Two wires each carrying a steady current \(I\) are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the \(4 \times 4\) matrix given in the ORS.

Two soap bubbles \(A\) and \(B\) are kept in a closed chamber where the air is maintained at pressure \(8 \mathrm{Nm}^{-2}\). The radii of bubbles \(A\) and \(B\) are \(2 \mathrm{~cm}\), respectively. Surface tension of the soap-water used to make bubbles is \(0.04\) \(\mathrm{Nm}^{-1}\). Find the ratio \(\frac{n_B}{n_A}\), where \(n_A\) and \(n_B\) are the number of moles of air in bubbles \(A\) and \(B\), respectively. [Neglect the effect of gravity]

A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field $\overrightarrow{B}$ points into the plane of the paper. At $t=0$ , the loop starts rotating about the common diameter as axis with a constant angular velocity in the magnetic field. Which of the following options is/are correct?

A point source \(\mathrm{S}\) emits unpolarized light uniformly in all directions. At two points \(\mathrm{A}\) and \(\mathrm{B}\), the ratio \(r=I_A / I_B\) of the intensities of light is 2. If a set of two polaroids having \(45^{\circ}\) angle between their pass-axes is placed just before point \(\mathrm{B}\), then the new value of \(r\) will be ______

Suppose a ${}_{88}{}^{226}Ra$ nucleus at rest and in ground state undergoes $\mathrm{\alpha }$ -decay to a ${}_{86}{}^{222}Rn$ nucleus in its excited state. The kinetic energy of the emitted $\mathrm{\alpha }$ particle is found to be $4.44\mathrm{ }\mathrm{M}\mathrm{e}\mathrm{V}.{}_{86}{}^{222}Rn$ nucleus then goes to its ground state by $\mathrm{\gamma }$ -decay. The energy of the emitted $\mathrm{\gamma }$ -photon is _______ $\mathrm{k}\mathrm{e}\mathrm{V},$
[Given: atomic mass of ${\mathrm{ }}_{88}^{226}\mathrm{R}\mathrm{a}=226.005\mathrm{u},$ atomic mass of ${\mathrm{ }}_{86}^{222}\mathrm{R}\mathrm{n}=222.000\mathrm{u},$ atomic mass of $\mathrm{\alpha }$ particle $=4.000\mathrm{u},1\mathrm{u}=931\mathrm{M}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2,\mathrm{c}$ is speed of the light]

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure).Initially the gas is at temperature ${\mathrm{T}}_1$ , pressure ${\mathrm{P}}_1$ and volume ${\mathrm{V}}_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature ${\mathrm{T}}_2$ , pressure ${\mathrm{P}}_2$ and volume ${\mathrm{V}}_2$ . During this process the piston moves out by a distance $\mathrm{x}$ . Ignoring the friction between the piston the cylinder, the correct statement(s) is (are)

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\(\mathbf{P}_{17 \text { - } 19}\) : Paragraph for Questions Nos. 17 to 19 Two discs \(A\) and \(B\) are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I, respectively about the common axis. Disc \(A\) is imparted an initial angular velocity \(2 \omega\) using the entire potential energy of a spring compressed by a distance \(x_1\). Disc \(B\) is imparted an angular velocity \(\omega\) by a spring having the same spring constant and compressed by a distance \(x_2\). Both the discs rotate in the clockwise direction.
Question :
When disc \(B\) is brought in contact with disc \(A\), they acquire a common angular velocity in time \(t\). The average frictional torque on one disc by the other during this period is

According to Bohr's model, the highest kinetic energy is associated with the electron in the

Let $\hat{i},\hat{j}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let $\overrightarrow{a}=3\hat{i}+\hat{j}-\hat{k}$ $\overrightarrow{b}=\hat{i}+b_2\hat{j}+b_3\hat{k}, b_2,b_3\in \mathrm{ℝ}$ $\overrightarrow{c}=c_1\hat{i}+c_2\hat{j}+c_3\hat{k},c_1,c_2,c_3\in \mathrm{ℝ}$ be three vectors such that $b_2{b}_3>0,\overrightarrow{a}·\overrightarrow{b}=0$ and $\left(\begin{array}{ccc}0& -c_3& c_2\\ c_3& 0& -c_1\\ -c_2& c_1& 0\end{array}\right)\left(\begin{array}{l}1\\ b_2\\ b_3\end{array}\right)=\left(\begin{array}{c}3-c_1\\ 1-c_2\\ -1-c_3\end{array}\right).$ Then, which of the following is/are TRUE?

Among \(\left[ I _3\right]^{+},\left[ SiO _4\right]^{4-}, SO _2 Cl _2, XeF _2, SF _4, ClF _3,\) \(Ni ( CO )_4, XeO _2 F_2,\left[ PtCl _4\right]^{2-}, XeF _4\), and \(SOCl _2\), the total number of species having \(sp ^3\) hybridised central atom is

Let \(\alpha(a)\) and \(\beta(a)\) be the roots of the equation \((\sqrt[3]{1+a}-1) x^{2}+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0\) where \(a\) \(>-1\). Then \(\lim _{a \rightarrow 0^{+}} \alpha(a)\) and \(\lim _{x \rightarrow 0^{+}} \beta(a)\) are

A transverse sinusoidal wave moves along a string in the positive \(x\)-direction at a speed of \(10 \mathrm{~cm} / \mathrm{s}\). The wavelength of the wave is \(0.5 \mathrm{~m}\) and its amplitude is \(10 \mathrm{~cm}\). At a particular time \(t\), the snap-shot of the wave is shown in figure. The velocity of point \(P\) when its displacement is \(5 \mathrm{~cm}\) is

Two resistances $R_1=X \mathrm{\Omega }$ and $R_2=1 \mathrm{\Omega }$ are connected to a wire $AB$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \mathrm{mm}$ at $A$ to $1 \mathrm{mm}$ at $B$. A galvanometer $\left(G\right)$ connected to the center of the wire, $50 \mathrm{cm}$ from each end along its axis, shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is _______.