List of top Questions asked in MET- 2008

The value of \( \sin^{-1}\left(\frac{2x}{1 + x^{2}}\right) \) is:

The focus of the parabola $y^{2 = 8x}$ is:

The solution of the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) is:

If \( |\vec{a}| = 3 \), \( |\vec{b}| = 4 \) and \( \vec{a} \cdot \vec{b} = 6 \), then the angle between \( \vec{a} \) and \( \vec{b} \) is:

The value of \( \int_{0}^{1} \frac{dx}{1 + x^{2}} \) is:

The value of \( \lim_{n \to \infty} \frac{1 + 2 + 3 + \dots + n}{n^{2}} \) is:

The value of \( \sin^{-1}\left(\frac{3}{5}\right) + \sin^{-1}\left(\frac{8}{17}\right) \) is:

If \( {}^{n}C_{12} = {}^{n}C_{8} \), then \( n \) is:

The projection of vector \( \vec{a} = 2\vec{i} + 3\vec{j} + 2\vec{k} \) on vector \( \vec{b} = \vec{i} + 2\vec{j} + \vec{k} \) is:

The value of \( \int \frac{dx}{x(x^{n} + 1)} \) is:

If \( y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots}}} \), then \( \frac{dy}{dx} \) is:

The center of the ellipse \( \frac{(x+1)^2}{9} + \frac{(y-2)^2}{4} = 1 \) is:

The value of \( \vec{i} \cdot (\vec{j} \times \vec{k}) + \vec{j} \cdot (\vec{i} \times \vec{k}) + \vec{k} \cdot (\vec{i} \times \vec{j}) \) is:

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

The solution of the equation \( 4^{x - 3 \cdot 2^{x+2} + 32} = 0 \) is:

The value of \( \sin^{-1}(\sin 10) \) is:

The passive voice of "They are playing football" is ________.

Find the missing number: 2, 6, 12, 20, 30, ?

Which word is the odd one out?

If 20% of a number is 80, what is the number?

Choose the correctly spelled word:

The synonym of the word 'Diligent' is ________.

The train ________ before I reached the station.

Choose the correctly punctuated sentence:

If 'MOON' is coded as 'NPPO', how is 'SUN' coded?