List of top Questions asked in CBSE CLASS XII

Evaluate: \( \int_0^1 \frac{2x}{5x^2 + 1} dx \)

Show that \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function in \( \left[ 0, \frac{\pi}{4} \right] \).

Find the particular solution of the differential equation \( \frac{dy}{dx} - \frac{y}{x} + \csc\left(\frac{y}{x}\right) = 0 \); given that \( y = 0 \), when \( x = 1 \).
Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]
Draw a rough sketch of the curve \( y = \sqrt{x} \). Using integration, find the area of the region bounded by the curve \( y = \sqrt{x} \), \( x = 4 \), and the x-axis, in the first quadrant.
Find the point on the line \( \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} \) at a distance of \( \sqrt{2} \) units from the point \( (-1, -1, 2) \).
The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
Find the domain of \( \sec^{-1}(2x + 1) \).
The radius of a cylinder is decreasing at a rate of 2 cm/s and the altitude is increasing at a rate of 3 cm/s. Find the rate of change of volume of this cylinder when its radius is 4 cm and altitude is 6 cm.
A man needs to hang two lanterns on a straight wire whose end points have coordinates A (4, 1, -2) and B (6, 2, -3). Find the coordinates of the points where he hangs the lanterns such that these points trisect the wire AB.
Differentiate \(\frac{\sin x}{\sqrt{\cos x}}\) with respect to x.
If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
If \( \left| \begin{matrix} 2x & 5 \\ 12 & x \end{matrix} \right| = \left| \begin{matrix} 6 & -5 \\ 4 & 3 \end{matrix} \right| \), then the value of x is:
If a matrix A is both symmetric and skew-symmetric, then A is:
\( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx \) is equal to:
If \( \int_0^a \frac{1}{1 + 4x^2} \, dx = \frac{\pi}{8} \), then the value of \(a\) is:

The respective values of \( |\vec{a}| \) and} \( |\vec{b}| \), if given \[ (\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 512 \quad \text{and} \quad |\vec{a}| = 3 |\vec{b}|, \] are:

The principal value of \( \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) \) is:
If A and B are two square matrices of the same order, then (A + B)(A - B) is equal to:

Identify the member of the Constituent Assembly with the help of the following information:

  •  He was the President of the Constituent Assembly.
  •  He was the first President of the Independent India.

Examine the role of Gandhiji in the Non-Cooperation Movement.

Examine the role of Gandhiji in the Civil Disobedience Movement.

Describe the teachings and beliefs of the Virshaiva tradition.

Describe the views of Meera Bai on devotionalism. 

Explain the role of G.B. Pant on the united approach of India.