Given below are two statements : Statements \(I\) : Astronomical unit \((Au)\). Parsec \((Pc)\) and Light year \((ly)\) are units for measuring astronomical distances. Statements \(II:\) \(Au < Parsec ( Pc ) < ly\) In the light of the above statements. choose the most appropriate answer from the options given below:

\(\mathrm{N}\) moles of a polyatomic gas \((f=6)\) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of \(\mathrm{N}\) is _______.

Match List-I with List-II.

LIST - I	LIST - II
(A) Isobaric	(I) ΔQ = ΔW
(B) Isochoric	(II) ΔQ = ΔU
(C) Adiabatic	(III) ΔQ = zero
(D) Isothermal	(IV) ΔQ = ΔU + PΔV

\(\Delta \mathrm{Q}=\) Heat supplied
\(\Delta \mathrm{W}=\) Work done by the system
\(\Delta \mathrm{U}=\) Change in internal energy
\(\mathrm{P}=\) Pressure of the system
\(\Delta \mathrm{V}=\) Change in volume of the system
Choose the correct answer from the options given below:

Muon \((\mu ^{-1})\) is negatively charged \(\left( {\left| q \right| = \left| e \right|} \right)\) with a mass \(m_{\mu}\, = 200\,m_e\), where \(m_e\) is the mass of the electron and \(e\) is the electronic charge. If \(\mu ^{-1}\) is bound to a proton to form a hydrogen like atom, identify the correct statements \((A)\) Radius of the muonic orbit is \(200\) times smaller than that of the electron \((B)\) the speed of the \(\mu ^{-1}\) in the \(n^{th}\) orbit is \(\frac{1}{{200}}\) times that of the election in the \(n^{th}\) orbit \((C)\) The Ionization energy of muonic atom is \(200\) times more than that of an hydrogen atom \((D)\) The momentum of the muon in the \(n^{th}\) orbit is \(200\) times more than that of the electron

Intensity of sunlight is observed as \(0.092\, {Wm}^{-2}\) at a point in free space. What will be the peak value of magnetic field at that point? \(\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.\) )

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency \(10\ GHz\). What is the frequency of the microwave measured by the observer?.......\(GHz\) ( speed of light \(= 3 \times  10^8 \) \(ms^{-1}\))

Two objects \(A\) and \(B\) are placed at \(15\,cm\) and \(25\,cm\) from the pole in front of a concave mirror having radius of curvature \(40 cm\). The distance between images formed by the mirror is \(..........\,cm\)

Velocity-time graph for a body of mass \(10\, kg\) is shown in figure. Work-done on the body in first two seconds of the motion is  ................ \(\mathrm{J}\)

Two light waves having the same wavelength \(\lambda\) in vacuum are in phase initially. Then the first wave travels a path \(L _{1}\) through a medium of refractive index \(n_{1}\) while the second wave travels a path of length \(L_{2}\) through a medium of refractive index \(n _{2}\). After this the phase difference between the two waves is:

The coercivity of a small magnet where the ferromagnet gets demagnetized is \(3 \times 10^3\) \( Am^{-1}\) The current required to be passed in a solenoid oflength \(10\ cm\) and number of turns \(100\), so that the magnet gets demagnetized when inside the solenoid, is

In a coil, the current changes form \(-2 \mathrm{~A}\) to \(+2 \mathrm{~A}\) in \(0.2 \mathrm{~s}\) and induces an emf of \(0.1 \mathrm{~V}\). The selfinductance of the coil is _______.

In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is

At an angle of \(30^{\circ}\) to the magnetic meridian, the apparent dip is \(45^{\circ} .\) Find the true dip :