A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is _______. (Given \(\left.\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

When an air bubble of radius \(r\) rises from the bottom to the surface of a lake, its radius becomes \(\frac{{5r}}{4}\).Taking the atmospheric pressure to be equal to \(10\,m\) height of water column, the depth of the lake would approximately be ....... \(m\) (ignore the surface tension and the effect of temperature)

Four bulbs \(B_1 , B_2, B_3\) and \(B_4\) of \(100\, W\) each are connected to \(220\, V\) main as shown in the figure. The reading in an ideal ammeter will be ............... \(A\)

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(D=0.2 \mathrm{~m}\). the minimum distance between the slits \(S_1\) and \(S_2\) is ____________ \(mm\).

Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). The value of \(x\) is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

If each diode has a forward bias resistance of \(25\,\Omega\) in the below circuit,Which of the following options is correct:

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \(27\,^oC\).The work done on the gas will be