List of top Questions asked in MET

If \( \vec{u} = \hat{i} + \hat{j}, \vec{v} = \hat{i} - \hat{j}, \vec{w} = \hat{i} + 2\hat{j} + 3\hat{k} \) and \( \hat{n} \) is a unit vector such that \( \vec{u} \cdot \hat{n} = 0 \) and \( \vec{v} \cdot \hat{n} = 0 \), then \( |\vec{w} \cdot \hat{n}| \) is

\( \lim_{x \to 0} \frac{\sqrt{1 - \cos(2x)}}{\sqrt{2} \cdot x} \) is

Radius of the circle \( \vec{r}^2 + \vec{r} \cdot (2\hat{i} - 2\hat{j} - 4\hat{k}) - 19 = 0, \vec{r} \cdot (\hat{i} - 2\hat{j} + 2\hat{k}) + 8 = 0 \) is

If \( x^y = e^{x - y} \), then \( \frac{dy}{dx} \) is equal to

The function \( f(x) = \frac{ax + b}{(x-1)(x-4)} \) has a local maxima at \( (2, -1) \), then

If \( z = \tan(y + ax) + \sqrt{y} - ax \), then \( z_{xx} - a^2 z_{yy} \) is equal to

\( \int \frac{x^2 + 4x^4 + 16}{dx} \) is equal to

If the solution of the differential equation \( \frac{dy}{dx} = ax + 32y + f \) represents a circle, then the value of \( a \) is

Solution of the differential equation \[ x = 1 + xy \frac{dy}{dx} + \frac{(xy)^2}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{(xy)^3}{3!} \left(\frac{dy}{dx}\right)^3 + \cdots \] is

Two bodies A and B having temperatures \( 327^\circ C \) and \( 427^\circ C \) are radiating heat to the surrounding. The surrounding temperature is \( 27^\circ C \). The ratio of rates of heat radiation of A to that of B is

If \( \cos x = \frac{2\cos y - 1}{2 - \cos y} \), where \( x, y \in (0, \pi) \), then \( \tan \frac{x}{2} \cot \frac{y}{2} \) is equal to:

The value of \[ \sin^{-1}\left[\cos\left(\sin^{-1}\left(\sqrt{\frac{2-\sqrt{3}}{4}}\right) + \cos^{-1}\left(\frac{\sqrt{12}}{4}\right) + \sec^{-1}\left(\sqrt{2}\right)\right)\right] \] is

Which of the following was the founder of Indian National Congress?

Which of the following is known as 'evening star'?

Namdhapha National Park is located in

Which of the following river is related with Bhakra-Nagal Project?

The first Indian woman to swim across the English channel is

The headquarters of NATO is situated at

Nehru Trophy is related with

Who is called 'Nightingale of India'?

The highest civilian award in India is

The classical dance, Kathakali belongs to