List of top Mathematics Questions

Prove that the function f(x) = |x| is continuous at x = 0.
Find the degree of the differential equation \( xy \frac{d^2y}{dx^2} + x \left(\frac{dy}{dx}\right)^2 - y\left(\frac{dy}{dx}\right) = 2 \)
Prove that (4, 4, 2), (3, 5, 2) and (-1, -1, 2) are vertices of a right angle triangle.
The value of \( \int_{0}^{\pi/2} \frac{dx}{1 + \sqrt{\tan x}} \) will be
If $ \cos^{-1}(x) - \sin^{-1}(x) = \frac{\pi}{6} $, then find } $ x $.
If \(\alpha\) is the angle made by the perpendicular drawn from origin to the line \(12x - 5y + 13 = 0\) with the positive X-axis in anti-clockwise direction, then \(\alpha =\)
If \[ A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}, \] where \( x \) and \( y \) are non-zero real numbers, trace of \( A = 0 \), and determinant of \( A = -6 \), then the minor of the element 1 of \( A \) is:}
Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2) =$
The number of solutions of the equation $4 \cos 2\theta \cos 3\theta = \sec \theta$ in the interval $[0, 2\pi]$ is
If \( 5 \sin^{-1} \alpha + 3 \cos^{-1} \alpha = \pi \), then \( \alpha = ? \)
\[ \int \frac{\tan^2 \sqrt{x}}{\sqrt{x}} \, dx \text{ is equal to:} \]
Find the maximum slope of the curve \( y = x^3 + 3x^2 + 9x - 30 \).

Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
\[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.

The domain of the function \( f(x) = \cos^{-1}(2x) \) is:
The equation of the circle passing through the point \( (1, 2) \) and touching both axes is:
Find the coordinates of the point which divides the line segment joining A(3, –2) and B(5, 4) in the ratio 2:3.

Prove that:
\( \tan^{-1}(\sqrt{x}) = \frac{1}{2} \cos^{-1}\left( \frac{1 - x}{1 + x} \right), \quad x \in [0, 1] \)

Find the general solution of the differential equation \[ x^2 \frac{dy}{dx} = x^2 + xy + y^2 \] OR
If \( \log_2 3 = p \), express \( \log_8 9 \) in terms of \( p \):
All the values of \(k\) such that the quadratic expression \(2kx^2 - (4k+1)x + 2\) is negative for exactly three integral values of \(x\), lie in the interval:
The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:
If \( g \circ f \) is a bijective function, then:
Suppose \( R_1 \) and \( R_2 \) are reflexive relations on a set \( A \). Which of the following statements is correct?
For a non-singular matrix \(X\), if \(X^2 = I\), then \(X^{-1}\) is equal to: