List of top Questions asked in CBSE CLASS XII- 2025

Sketch a graph of $ y = x^2 $. Using integration, find the area of the region bounded by $ y = 9 $, $ x = 0 $, and $ y = x^2 $.

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ such that $|\vec{a}| = 3$, $|\vec{b}| = 5$, $|\vec{c}| = 7$, then find the angle between $\vec{a}$ and $\vec{b}$.

In the Linear Programming Problem (LPP), find the point/points giving the maximum value for $ Z = 5x + 10y$ subject to the constraints:
\[x + 2y \leq 120 \\ x + y \geq 60 \\ x - 2y \geq 0 \\ x \geq 0, y \geq 0\]

Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]

Find: \[ \int \frac{2x}{(x^2 + 3)(x^2 - 5)} \, dx \]

Let $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be three vectors such that $\mathbf{a} \times \mathbf{b} = \mathbf{a} \times \mathbf{c} \text{ and } \mathbf{a} \times \mathbf{b} \neq 0 \text{ Show that } \mathbf{b} = \mathbf{c}$.

Find a vector of magnitude 5 which is perpendicular to both the vectors $ 3\hat{i} - 2\hat{j} + \hat{k} \text{ and } 4\hat{i} + 3\hat{j} - 2\hat{k} $.

If $y = 5 \cos x - 3 \sin x, \text{ prove that } \frac{d^2y}{dx^2} + y = 0$.

Differentiate $\frac{\sin x}{\sqrt{\cos x}}$ $\text{ with respect to } x$.

Find the domain of the function $ f(x) = \cos^{-1}(x^2 - 4) $.

Find the angle of deviation produced by the prism.

In which case is the potential energy of the magnet minimum?

The magnetic moment (5 J/T) of a bar magnet points along a uniform magnetic field 0.4 T.

Light of wavelength 750 nm is incident normally on a slit of width 1.5 mm. Diffraction pattern is obtained on a screen 1.0 m away from the slit. Find the distance of the nearest point from the central maxima at which the intensity is zero.

“You cannot see a person standing on the other side of a boundary wall but can hear him.” Explain with reason.

Find the effective resistance of the network of resistors between points A and F as shown in the figure.