List of top Questions asked in MET

The radius \(R\) of a soap bubble is doubled under isothermal condition. If \(T\) be the surface tension of soap bubble, the work done in doing so is given by
Radius of orbit of satellite of earth is \(R\). Its kinetic energy is proportional to
Threshold wavelength of a metal is \(4000\ \text{Å}\). If light of wavelength \(3000\ \text{Å}\) irradiates the surface, the maximum kinetic energy of photoelectron is
A body of specific heat \(0.2\ \text{kcal/kg}^\circ\text{C}\) is heated through \(100^\circ\text{C}\). The percentage increase in its mass is
Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown
A car travelling on a straight track moves with uniform velocity \(v_1\) for some time and with uniform velocity \(v_2\) for the next equal time. The average velocity of the car is
A balloon contains \(1500\ \mathrm{m}^3\) of helium at \(27^{\circ}\mathrm{C}\) and 4 atmospheric pressure. The volume of helium at \(-3^{\circ}\mathrm{C}\) temperature and 2 atmospheric pressure will be
A car is moving along a straight horizontal road with a speed \(v_0\). If the coefficient of friction between the tyres and the road is \(\mu\), the shortest distance in which the car can be stopped is
The angular velocities of three bodies in simple harmonic motion are \(\omega_{1},\omega_{2},\omega_{3}\) with their respective amplitudes as \(A_{1},A_{2},A_{3}\). If all the three bodies have same mass and velocity, then
Super cooled water is liquid water that has been cooled below its normal freezing point.This state is thermodynamically
Consider the following statements I. Repulsive forces are significant when the molecules are close together on average. II. Attractive intermolecular forces are important when the molecules are fairly close together but not necessarily touching. III. Attractive forces are ineffective when the molecules are for apart. Select correct statements.
An operon unit consist of
$ Ca{{(HC{{O}_{3}})}_{2}}(s) $ decomposes as $ Ca{{(HC{{O}_{3}})}_{2}}(s)\xrightarrow[{}]{{}}CaC{{O}_{3}}(s)+{{H}_{2}}O(g) $ $ +C{{O}_{2}}(g) $ Total pressure at equilibrium is found to be 0.12 bar. Thus, $ {{K}_{p}} $ is
In intrinsic semiconductor at room temperature number of electrons and holes are
A capacitor of capacitance \( 5\,\mu\mathrm{F} \) is connected as shown in the figure. The internal resistance of the cell is \( 0.5\,\Omega \). The amount of charge on the capacitor plate is
An alternating voltage \( E = 200\sqrt{2} \sin(100t) \, \mathrm{V} \) is connected to a \( 1\,\mu\mathrm{F} \) capacitor through an AC ammeter. The reading of ammeter is:
The domain and range of \( f(x) = \sin^{-1}(x) \) are:
If \( S = \sum_{n=0}^{\infty} \frac{(\log x)^{2n}}{(2n)!} \), then \( S \) is equal to
Let \( A = \{(x, y) : y = e^x, x \in \mathbb{R} \} \) and \( B = \{(x, y) : y = e^{-x}, x \in \mathbb{R} \} \). Then,
The function \( f(x) = \max\left\{(1 - x), (1 + x), 2\right\}, \, x \in (-\infty, \infty) \) is equivalent to
If \( \frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3} \), then \( a + b \) is equal to
If \( \lim_{x \to \infty} \left( 1 + \frac{a}{x} + \frac{b}{x^2} \right)^{2x} = e^2 \), then
The value of \( f(0) \), so that the function \( f(x) = \frac{2 - (256 - 7x)^{1/8}}{(5x + 3x)^{1/5} - 2} \), \( x \neq 0 \), is continuous everywhere, is given by
If \( \frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3} \), then \( a + b \) is equal to
If \( \frac{e^x + 2}{(e^x - 1)(2e^x - 3)} = -\frac{3}{e^x - 1} + \frac{B}{2e^x - 3} \), then \( B \) is equal to