In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of \(\left[M^P L^{\circ} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\right]\). The value of P and Q are :

A tuning fork of frequency \(340\,Hz\) resonates in the fundamental mode with an air column of length \(125\,cm\) in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ \(cm\) (Velocity of sound in air is \(340\,ms ^{-1}\) )

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \(P_1\) and \(P_2\) are orthogonal to each other. The polarizer \(P_3\) covers both the slits with its transmission axis at \(45^{\circ}\) to those of \(P_1\) and \(P_2\). An unpolarized light of wavelength \(\lambda\) and intensity \(I_0\) is incident on \(P_1\) and \(P_2\). The intensity at a point after \(P_3\) where the path difference between the light waves from \(s_1\) and \(s_2\) is \(\frac{\lambda}{3}\), is _______.

The amount of heat needed to raise the temperature of \(4\, moles\) of a rigid diatomic gas from \(0^{\circ} {C}\) to \(50^{\circ} {C}\) when no work is done is ......\({R}\) (\(R\) is the universal gas constant)

Two wires each of radius \(0.2\,cm\) and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is \(.........\times 10^{-6}\,m\). [Young's modulus for steel \(=2 \times 10^{11}\,Nm ^{-2}\) and \(g =10\,ms ^{-2}\) ]

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the \(2^{\text{nd}}\) and \(4^{\text{th}}\) orbits of hydrogen atom _______.

Equivalent resistance of the following network is _______ \(\Omega\).

A screw gauge of pitch \(0.5\,mm\) is used to measure the diameter of uniform wire of length \(6.8\,cm\), the main scale reading is \(1.5\,mm\) and circular scale reading is \(7\). The calculated curved surface area of wire to appropriate significant figures is \(......cm^2\) . [Screw gauge has \(50\) divisions on the circular scale]

A plane electromagnetic wave in a non-magnetic dielectric medium is given by \(\vec E\, = \,{\vec E_0}\,(4 \times {10^{ - 7}}\,x - 50t)\) with distance being in meter and time in seconds. The dielectric constant of the medium is

A planar loop made of wire is rotating in a uniform magnetic field. At time \(t=0\), the plane of the loop is perpendicular to the magnetic field. If the loop is rotating about an axis passing through its plane with a period of \(10\) seconds, at which of the following times will the induced electromotive force (emf) be maximum and minimum, respectively?

A physical quantity \(p\) is described by the relation \(p\, = a^{1/2}\, b^2\, c^3\, d^{-4}\) If the relative errors in the measurement of \(a, b, c\) and \(d\) respectively, are \(2\% , 1\%, 3\%\) and \(5\%\), then the relative error in \(P\) will be ........... \(\%\)