A long solenoid is formed by winding \(70\) turns \(cm ^{-1}\). If \(2.0\,A\) current flows, then the magnetic field produced inside the solenoid is \(.......\times 10^{-4}\,T\) \(\left(\mu_0=4 \pi \times 10^{-7}\,TmA ^{-1}\right)\)

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 _______.

\(AC\) voltage \(V(t)=20\,sin\omega \,t\) of frequency \(50\, {Hz}\) is applied to a parallel plate capacitor. The separation between the plates is \(2\, {mm}\) and the area is \(1 \,{m}^{2}\). The amplitude of the oscillating displacement current for the applied \(AC\) voltage is ...... \(\mu {A}\). [Take \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \,{F} / {m}\right]\)

The velocity of a particle executing simple harmonic motion along \(x\)-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7}\) s, the value of \(x\) is _____.

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

	List \(-I\)		List \(-II\)
\(A\).	Coefficient of Viscosity	\(I\).	\([M L^2T^{–2}]\)
\(B\).	Surface Tension	\(II\).	\([M L^2T^{–1}]\)
\(C\).	Angular momentum	\(III\).	\([M L^{-1}T^{–1}]\)
\(D\).	Rotational Kimeatic energy	\(IV\).	\([M L^0T^{–2}]\)

A cylindrical wire of mass \((0.4 \pm 0.01)\,g\) has length \((8 \pm 0.04)\,cm\) and radius \((6 \pm 0.03)\,mm\).The maximum error in its density will be \(......\,\%\)

The radiation corresponding to \(3 \rightarrow 2\) transition ofhydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of \(3 \times  10^{-4}\) \(T\) If the radius of the largest circular path followed by these electrons is \(10.0\ mm\), the work function of the metal is close to......\( eV\)

An air bubble of diameter \(6\,mm\) rises steadily through a solution of density \(1750\,kg / m ^3\) at the rate of \(0.35\,cm / s\). The co-efficient of viscosity of the solution (neglect density of air) is \(..........\,Pas\) (given, \(g =10\,ms ^{-2}\))

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is \(30^{\circ}\) in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _______ \(\mu \mathrm{m}\).

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly _______.