \( |\vec{p}| = 25 \), then the value of \( n \) is :

The integral \( \int \sqrt{\frac{1 - \cos 2x}{1 + \cos 2x}} \, dx \) is equal to :

The value of \( \int_{0}^{1} \frac{1}{3x - 4} \, dx \) is :

If \( A \) is a non-singular matrix, then which of the following is not true ?

If the area of \( \Delta ABC \) with vertices \( A(3, 1) \), \( B(-2, 1) \) and \( C(0, k) \) is \( 5 \) sq. units, then values of \( k \) are :

Derivative of \( \cos^{-1}\left( \frac{\sin x + \cos x}{\sqrt{2}} \right) \), \( -\frac{\pi}{4} < x < \frac{\pi}{4} \) with respect to \( x \) is :

Absolute minimum value of \( f(x) = (x - 2)^2 + 5 \) in the interval \( [-3, 2] \) is :

If \( A \) is a symmetric matrix, then for any matrix \( B \) of order same as \( A \), \( BAB' \) is a/an :