A cube is placed inside an electric field, \(\overrightarrow{{E}}=150\, {y}^{2}\, \hat{{j}}\). The side of the cube is \(0.5 \,{m}\) and is placed in the field as shown in the given figure. The charge inside the cube is \(.....\times 10^{-11} {C}\)

The length of a potentiometer wire is \(1200\; \mathrm{cm}\) and it carries a current of \(60 \;\mathrm{mA}\). For a cell of \(emf\;5\; \mathrm{V}\) and intemal resistance of \(20\; \Omega,\) the null point on it is found to be a \(1000\; \mathrm{cm} .\) The resistance of whole wire is .............. \(\Omega\)

A plane electromagnetic wave of wavelength \(\lambda \) has an intensity \(I.\)  It is propagating along the positive \(Y-\)  direction. The allowed expressions for the electric and magnetic fields are given by

Starting from the origin at time \(t=0,\) with initial velocity \(5 \hat{ j }\, ms ^{-1},\) a particle moves in the \(x-y\) plane with a constant acceleration of \((10 \hat{ i }+4 \hat{ j })\, ms ^{-2}\). At time \(t\), its coordinates are \(\left(20\, m , y _{0}\, m \right) .\) The values of \(t\) and \(y _{0},\) are respectively

A ball is spun with angular acceleration \(\alpha=6 t ^{2}-2 t\) where \(t\) is in second and \(\alpha\) is in \(rads\) \(^{-2}\). At \(t=0\), the ball has angular velocity of \(10\,rads\) \(^{-1}\) and angular position of \(4\,rad\). The most appropriate expression for the angular position of the ball is

The truth table for the followng logic circuit is ...... .

The effect of increase in temperature on the number of electrons in conduction band \(\left( n _{ e }\right)\) and resistance of a semiconductor will be as:

In finding the electric field using Gauss Law the formula \(|\overrightarrow{\mathrm{E}}|=\frac{q_{\mathrm{enc}}}{\varepsilon_{0}|\mathrm{A}|}\) is applicable. In the formula \(\varepsilon_{0}\) is permittivity of free space, \(A\) is the area of Gaussian surface and \(q_{enc}\) is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?

Let \(S=\left\{ x : x \in R \text { and }(\sqrt{3}+\sqrt{2})^{ x ^2-4}+(\sqrt{3}-\sqrt{2})^{ x ^2-4}=10\right\} \text {. }\) Then \(n ( S )\) is equal to

The numbers of pairs \((a, b)\) of real numbers, such that whenever \(\alpha\) is a root of the equation \(x^{2}+a x+b=0, \alpha^{2}-2\) is also a root of this equation, is :

An asteroid is moving directly towards the centre of the earth. When at a distance of \(10 \mathrm{R}\) (\(R\) is the radius of the earth) from the earths centre, it has a speed of \(12 \;\mathrm{km} / \mathrm{s}\). Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is \(11.2 \;\mathrm{km} / \mathrm{s}\) ) \(?\) Give your answer to the nearest integer in \(km/s\)

The translational degrees of freedom \((f)\) and rotational degrees of freedom \((f)\) of \(\mathrm{CH}_4\) molecule are _______.

All five letter words are made using all the letters \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and arranged as in an English dictionary with serial numbers. Let the word at serial number \(n\) be denoted by \(W_n\). Let the probability \(\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)\) of choosing the word \(\mathrm{W}_{\mathrm{n}}\) satisfy \(\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)=2 \mathrm{P}\left(\mathrm{W}_{\mathrm{n}-1}\right), \mathrm{n} \gt 1\).
If \(\mathrm{P}(\mathrm{CDBEA})=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in \mathbb{N}\), then \(\alpha+\beta\) is equal to : _______