Which of the following combinations has the dimension of electrical resistance ( \({ \varepsilon _0}\) is the permittivity of vacuum and \({\mu _0}\) is the permeability of vacuum) ?

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes \(32\) times of its initial value. If the final pressure of gas is \(128\) atmosphers, the value of \(\gamma\) the gas is

In the figure, potential difference between \(A\) and \(B\) is......\(V\)

Consider a block kept on an inclined plane (inclined at \(45^{\circ}\) ) as shown in the figure. If the force required to just push it up the incline is \(2\) times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane \((\mu)\) is equal to

A car is moving on a horizontal curved road with radius \(50\,m\). The approximate maximum speed of car will be \(............\,ms^{-1}\), if friction between tyres and road is \(0.34.\left[\right.\) Take \(\left.g =10 ms ^{-2}\right]\)

The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is

A block of mass \(5\,kg\) starting from rest pulled up on a smooth incline plane making an angle of \(30^{\circ}\) with horizontal with an affective acceleration of \(1\,ms ^{-2}\). The 10.Power delivered by the pulling force at \(t =10\,s\) from the start is \(.....\,W.\) \(\left[\right.\) Use \(\left.g =10\,ms ^{-2}\right]\) (calculate the nearest integer value)  

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).

A solid metallic cube having total surface area \(24\;m ^{2}\) is uniformly heated. If its temperature is increased by \(10\,^{\circ} C\), calculate the increase in volume of the cube \(\left(\right.\) Given \(\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)\)

This question has Statement \(-1\) and Statement \(-2.\) Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement \(-1:\) In Young's double slit experiment, the number of fringes observed in the field of view is small With longer wavelength of light and is large with shorter wavelength of light. Statement \(-2:\) In the double slit experiment the fringe width depends directly on the wavelength of light.

A \(100\,m\) long wire having cross-sectional area \(6.25 \times 10^{-4}\,m ^2\) and Young's modulus is \(10^{10}\,Nm ^{-2}\) is subjected to a load of \(250\,N\), then the elongation in the wire will be :