List of top Mathematics Questions asked in CBSE CLASS XII

\[ \int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \, dx \] is equal to :
Find the distance of the point $P(2, 4, -1)$ from the line \[ \frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-9}. \]
(a) Find the point Q on the line \( \frac{2x + 4}{6} = \frac{y + 1}{2} = \frac{-2z + 6}{-4} \) at a distance of \( \frac{\sqrt{5}}{2} \) from the point \( P(1, 2, 3) \).
Solve for \( x \), \[ 2 \tan^{-1} x + \sin^{-1} \left( \frac{2x}{1 + x^2} \right) = 4\sqrt{3} \]
Solve the differential equation \( 2(y + 3) - xy \frac{dy}{dx} = 0 \); given \( y(1) = -2 \).
The integrating factor of the differential equation \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \) is:
Find: \[ \int \frac{2x}{(x^2 + 3)(x^2 - 5)} \, dx \]
The corner points of the feasible region in graphical representation of a L.P.P. are \( (2, 72), (15, 20) \) and \( (40, 15) \). If \( Z = 1x + 9y \) be the objective function, then:
If a line makes angles of \( \frac{3\pi}{4} \) and \( \frac{\pi}{3} \) with the positive directions of \( x \), \( y \), and \( z \)-axes respectively, then \( \theta \) is:
If \( x = e^{\frac{x}{y}} \), then prove that \( \frac{dy}{dx} = \frac{x - y}{x \log x} \).
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.
Let the volume of a metallic hollow sphere be constant. If the inner radius increases at the rate of 2 cm/s, find the rate of increase of the outer radius when the radii are 2 cm and 4 cm respectively.
Determine the values of $x$ for which the function $f(x) = \frac{x-4}{x+1}$ is an increasing or a decreasing function.
Sum of two skew-symmetric matrices of the same order is always a/an:
If $y = \sin^{-1} x$, then $(1 - x^2) \frac{d^2y}{dx^2}$ is equal to :
Evaluate \( \int_0^{\frac{\pi}{2}} \frac{x}{\cos x + \sin x} \, dx \)
For a positive constant \( a \), differentiate \( \left( t + \frac{1}{t} \right)^a \) with respect to \( t \), where \( t \) is a non-zero real number.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]
Find: \[ \int \frac{\sqrt{x}}{1 + \sqrt{x^{3/2}}} \, dx \]
(a) Differentiate $ \left( \frac{5x}{x^5} \right)$ with respect to $x$.
If \( A \) and \( B \) are square matrices of order \( m \) such that \( A^2 - B^2 = (A - B)(A + B) \), then which of the following is always correct?
Differentiate \( \log(x^2 + \csc^2 x) \) with respect to \( x \).
Find the domain of the function $f(x) = \sin^{-1}(-x^2)$.
$ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :
Find the domain of \( \sin^{-1}(x^2 - 3) \).