List of top Mathematics Questions asked in CBSE CLASS XII

Find \( \frac{dy}{dx} \) if \( x^3 + y^3 + x^2 = a^b \), where \( a \) and \( b \) are constants.
Find the foot of the perpendicular drawn from the point \( (1, 1, 4) \) on the line \( \frac{x+2}{5} = \frac{y+1}{2} = \frac{z-4}{-3} \).
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 \( (-1, -1, 2) \).
Solve the differential equation: \[ x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x \]
Find the interval/intervals in which the function \( f(x) = \sin 3x - \cos 3x \), \( 0<x<\frac{\pi}{2} \) is strictly increasing.
Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]
Find: \[ \int \frac{2x}{(x^2 + 3)(x^2 - 5)} \, dx \]
Evaluate: \( \int_0^1 \frac{2x}{5x^2 + 1} dx \)
\( \int \frac{\cos 2x - \cos 2\theta}{\cos x - \cos \theta} dx \) is equal to:
The area of the region enclosed between the curve \( y = |x| \), x-axis, \( x = -2 \) and \( x = 2 \) is:
Let \( A \) and \( B \) be two matrices of suitable orders. Then, which of the following is not correct?

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

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 particular solution of the differential equation \( \frac{dy}{dx} - \frac{y}{x} + \csc\left(\frac{y}{x}\right) = 0 \); given that \( y = 0 \), when \( x = 1 \).
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 \( (-1, -1, 2) \).
Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]
Differentiate \(\frac{\sin x}{\sqrt{\cos x}}\) with respect to x.
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:
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.
Find the domain of \( \sec^{-1}(2x + 1) \).
If \( \int_0^a \frac{1}{1 + 4x^2} \, dx = \frac{\pi}{8} \), then the value of \(a\) is:
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: