The wavelength of an \(X-\)ray beam is \(10 \, \mathring A\). The mass of a fictitious particle having the same energy as that of the \(X-\)ray photons is \(\frac{ x }{3} h \,kg\). The value of \(x\) is ....... . \((h =\) Planck's constant \()\)

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius \(9 \mathrm{~m}\) and completes \(120\) revolutions in \(3\) minutes. The magnitude of centripetal acceleration of monkey is _______ (in \(\mathrm{m} / \mathrm{s}^2\) ).

A 2 A current carrying straight metal wire of resistance \(1 \Omega\), resistivity \(2 \times 10^{-6} \Omega m\), area of cross-section \(10 mm^2\) and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field \(\vec{B}\). The magnitude of \(B\) is _______ \(\times 10^{-1} T\) (given, \(g =10 m / s ^2\) ).

Match List \(I\) with List \(II\)

List - \(I\)	List - \(II\)
\((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below :

For \(a\) gas \(C_{p}-C_{V}=R\) in a state \(P\) and \(C_{p}-C_{V}=1.10 R\) in a state \(Q, T_{p}\) and \(T_{Q}\) are the temperatures in two different states \(P\) and \(Q\) respectively. Then

When resonance is produced in a series \(LCR\) circuit, then which of the following is not correct ?

The induced \(emf\) can be produced in a coil by \(A.\) moving the coil with uniform speed inside magnetic field \(B.\) moving the coil with non-uniform speed inside uniform magnetic field \(C.\) rotating the coil inside the uniform magnetic field \(D.\) changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:

An electric appliance supplies \(6000\, {J} / {min}\) heat to the system. If the system delivers a power of \(90\, {W}\). How long (in \(sec\)) it would take to increase the internal energy by \(2.5 \times 10^{3}\, {J}\) ?

A particle of mass \(m\) is acted upon by a force \(F\) given by the empirical law \(F = \frac{R}{{{t^2}}}\,v(t)\). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot 

Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

A test particle is moving in a circular orbit in the gravitational field produced by a mass density \(\rho \left( r \right) = \frac{K}{{{r^2}}}\). Identify the correct relation between the radius \(R\) of the particle’s orbit and its period \(T\)

A current of 5A exists in a square loop of side \(\frac{1}{\sqrt{2}} \mathrm{~m}\). Then the magnitude of the magnetic field \(B\) at the centre of the square loop will be \(p \times 10^{-6} \mathrm{~T}\). where, value of p is _____ .
\(\left[\right.\) Take \(\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\).

In a Young's double slit experiment, the separation between the slits is \(0.15\; \mathrm{mm}\). In the experiment, a source of light of wavelength \(589 \;\mathrm{nm}\) is used and the interference pattern is observed on a screen kept \(1.5\; \mathrm{m}\) away. The separation between the successive bright fringes on the screen is......\(mm\)