What will be the magnitude of electric field at point \(O\) as shown in figure ? Each side of the figure is \(I\) and perpendicular to each other.

A parallel plate capacitor is formed by two plates each of area \(30 \pi\, cm ^{2}\) separated by \(1\, mm\). A material of dielectric strength \(3.6 \times 10^{7} \,Vm ^{-1}\) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \(7 \times 10^{-6}\, C\), the value of dielectric constant of the material is \(\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}\)

The electric field intensity produced by the radiation coming from a \(100\, W\) bulb at a distance of \(3\, m\) is \(E\). The electric field intensity produced by the radiation coming from \(60\, W\) at the same distance is \(\sqrt{\frac{x}{5}} E\). Where the value of \(x=......... .\)

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

Given that \(1\,g\) of water in liquid phase has volume \(1\,cm^3\) and in vapour phase \(1671\, cm^3\) at atmospheric pressure and the latent heat of vaporization of water is \(2256\,J/g;\) the change in the internal energy in joules for \(1\,g\) of water at \(373\,K\) when it changes from liquid phase to vapour phase at the same temperature is ....... \(J\)

The equivalent resistance between \(A\) and \(B\) as shown in figure is \(........\,k\Omega\)

India's Mangalyan was sent to the Mars by launching it into a transfer orbit \(EOM\) around the sun . It leaves the earth at \(E\) and meets Mars at \(M\) . If the semi-major axis of Earth's orbit is \(a_e = 1.5 \times 10^{11}\, m\), that of Mars orbit \(a_m= 2.28 \times 10^{11}\, m\), taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to ........ \(days\).

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\overrightarrow{ a }, \overrightarrow{ b }\) and \(\overrightarrow{ c }\) respectively. Then choose the correct relation for these vectors.

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R) : In isothermal process, \(\mathrm{PV}=\) constant, while in adiabatic process \(\mathrm{PV}^\gamma=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below :