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When a system is taken through the process $abc$ shown in the figure, $90\text{J}$ of heat is absorbed by the system and $40\text{J}$ of work is done by it. If the system does $30\text{J}$ of work during the process $adc$, how much heat flows into it during the process?

A network consisting of three resistors, three batteries, and a capacitor is shown in the figure

$\begin{array}{ccc}& \text{Column I}& \text{Column II}\\ \left(A\right)& \text{Current in branch EB is}& \text{(P)}10\mu C\\ \left(B\right)& \text{Current in branch CB is}& \text{(Q)}0.5\mu C\\ \left(C\right)& \text{Current in branch ED is}& \text{(R)}1.5\mu C\\ \left(D\right)& \text{Charge on capacitor is}& \text{(S)}5\mu C\\ & & \text{(T)}7.5\mu C\end{array}$
Which of the following option has the correct combination considering column - I and Column - II.

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercuty = 13.6, Density of water = ${10}^{3}kg/m^3$, g = $9.8m/s^2$ at Calcutta. Pressure = hpg in usual symbols.

1. 10

Four thin uniform rods, each of length $L$ and mass $M$ are joined to form a square. The moment of inertia of square about an axis along one of its diagonal is

The maximum torque that a dipole of dipole moment $2\times {10}^{-9}\text{Cm}$ would experience in a uniform electric field of magnitude $4\text{N/C}$ is



$[$0.77 Mark$]$

If $y=\frac{(x-2{)}^2(x+1{)}^3(x-3{)}^2}{(x+2)(x+4)},$ then the value of $\left(\frac{15}{32}\frac{dy}{dx}\right)$ at $x=1$ is

A parallel plate capacitor is made using three different dielectric materials as shown in figure. Separation between the plates of the capacitor is $d$. The equivalent capacitance between the plates is

A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength 200 nm is incident on the ball for some time during which a total light energy of 1.0 $\times {10}^{-7}$ J falls on the surface. Assuming that on the average one photon out of every ten thousand is able to eject a photo electron, find the electric potential at the surface of the ball assuming zero potential at infinity. What is the potential at the center of the ball ?

You have
learnt that a travelling wave in one dimension is represented by a
function y = f
(x,
t)where x and
t must appear
in the combination x –
v t or x + v t,
i.e. y = f (x
± v t).
Is the converse true? Examine if the following functions for y
can possibly represent a travelling wave:

(a) (x – vt)²

(b)

(c)

The diode used in the circuit shown in the figure has a constant voltage drop of $0.5\text{V}$ at all currents and a maximum power rating of $100\text{mW}.$ What should be the value of the resistor $R,$ connected in series with the diode for obtaining maximum current is

In a two block system shown in figure, match the following.



$\begin{array}{cc}\text{Table -1}& \text{Table -2}\\ \text{(A) Velocity of centre of}& \text{(P) Keep on changing all}\\ \text{mass}& \text{the time}\\ \text{(B) Momentum of centre of}& \text{(Q) First decreases then}\\ \text{mass}& \text{becomes zero}\\ \text{(C) Momentum of 1 kg block with respect to 2 kg block}& \text{(R) zero}\\ & \text{(S) constant}\end{array}$

A bullet of mass $m$ moving vertically upwards instantaneously with a velocity $u$, hits the hanging block of mass $m$ and gets embedded in it, as shown in the figure. The height through which the block rises after the collision, is, (Assume that there is sufficient space above the block for the block to rise.)

Find net dipole moment of given charge configuration.

Two coherent sources separated by a distance $d$ are radiating in phase having wavelength $\lambda$. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of $n=4$ interference maxima is given as :

Two coherent light sources of intensity ratio n are employed in an inteference experiment. The ratio of the intensities of the maxima and minima in the inteference pattern is

A
100 W sodium lamp radiates energy uniformly
in all directions. The lamp is located at the centre of a large
sphere that absorbs all the sodium light which is incident on it. The
wavelength of the sodium light is 589 nm. (a) What is the energy per
photon associated with the sodium light? (b) At what rate are the
photons delivered to the sphere?

The total current supplied to the circuit by the battery as shown in figure is

The magnetic susceptibility of a paramagnetic material at -73 ${}^{\circ }$C is 0.0075 and its value at - 173 ${}^{\circ }$ C will be

The actual value of resistance $R$, shown in the figure is $30\Omega$. This is measured in an experiment as shown using the standard formula $R=\frac{V}{I}$, where $V$ and $I$ are the reading of the voltmeter and ammeter, respectively. If the measured value of $R$ is $5\%$ less, then the internal resistance of the voltmeter is

Consider a long cylindrical tube of inner and outer radii, $r_{i}and{r}_o$, respectively, length L and thermal conductivity, k. Its inner and outer surfaces are maintained at $T_i$ and $T_o$, respectively $(T_i>T_o$). Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

Figures
14.29 correspond to two circular motions. The radius of the circle,
the period of revolution, the initial position, and the sense of
revolution (i.e. clockwise or anti-clockwise) are indicated on each
figure.

Obtain
the corresponding simple harmonic motions of the x-projection
of the radius vector of the revolving particle P, in each case.

An Ideal gas undergoes state change according to the given $\text{P-V}$ diagram. What is the value of $V_x?$