A Conductor (shown in the figure) carrying constant current $\mathrm{I}$ is kept in the $\mathrm{x}$ - $\mathrm{y}$ plane in a uniform magnetic field $\overrightarrow{\mathrm{B}}$ . If $\mathrm{F}$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are)

A metal rod \(A B\) of length \(10 x\) has its one end \(A\) in ice at \(0^{\circ} \mathrm{C}\) and the other end \(B\) in water at \(100^{\circ} \mathrm{C}\). If a point \(P\) on the rod is maintained at \(400^{\circ} \mathrm{C}\), then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is \(540 \mathrm{calg}^{-1}\) and latent heat of melting of ice is \(80 \mathrm{calg}^{-1}\). If the point \(P\) is at a distance of \(\lambda x\) from the ice end \(A\), find the value of \(\lambda\). [Neglect any heat loss to the surrounding.]

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The capacitor of capacitance \(C\) can be charged (with the help of a resistance \(R\) ) by a voltage source \(V\), by closing switch \(S_1\) while keeping switch \(S_2\) open. The capacitor can be connected in series with an inductor \(L\) by closing switch \(S_2\) and opening \(S_1\).

Question :
After the capacitor gets fully charged, \(S_1\) is opened and \(S_2\) is closed so that the inductor is connected in series with the capacitor. Then,

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?

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Two trains \(A\) and \(B\) are moving with speeds \(20 \mathrm{~m} / \mathrm{s}\) and \(30 \mathrm{~m} / \mathrm{s}\), respectively in the same direction on the same straight track, with \(B\) ahead of \(A\). The engines are at the front ends. The engine of train \(A\) blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from \(f_1=800 \mathrm{~Hz}\) to \(f_2=1120 \mathrm{~Hz}\), as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus \(320 \mathrm{~Hz}\). The speed of sound in still air is \(340 \mathrm{~m} / \mathrm{s}\).
Question:
The speed of sound of the whistle is

A particle of mass $\text{0.2 kg}$ is moving in one dimension under a force that delivers a constant power $\text{0.5 W}$ to the particle. If the initial speed $\left({in\; ms}^{-1}\right)$ of the particle is zero, the speed $\left({in\; ms}^{-1}\right)$ after $\text{5 s}$ is

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma =\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{\mathrm{a}2}$, the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$, respectively. Which of the following statement(s) is(are) correct?

A colorless aqueous solution contains nitrates of two metals, $\mathrm{X}$ and $\mathrm{Y}$. When it was added to an aqueous solution of $\mathrm{NaCl}$, a white precipitate was formed. This precipitate was found to be partly soluble in hot water to give a residue $\mathrm{P}$ and a solution $\mathrm{Q}$. The residue $\mathrm{P}$ was soluble in aq. ${\mathrm{NH}}_3$ and also in excess sodium thiosulfate. The hot solution $\mathrm{Q}$ gave a yellow precipitate with $\mathrm{KI}$. The metals $\mathrm{X}$ and $\mathrm{Y}$, respectively, are

Consider a system of three connected strings, \(S_1, S_2\) and \(S_3\) with uniform linear mass densities \(\mu \mathrm{kg} / \mathrm{m}\), \(4 \mu \mathrm{~kg} / \mathrm{m}\) and \(16 \mu \mathrm{~kg} / \mathrm{m}\), respectively, as shown in the figure. \(S_1\) and \(S_2\) are connected at the point \(P\), whereas \(S_2\) and \(S_3\) are connected at the point \(Q\), and the other end of \(S_3\) is connected to a wall. A wave generator O is connected to the free end of \(S_1\). The wave from the generator is represented by \(y=y_0\) \(\cos (\omega t-k x) \mathrm{cm}\), where \(y_0, \omega\) and \(k\) are constants of appropriate dimensions. Which of the following statements is/are correct:

Addition of excess aqueous ammonia to a pink coloured aqueous solution of $MC{l}_2.6H_{2}O \left(X\right)$ and $N{H}_{4}Cl$ gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1 : 3 electrolyte. The reaction of X with excess HCl at room temperature results in the formation of a blue coloured complex Z. The calculated spin only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y.
Among the following options, which statement(s) is(are) correct ?

Let $x\in R$ and let $P=\left[\begin{array}{ccc}1& 1& 1\\ 0& 2& 2\\ 0& 0& 3\end{array}\right], Q=\left[\begin{array}{ccc}2& x& x\\ 0& 4& 0\\ x& x& 6\end{array}\right]$ and $R=PQ{P}^{-1}.$
Then which of the following options is/are correct?

The IUPAC name of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCl}\) is

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that