The electric field in a region is given by \(\vec E = \frac{3}{5}{E_0}\hat i + \frac{4}{5}{E_0}\hat j\) and \(E_0 = 2\times10^3\, N/C\). Then, the flux of this field through a rectangular surface of area \(0.2\, m^2\) parallel to the \(y-z\) plane is......\(\frac{{N - {m^2}}}{C}\)

Given below are two statements: Statement \(I:\) Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement \(II:\) Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer from the options given below:

Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is \(L\) about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :

Charges \(-q\) and \(+ q\) located at \(A\) and \(B\), respectively, constitute an electric dipole. Distance \(AB = 2a\), \(O\) is the mid point of the dipole and \(OP\) is perpendicular to \(AB\). A charge \(Q\) is placed at \(P\) where \(OP = y\) and \(y >> 2a\). The charge \(Q\) experiences an electrostatic force \(F\). If \(Q\) is now moved along the equatorial line to \(P'\) such that \(OP' = \frac{y}{3}\), the force on \(Q\) will be close to: \(\left( {\frac{y}{3} >  > 2a} \right)\)

An inductor of self inductance 1 H connected in series with a resistor of \(100 \pi \mathrm{ohm}\) and an ac supply of \(100 \pi\) volt, 50 Hz. Maximum current flowing in the circuit is ________ A.

A small square loop of wire of side \(\ell\) is placed inside a large square loop of wire of side \(L\) \(\left(\mathrm{L}=\ell^2\right)\). The loops are coplanar and therr centers coinside. The value of the mutual inductance of the system is \(\sqrt{\mathrm{x}} \times 10^{-7} \mathrm{H}\), where X = _______.

In the given circuit all resistances are of value \(R\,ohm\) each. The equivalent resistance between \(A\) and \(B\) is 

Two cylindrical vessels of equal cross-sectional area \(16\,cm ^{2}\) contain water upto herghts \(100\,cm\) and \(150\,cm\) respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is \(......J\) [Take density of water \(=10^{3}\,kg / m ^{3}\) and \(g =10\,ms ^{-2}\) ]

In a meter bridge experiment the balance point in obtained if the gaps are closed by \(2\,\Omega\) and \(3\,\Omega\). A shunt of \(x\,\Omega\) is added to \(3\,\Omega\) resistor to shift the balancing point by \(22.5\,cm\). The value of \(X\) is \(................\)

A thin convex lens \(L\) (refractive index \(= 1.5\)) is placed on a plane mirror \(M\). When a pin is placed at \(A\), such that \(OA = 18\, cm\), its real inverted image is formed at \(A\) itself, as shown in figure. When a liquid of refractive index \({\mu _1}\) is put between the lens and the mirror, the pin has to be moved to \(A’\). such that \(OA’ = 27\,cm\), to get its inverted real image at \(A'\) itself. The value of \({\mu _1}\) will be