List of top Mathematics Questions asked in MET

The derivative of \(\sin^{-1}(2x\sqrt{1-x^2})\) with respect to \(\sin^{-1}(3x - 4x^3)\) is

\[ \int \frac{(2x^{12} + 5x^9)}{(1 + x^3 + x^5)^3} \, dx \] equals:

\[ \begin{vmatrix} \sin\theta & \cos\theta & \sin 2\theta \\ \sin\left(\theta + \frac{2\pi}{3}\right) & \cos\left(\theta + \frac{2\pi}{3}\right) & \sin\left(2\theta + \frac{4\pi}{3}\right) \\ \sin\left(\theta - \frac{2\pi}{3}\right) & \cos\left(\theta - \frac{2\pi}{3}\right) & \sin\left(2\theta - \frac{4\pi}{3}\right) \end{vmatrix} \] equals:

Area bounded by the curves \(y = x^2\) and \(y = 2 - x^2\) is

\(\lim_{n \to \infty} \left( \frac{1^2}{1 - n^3} + \frac{2^2}{1 - n^3} + \dots + \frac{n^2}{1 - n^3} \right)\) is equal to

The value of \(\int \frac{\sin x + \cos x}{3 + \sin 2x} dx\) is

The equation of the circle passing through the point \((2a, 0)\) and whose radical axis is \(x = \frac{a}{2}\) with respect to the circle \(x^2 + y^2 = a^2\), will be

The coordinates of the point on the parabola \(y = x^2 + 7x + 2\), which is nearest to the straight line \(y = 3x - 3\), are

The area bounded by the parabolas \(y^2 = 4a(x + a)\) and \(y^2 = -4a(x - a)\) is

The solution of the differential equation \(\frac{dy}{dx} = \sin(x + y) \tan(x + y) - 1\) is

Fifteen coupons are numbered 1, 2, …, 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

Let \(h(x) = \min(x, x^2)\), for every real number \(x\). Then,

If the function \[ f(x) = \begin{cases} (\cos x)^{1/x^2}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases} \] is continuous at \( x = 0 \), then the value of \( k \) is:

If \[ f(x) = \frac{e^{1/x} - 1}{e^{1/x} + 1}, \quad x \neq 0 \quad \text{and} \quad f(0) = 0, \] then \(f(x)\) is:

The value of \(S = \frac{1}{6} \left( \frac{\pi}{2} - \sin^2 \frac{2\pi}{7} - \cos^2 \frac{2\pi}{7} \right)\) is

A letter lock contains 5 rings each marked with four different letters. The number of all possible unsuccessful attempts to open the lock is

The domain of definition of the function \[ f(x) = \frac{1}{| |x| - 1 | - 5} \] is:

The condition that the straight line \(cx - by + b^2 = 0\) may touch the circle \(x^2 + y^2 = ax + by\) is

If \(0 < \alpha, \beta, \gamma < \frac{\pi}{2}\), such that \(\alpha + \beta + \gamma = \frac{\pi}{2}\) and \(\cot \alpha, \cot \beta, \cot \gamma\) are in AP, then the value of \(\cot \alpha \cot \gamma\) is

In a \(\triangle ABC\), if \(b = 2\), \(\angle B = 30^\circ\), then the area of the circumcircle of \(\triangle ABC\) (in sq units) is

The sum of the series \(\frac{3}{4 \times 8} - \frac{3 \times 5}{4 \times 8 \times 12} + \frac{3 \times 5 \times 7}{4 \times 8 \times 12 \times 16} - \cdots\) is

The value of \(\int_0^\pi |\sin 3\theta| \, d\theta\) is

The value of \(\int \frac{\cos x + \sin x}{\cos x + x \sin x} \, dx\) is

Tangent to the ellipse \(\frac{x^2}{32} + \frac{y^2}{18} = 1\) having slope \(-\frac{3}{4}\) meet the coordinate axis at A and B. Then, the area of \(\triangle AOB\), where O is the origin, is

The value of \(\lim_{x \to \pi/6} \frac{\sin x + \sin 2x - 1}{\sin 2x - \sin 3x + 1}\) is