List of top Questions asked in MET

The value of \( \vec{a} \times (\vec{b} \times \vec{c}) \) is:

The value of \( (1 + i)^{4} + (1 - i)^{4} \) is:

The number of terms in the expansion of \( (x + a)^{n} \) is:

The radius of the circle \( x^{2} + y^{2} - 4x + 6y - 12 = 0 \) is:

The value of \( \int_{0}^{1} x e^{x} \, dx \) is:

The function \( y = -x^{2} + 6x - 3 \) is increasing when:

The area of the region bounded by the curve \( x = 4 - y^{2} \) and the y-axis is:

The radius of the circle \( x^{2} + y^{2} - 4x + 6y - 12 = 0 \) is:

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

The value of \( \int_{0}^{1} x e^{x} \, dx \) is:

The value of \[ \begin{vmatrix} 1 & a & b + c \\ 1 & b & c + a \\ 1 & c & a + b \end{vmatrix} \] is:

The value of \( \cos 1^\circ \cos 2^\circ \dots \cos 100^\circ \) is:

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: