Two inductors $L_i$ (inductance $1 \mathrm{mH}$, internal resistance $3 \mathrm{\Omega }$ ) and $L_2$ (inductance $2 \mathrm{mH}$, internal resistance $4 \mathrm{\Omega }$ ), and a resistor $R$(resistance $12 \mathrm{\Omega }$ ) are all connected in parallel across a $5 \mathrm{V}$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum current $\left(\frac{I_{max}}{I_{min}}\right)$ drawn from the battery is:

For a prism of prism angle $\theta =60°$, the refractive indices of the left half and the right half are, respectively, $n_1$ and $n_2$, $\left(n_2\ge n_1\right)$ as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays will have minimum deviation if $n_1=n_2=n=1.5.$ For the case of unequal refractive indices, $n_1=n$ and $n_2=n+∆n$ (where $∆n<<n$), the angle of emergence $e=i+∆e$. Which of the following statement(s) is(are) correct?

For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that:
\(V=\frac{q}{4 \pi \varepsilon_0 R_0} \text { for } r \leq R_0\)
and \(V=\frac{q}{4 \pi \varepsilon_0 r}\) for \(r \geq R_0\)
Then which option(s) are correct

The work done on a particle of mass m by a force $\text{K}\left[\frac{\text{x}}{{\left({\text{x}}^2+{\text{y}}^2\right)}^{3/2}}\widehat{\text{i}}+\frac{\text{y}}{{\left({\text{x}}^2+{\text{y}}^2\right)}^{3/2}}\widehat{\text{j}}\right]$ (K being a constant of appropriate dimensions, when the particle is taken from the point (a,0) to the point (0,a) along a circular path of radius a about the origin in the x-y plane is

A ball of mass \((m) 0.5 \mathrm{~kg}\) is attached to the end of a string having length \((L) 0.5 \mathrm{~m}\). The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is \(324 \mathrm{~N}\). The maximum possible value of angular velocity of ball (in rad/s) is

Figure shows three resistor configurations \(R_1, R_2\) and \(R_3\) connected to \(3 \mathrm{~V}\) battery. If the power dissipated by the configuration \(R_1, R_2\) and \(R_3\) is \(P_1, P_2\) and \(P_3\), respectively, then

Paragraph:
When a particle is restricted to move along \(x\)-axis between \(x=0\) and \(x=a\), where \(a\) is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends \(x=0\) and \(x=a\). The wavelength of this standing wave is related to the liner momentum \(p\) of the particle according to the de Broglie relation. The energy of the particle of mass \(m\) is related to its linear momentum as \(E=\frac{p^2}{2 m}\). Thus, the energy of the particle can be denoted by a quantum number \(n\) taking values \(1,2,3, \ldots(n=1\), called the ground state) corresponding to the number of loops in the standing wave.
Use the model described above to answer the following three questions for a particle moving in the line \(x=0\) to \(x=a\) [Take \(h=6.6 \times 10^{-34} \mathrm{Js}\) and \(e=1.6 \times 10^{-19} \mathrm{C}\) ]
Question:
If the mass of the particle is \(m=1.0 \times 10^{-30} \mathrm{~kg}\) and \(a=6.6 \mathrm{~nm}\), the energy of the particle in its ground state is closest to

Consider the following linear equations
\[
a x+b y+c z=0, b x+c y+a z=0, c x+a y+b z=0
\]
Match the conditions/expressions in Column I with statements in Column II.

A uniform magnetic field B exists in the region between $x=0$ and $x=\frac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum p directed along $x$ -axis enters region 2 from region 1 at point $P_1\left(y=-R\right).$ Which of the following option(s) is/are correct?

Match the orbital overlap figures shown in List-I with the description given in List-II and select the correct
answer using the code given below the lists.

	List – I		List - II
A.		P	$\mathrm{p}-\mathrm{d}\mathrm{}\mathrm{\pi }$ antibonding
B.		Q	$\mathrm{d}-\mathrm{d}\mathrm{}\mathrm{\sigma }$ bonding
C.		R	$\mathrm{p}-\mathrm{d}\mathrm{}\mathrm{\pi }$ bonding
D.		S	$\mathrm{d}-\mathrm{d}\mathrm{}\mathrm{\sigma }$ antibonding

The atomic masses of $\mathrm{He}$ and $\mathrm{Ne}$ are $4$ and $20 \mathrm{amu}$, respectively. The value of the de Broglie wavelength of $\mathrm{He}$ gas at $-73° \mathrm{C}$ is "M" times that of the de Broglie wavelength of $\mathrm{Ne}$ at $727° \mathrm{C}$. M is:

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There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of \(\mathrm{NH}_3\) and \(\mathrm{PH}_3\). Phosphine is a flammable gas and is prepared from white phosphorus.
Question:
Among the following, the correct statement is

Four point charges, each of \(+q\), are rigidly fixed at the four corners of a square planar soap film of side \(a\). The surface tension of the soap film is \(\gamma\). The system of charges and planar film are in equilibrium, and \(a=k\left[\frac{q^2}{\gamma}\right]^{1 / N}\), where \(k\) is a constant. Then, \(N\) is