A liquid at ${30\mathrm{ }}^{\mathrm{o}}\mathrm{C}$ is poured very slowly into a Calorimeter that is at temperature of ${110\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ The boiling temperature of the liquid is ${80\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ It is found that the first $5\mathrm{ }\mathrm{g}\mathrm{m}$ of the liquid completely evaporates. After pouring another $80\mathrm{ }\mathrm{g}\mathrm{m}$ of the liquid the equilibrium temperature is found to be ${50\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ The ratio of the Latent heat of the liquid to its specific heat will be ______ ${\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$
[Neglect the heat exchange with surrounding]

Two satellites $P$ and $Q$ are moving in different circular orbits around the Earth(radius $R$). The heights of $P$ and $Q$ from the Earth surface are $h_P$ and $h_Q$, respectively, where $h_P=\frac{R}{3}$. The accelerations of $P$ and $Q$ due to Earth’s gravity are $g_P$ and $g_Q$, respectively. If $\frac{g_P}{g_Q}=\frac{36}{25}$, what is the value of $h_Q$?

An infinitely long uniform line charge distribution of charge per unit length $\mathrm{\lambda }$ lies parallel to the $\mathrm{y}$ -axis in the $\mathrm{y}$ - $\mathrm{z}$ plane at $\mathrm{z}=\frac{\sqrt{3}}{2}\mathrm{\alpha }$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ lying in the $\mathrm{x}$ - $\mathrm{y}$ plane with its centre at the origin is $\frac{\mathrm{\lambda }\mathrm{L}}{\mathrm{n}{\mathrm{\epsilon }}_0}$ ( ${\mathrm{\epsilon }}_0=$ permittivity of free space), then the value of $\mathrm{n}$ is

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1m at ${10}^{o}C.$ Now the end P is maintained at ${10}^{o}C,$ while the end S is heated and maintained at ${400}^{o}C.$ The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is $1.2\times {10}^{-5} K^{-1},$ the change in length of the wire PQ is

In the given circuit, a charge of \(+80 \mu C\) is given to the upper plate of the \(4 \mu F\) capacitor. Then in the steady state, the charge on the upper plate of the \(3 \mu F\) capacitor is

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it, the correct statement(s) is(are)

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses \(0.36 \mathrm{~kg}\) and \(0.72 \mathrm{~kg}\). Taking \(g=10 \mathrm{~ms}^{-2}\), find thework done (in Joule) by string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the system is released from rest.

A small mass \(m\) is attached to a massless string whose other end is fixed at \(P\) as shown in the figure. The mass is undergoing circular motion in the \(x-y\) plane with centre at \(O\) and constant angular speed \(\omega\). If the angular momentum of the system, calculated about \(O\) and \(P\) are denoted by \(\vec{L}_{O}\) and \(\vec{L}_{P}\) respectively, then

The circle $C_1:x^2+y^2=3,$ with centre at O, intersects the parabola $x^2=2y$ at the point P in the first quadrant. Let the tangent to the circle $C_1$ at P touches other two circles $C_2$ and $C_3$ at $R_2$ and $R_3$ , respectively. Suppose $C_2$ and $C_3$ have equal radii $2\sqrt{3}$ and centres $Q_2$ and ${ Q}_3$ , respectively. If $Q_2$ and $Q_3$ lie on the y - axis, then

Among the following metal carbonyls, the \(\mathrm{C}-\mathrm{O}\) bond order is lowest in

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Consider the polynomial \(f(x)=1+2 x+3 x^2+4 x^3\). Let \(s\) be the sum of all distinct real roots of \(f(x)\) and let \(t=|s|\).Question:
The function \(f^{\prime}(x)\) is

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Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.
There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.
Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.
Question:
What is the disadvantage of this system?

let $f_1 :R\to R, f_2 :\left[0, \infty \right)\to R, f_3 :R\to R and f_4 :R\to [0, \infty )$ be defined by
$f_1\left(x\right)=\left\{\begin{array}{ccc}\left|x\right|& if& x<0\\ e^x& if& x\ge 0\end{array}\right. ;f_2\left(x\right)=x^2;f_3\left(x\right)=\left\{\begin{array}{ccc}\sin x& if& x<0\\ x& if& x\ge 0\end{array}\right. and f_4\left(x\right)=\left\{\begin{array}{ccc}{f}_2\left(f_1\left(x\right)\right)& if& x<0\\ f_2\left(f_1\left(x\right)\right)-1& if& x\ge 0\end{array}\right.$
 

	List – I		List – II
(A)	$f_4$ is	(P)	Onto but not one – one
(B)	$f_3$ is	(Q)	neither continuous nor one-one
(C)	$f_2$ of $f_1$ is	(R)	differentiable but not one-one
(D)	$f_2$ is	(S)	continuous and one-one