List of top Mathematics Questions

Find \( \frac{dy}{dx} \), if \( y = \tan^{-1} \left( \frac{2x}{1 - x^2} \right) \)

Evaluate \( \int \frac{\sin^{-1}(x)}{1 + x^2} \, dx \)

Evaluate \( \int \frac{2x - 3}{x^2 + 1} \, dx \)

Find the value of \( p \) if the vectors \( \vec{p} \hat{i} - 8 \hat{j} + 5 \hat{k} \) and \( 5 \hat{i} + 2 \hat{j} - 3 \hat{k} \) are perpendicular to each other.

Find the area of the triangle whose sides are given by vectors: \[ \vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \vec{b} = \hat{i} - \hat{j} + 3\hat{k} \]

Principal value of \( \sin^{-1}(1) \) is:

Using integration, find the area bounded by the circle \( x^2 + y^2 = 16 \) in the first quadrant.

Find the critical points of the function \( f(x) = 2x^3 - 3x^2 - 12x + 15 \):

If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of matrix \( A^T \) is:

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

Evaluate \( \int_{\pi/6}^{\pi/3} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \):

Find the order of the differential equation \( \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 3y = 0 \):

If \( y = \log x \), then \( \frac{dy}{dx} \) is:

The radius of a circle is increasing at the rate of 2 m/s. The rate of change of its circumference is:

If \( A \) is a square matrix of order \( 2 \times 2 \) and \( |A| = 5 \), then \( | \text{Adj}(A) | \) is:

Vector equation of the line \( \frac{x - 5}{4} = \frac{y - 3}{5} = \frac{z + 3}{-8} \) is:

Range of the function \( \cos^{-1} \):

Relation \( R = \{(x, y): x<y^2 \text{ where } x, y \in \mathbb{R}\} \) is:

Objective function of a linear programming problem is:

If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:

Name of the inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) is:

Find the A.P. whose third term is 16 and seventh term exceeds the fifth term by 12. Also, find the sum of first 29 terms of the A.P.

Solve the equation \(4x^2 - 9x + 3 = 0\), using quadratic formula.

Check whether the following pair of equations is consistent or not. If consistent, solve graphically:
\[ x + 3y = 6\\ 3y - 2x = -12 \]

If \(\alpha, \beta\) are zeroes of the polynomial \(8x^2 - 5x - 1\), then form a quadratic polynomial in x whose zeroes are \(\frac{2}{\alpha}\) and \(\frac{2}{\beta}\).