Column-II gives certain systems undergoing a process. Column-I suggests changes in some of the parameters related to the system. Match the statements in Column-I to the appropriate process (es) from Column-II.

A \(2 \mu \mathrm{F}\) capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch \(S\) is turned to position 2 , is

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers $R_c<\frac{R}{2},$ which of the following statement(s) about any one of the galvanometers
is(are) true ?

A train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0\left(S_0=4S_t\right)$. Assume that almost all the air (density $\rho$) in front of the train flows back between its sides and the walls of the tunnel. Also, the airflow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $P_0$. If the pressure in the region between the sides of the train and the tunnel walls is $P$, then $\left(P_0-P\right)=\frac{7}{2N}\rho v_t^2.$ The value of $N$ is _______.

A block of mass $2\mathrm{M}$ is attached to a massless spring with spring-constant $\mathrm{k}.$ This block is connected to two other blocks of masses $\mathrm{M}$ and $2\mathrm{M}$ using two massless pulleys and strings. The accelerations of the blocks are ${\mathrm{a}}_1,{\mathrm{a}}_2$ and ${\mathrm{a}}_3$ as shown in figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is ${\mathrm{x}}_0.$ Which of the following option(s) is/are correct?
[ $\mathrm{g}$ is the acceleration due to gravity. Neglect friction]

A metal rod of length \(L\) and mass \(m\) is pivoted at one end. A thin disc of mass \(M\) and radius \(R( < L)\) is attached at its centre to the free end of the rod. Consider two ways the disc is attached. Case A-the disc is not free to rotate about its centre and case \(B\)-the disc is free to rotate about its centre. The rod-disc system performs
SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is/are true?

Paragraph:

The figure shows a circular loop of radius \(a\) with two long parallel wires (numbered \(1\) and \(2\) ) all in the plane of the paper. The distance of each wire from the centre of the loop is \(d\). The loop and the wires are carrying the same current \(I\). The current in the loop is in the counterclockwise direction if seen from above.



Question:

Consider \(d \gg a\), and the loop is rotated about its diameter parallel to the wires by \(30^{\circ}\) from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

The number of geometric isomers possible for the complex ${\left[\text{C}\text{o}{\text{L}}_2\text{C}{\text{l}}_2\right]}^{-}\left(\text{L}={\text{H}}_2\text{N}\text{C}{\text{H}}_2\text{C}{\text{H}}_2{\text{O}}^{-}\right)$ is
 

Consider a hydrogen-like ionized atom with atomic number $Z$ with a single electron. In the emission spectrum of this atom, the photon emitted in the $n=2 \mathrm{t}\mathrm{o} n= 1$ transition has energy $74.8 \mathrm{eV}$ higher than the photon emitted in the $n=3 \mathrm{t}\mathrm{o} n=2$ transition. Given that the ionization energy of the hydrogen atom is $13.6 \mathrm{eV}$, what is the value of $Z$?

The colour of light absorbed by an aqueous solution of \(\mathrm{CuSO}_{4}\) is:

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is

A cubical region of side \(a\) has its centre at the origin. It encloses three fixed point charges, \(-q\) at \((0,-a / 4,0),+3 q\) at \((0,0,0)\) and \(-q\) at \((0,+a / 4,0)\). Choose the correct options(s)

The wave function, ${\mathrm{\psi }}_{\mathrm{n},\mathrm{}\mathrm{l},\mathrm{}{\mathrm{m}}_{\mathrm{l}}}$ is a mathematical function whose value depends upon spherical polar coordinates $\left(\mathrm{r},\mathrm{}\mathrm{\theta },\mathrm{}\mathrm{\varphi }\right)$ of the electron and characterized by the quantum numbers $\mathrm{n},\mathrm{}\mathrm{l}$ and ${\mathrm{m}}_{\mathrm{l}}$ . Here $\mathrm{r}$ is the distance from the nucleus, $\mathrm{\theta }$ is colatitude and $\mathrm{\varphi }$ is azimuth. In the mathematical functions given in the Table, $\mathrm{Z}$is the atomic number and ${\mathrm{a}}_{\mathrm{o}}$ is Bohr radius

Column 1	Column 2	Column 3
(I) 1s orbital	\(\text {(i) } \psi_{ n , 1, m_1}\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\)	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at the nucleus \(\propto \frac{1}{ a _{ o }^3}\).
(III) \(2 p _{ z }\) orbital	\(\text {(iii) } \psi_{ n }, 1, m_{ l }\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\)	(R) Probability density is maximum at the nucleus.
(IV) \(3 d_{ z }^2\) orbital	(iv) \(x y\)-plane is a nodal plane	(S) Energy needed to excite an electron from \(n =2\) state to \(n =4\) state is \(\frac{27}{32}\) times the energy needed to excite are electron from \(n =2\) state to \(n =6\) state.

For hydrogen atom, what is the only CORRECT combination?