List of top Questions asked in MET

The velocity of sound in air at STP is 332 m/s. The velocity of sound in air at \( 27^\circ \text{C} \) is:

The magnetic susceptibility of a paramagnetic material at \( -73^\circ \text{C} \) is 0.0075. Its value at \( -173^\circ \text{C} \) will be:

A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in \( \text{m/s}^{2} \) is:

The power of a water pump is 2 kW. If \( g = 10 \text{ m/s}^{2} \), the amount of water it can raise in one minute to a height of 10 m is:

The value of \( \cos^{2} 48^\circ - \sin^{2} 12^\circ \) is:

The value of \( \cot 70^\circ + 4\cos 70^\circ \) is:

If \( \sin \theta \) and \( \cos \theta \) are the roots of the equation \( ax^{2} - bx + c = 0 \), then:

The value of \( \sum_{k=1}^{n} \frac{1}{\sqrt{a_{k}} + \sqrt{a_{k+1}}} \), where \( a_{1}, a_{2}, \dots, a_{n} \) are in A.P. with common difference \( d \), is:

If the sum of \( n \) terms of two A.P.s are in the ratio \( (3n + 8) : (7n + 15) \), then the ratio of their \( 12^{\text{th}} \) terms is:

The value of \( \sqrt{6 + \sqrt{6 + \sqrt{6 + \cdots}}} \) is:

The number of real solutions of \( x^{2} - 3|x| + 2 = 0 \) is:

If \( \log_{10} 2,\ \log_{10}(2^{x} - 1),\ \log_{10}(2^{x} + 3) \) are in A.P., then \( x \) is:

The eccentricity of the hyperbola \( x^{2} - 4y^{2} = 1 \) is:

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: