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

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

\(\sqrt{d_{1}}\) and \(\sqrt{d_{2}}\) are the impact parameters corresponding to scattering angles \(60^{\circ}\) and \(90^{\circ}\) respectively, when an \(\alpha\) particle is approaching a gold nucleus. For \(d_{1}=x d_{2}\), the value of \(x\) will be ________

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. \(A\). In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. \(B.\) The energy in electromagnetic wave is divided equally between electric and magnetic fields. \(C.\) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. \(D.\) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. \(E.\) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below:

Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

A circular coil of \(1000 \,\,turns\) each with area \(1\, m ^{2}\) is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of \(0.07 \,T\). The maximum voltage generation will be......... \(V\).

A Carnot engine with efficiency \(50\,\%\) takes heat from a source at \(600\,K\). In order to increase the efficiency to \(70\,\%\), keeping the temperature of sink same, the new temperature of the source will be \(.........\,K\)

Work done by a Carnot engine operating between temperatures \(127^{\circ}\,C\) and \(27^{\circ}\,C\) is \(2\,kJ\). The amount of heat transferred to the engine by the reservoir is \(........\,kJ\)

Under steady state condition the potential difference across the capacitor in the circuit is _______ V.

\(\lim _{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}\) is equal to

The value of \(\left(\sin 70^{\circ}\right)\left(\cot 10^{\circ} \cot 70^{\circ}-1\right)\) is

A convex mirror of radius of curvature \(30 \mathrm{~cm}\) forms an image that is half the size of the object. The object distance is :

Let \(\vec{a}, \vec{b}, \vec{c}\) be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle \(\theta\), with the vector \(\vec{a}+\vec{b}+\vec{c}\). Then \(36 \cos ^{2} 2 \theta\) is equal to \(.....\)

A shunt of resistance \(1\,\Omega \) is connected across a galvanometer of \(120\,\Omega \) resistance. A current of \(5.5\, ampere\) gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly ............... \(ampere\)