Which one is the correct option for the two different thermodynamic processes ?

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A\) : If \(dQ\) and \(dW\) represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics \(d Q=d U-d W\). Reason \(R :\) First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the option given below :

A particle of mass \(m\) projected with a velocity ' \(u\) ' making an angle of \(30^{\circ}\) with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height \(\mathrm{h}\) is _______.

The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is :
(Give : Molar mass of helium \(=4 \mathrm{~g} / \mathrm{mol}\), Molar mass of argon \(=40 \mathrm{~g} / \mathrm{mol}\))

Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\)

A circular coil of radius \(8.0 \,{cm}\) and \(20\) turns is rotated about its vertical diameter with an angular speed of \(50\, {rad} {s}^{-1}\) in a uniform horizontal magnetic field of \(3.0 \times 10^{-2}\, {T}\). The maximum \(emf\) induced the coil will be \(\ldots \ldots \ldots \times 10^{-2}\) \(volt\) (rounded off to the nearest integer)

A parallel beam of light of wavelength \(900\,nm\) and intensity \(100\,Wm ^{-2}\) is incident on a surface perpendicular to the beam. Tire number of photons crossing \(1\,cm ^{2}\) area perpendicular to the beam in one second is :

In the given figure, there is a circuit of potentiometer of length \(A B=10 \,{m}\). The resistance per unit length is \(0.1 \,\Omega\) per \({cm}\). Across \({AB}\), a battery of emf \({E}\) and internal resistance ' \({r}^{\prime}\) is connected. The maximum value of emf measured by this potentiometer is : (In \(V\))

The distance of centre of mass from end \(A\) of a one dimensional rod \(( AB )\) having mass density \(\rho=\rho_{0}\left(1-\frac{ x ^{2}}{ L ^{2}}\right)\,kg / m\) and length \(L\) (in meter) is \(\frac{3 L }{\alpha} m\). The value of \(\alpha\) is \(\ldots \ldots \ldots . .\) (where \(x\) is the distance form end \(A\) )

The \(X-Y\) plane be taken as the boundary between two transparent media \(M _{1}\) and \(M _{2} . M _{1}\) in \(Z \geq 0\) has a refractive index of \(\sqrt{2}\) and \(M _{2}\) with \(Z <0\) has a refractive index of \(\sqrt{3}\). A ray of light travelling in \(M_{1}\) along the direction given by the vector \(\overrightarrow{ A }=4 \sqrt{3 i }-3 \sqrt{3 \hat{j}}-5 \hat{ k }\), is incident on the plane of separation. The value of difference between the angle of incident in \(M _{1}\) and the angle of refraction in \(M _{2}\) will be \(....\) degree.

An ideal gas occupies a volume of \(2\, m^3\) at a pressure of \(3\times10^6\, Pa\). The energy of  the gas is

When UV light of wavelength \(300 \mathrm{~nm}\) is incident on the metal surface having work function \(2.13 \mathrm{eV}\), electron emission takes place. The stopping potential is _______. (Given hc \(=1240 \mathrm{eV} \mathrm{nm}\) )