List of top Questions asked in MET- 2008

The value of \( \lim_{x \to 0} \frac{1 - \cos x}{x^{2}} \) is:

If \( y = \tan^{-1}\left(\frac{3x - x^{3}}{1 - 3x^{2}}\right) \), then \( \frac{dy}{dx} \) is:

The derivative of \( e^{x^{3}} \) with respect to \( \log x \) is:

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

The degree of the differential equation \( \left[ 1 + \left(\frac{dy}{dx}\right)^{2} \right]^{3/2} = \frac{d^{2}y}{dx^{2}} \) is:

The value of \( \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \) is:

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors and \( \theta \) is the angle between them, then \( |\vec{a} + \vec{b}| \) is a unit vector if \( \theta \) is:

The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is:

The value of \( \frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} \) is:

The term independent of \( x \) in the expansion of \( \left(x + \frac{1}{x}\right)^{2n} \) is:

The eccentricity of the ellipse \( 9x^{2} + 5y^{2} = 45 \) is:

The value of \( \int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \, dx \) is:

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: