Identify the logic operation carried out by the given circuit :-

A body cools in \(7\) minutes from \(60^{\circ}\,C\) to \(40^{\circ}\,C\). The temperature of the surrounding is \(10^{\circ}\,C\). The temperature of the body after the next \(7\) minutes will be

Arrange the following in the ascending order of wavelength : \((A)\) Gamma rays \(\left(\lambda_1\right)\) \((B)\) x-ray \(\left(\lambda_2\right)\) \((C)\) Infrared waves \(\left(\lambda_3\right)\) \((D)\) Microwaves \(\left(\lambda_4\right)\) Choose the most appropriate answer from the options given below :

An \(HCl\) molecule has rotational, translational and vibrational motions. If the \(rms\) velocity of \(HCl\) molecules in its gaseous phase is \(\bar v ,\,m\) is its mass and \(k_B\) is Boltzmann constant, then its temperature will be

Suppose a uniformly charged wall provides a uniform electric field of \(2 \times 10^4 \mathrm{~N} / \mathrm{C}\) normally. A charged particle of mass \(2 \mathrm{~g}\) being suspended through a silk thread of length \(20 \mathrm{~cm}\) and remain stayed at a distance of \(10 \mathrm{~cm}\) from the wall. Then the charge on the particle will be \(\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}\) where \(\mathrm{x}=\) _______ [use \(g=10 \mathrm{~m} / \mathrm{s}^2\)]

Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is

This question has Statement-I and Statement-2. Of the four ch.oices given after the Statements, choose the one that best describes the two Statetnents. Statement \(-1\) : A capillary is dipped in a liquid and liquid rises to a height \(h\) in it. As the temperature of the liquid is raised, the height \(h\) increases (if the density of the liquid and the angle of contact remain the same). Statement \(-2\) : Surface tension of a liquid decreases with the rise in its temperature.

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is change in internal energy of the system

Process	Condition
\((I)\) Adiabatic	\((A)\; \Delta W =0\)
\((II)\) Isothermal	\((B)\; \Delta Q=0\)
\((III)\) Isochoric	\((C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0\)
\((IV)\) Isobaric	\((D)\; \Delta U =0\)

A body of mass (\(2 {M}\)) splits into four masses \(\{{m}, {M}-{m}, {m}, {M}-{m}\}\), which are rearranged to form a square as shown in the figure. The ratio of \(\frac{{M}}{{m}}\) for which, the gravitational potential energy of the system becomes maximum is \({x}: 1\). The value of \(x\) is ..... .

The equivalent resistance between points \(A\) and \(B\) in the given network is ............ \(\Omega\)