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A Carnot engine, having an efficiency of $\eta =1/10$ as heat engine, is used as a refrigerator. If the work done on the system is $10J$, the amount of energy absorbed from the reservoir at lower temperature is

For the arrangement shown in the figure, $m_1=6\text{kg}$ and $m_2=4\text{kg}$. If the string is light and inextensible and the pulley and surfaces are frictionless, find the magnitude of the acceleration of the center of mass.

(Take $g=10m/s^2$)

The initial velocity of a body moving along a straight line is 7 $\frac{m}{s}$. It has a uniform acceleration of 4 $\frac{m}{s^2}$. The distance covered by the body in the $5^{th}$ second of its motion is

Two particles of mass 'm' and charge 'q' each are suspended by means of two silk threads of length 'l' each from the same point. If they are taken into an artificial satellite, the angle between the threads in equilibrium is

If the shown system is in equilibrium, then the tension in the silk thread is

In the digital circuit shown in figure the flip-flops have set time of $5ns$ and a worst case delay of $15ns$. The AND gate has a delay of $5ns.$ Maximum possible clock rate for the circuit to operate faithfully is

The current in a coil of self inductance $2.0\text{H}$ is increasing according to $I=2\sin \left(t^2\right)\text{A}.$ Find the amount of energy spent during the period when the current changes from $0$ to $2\text{A}.$

The integrating factor of reversible heat transfer is

Two electrostatic field lines are drawn between two point charges $q_1\&q_2$ as shown in the diagram , If $\alpha \&\beta$ are planar angles. then the ratio $q_1/q_2$ will be

A boy walks to his school at a distance of $9km$ with constant speed of $3km{h}^{-1}$ and walks back with a constant speed of $6km{h}^{-1}$. His average speed for round trip in ($km{h}^{-1}$) is

If $|\overrightarrow{A}-\overrightarrow{B}|=|\overrightarrow{A}|=|\overrightarrow{B}|,$ the angle between \( \vec{A}\) and $\overrightarrow{B}$

Can you explain e.m.f breifly??

The electric filed intensity at all point in space is given by $\overrightarrow{E}=(\sqrt{3}\hat{i}-\hat{j})\text{V/m}$. The equipotential lines in $xy$ plane will be represented by :

Consider the set up shown, where we have an ideal gas trapped in a cylindrical container, kept on a thermal reservoir which provides heat to the system. The weight on top maintains a constant pressure P on the gas. Supplying heat Q changes the temperature by $\Delta T$, and expands the volume by $\Delta V$. The expanding gas displaces the container and does work, W. Choose the correct inferences from the following options

A circular loop of radius $0.3\text{cm}$ lies parallel to a much bigger circular loop of radius $20\text{cm}$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15\text{cm}$. If a current of $2.0\text{A}$ flows through the smaller loop, then the flux linked with bigger loop is :

The $K_{\beta }$ X -ray of argon has a wavelength of 0.36 nm. The minimum energy needed to ionize an argon atom is 16 eV. Find the energy needed to knock out an electron from the K shell of an argon atom.

A beam of unpolarised light passes through a tourmaline crystal A and then it passes through a tourmaline crystal B oriented so that its principal plane is parallel to that of A. the intensity of emergent light is $I_0$. Now B is rotated by ${45}^{\circ }$ about the ray. The emergent light will have intensity:

If a wire of resistance 20 ohm is covered with ice at zero degree Celsius and voltage of 210 V is applied across the wire then the rate of melting of ice is

In the following circuit the resultant capacitance between $A$ and $B$ is $1\mu F$. Then the value of capacitance $C$ is

Find the momentum of a particle with de Brogile wavelength $2\stackrel{\circ }{\text{A}},$ is:

$\text{(Planck's constant,}h=6.62\times {10}^{-34}\text{J s})$

A car is moving along a circle with constant speed on an inclined plane as shown in diagram. Then friction force on car will be in horizontal direction at least at one point:

A variable force acts on a $1\text{kg}$ particle such that acceleration as a function of time is given by $a=2t$. The particle is starting from rest. Find the work done by the force on particle in first $3$ seconds.

The kinetic energy of a projectile at the highest point is half of the initial kinetic energy. What is the angle of projection with the horizontal?

At what temperature will the rms speed of oxygen molecules becomes just sufficient to escape from the earth's atmosphere?(Given: Mass of oxygen molecule $\left(m\right)=2.76\times {10}^{-26}kg$, Boltzmann constant i.e. $k_B=1.38\times {10}^{-23}J{K}^{-1}$)

A Pump supplies oil at $0.002m^3/sec.$ to a 50 mm diameter double acting cylinder and a rod diameter is 20 mm. If the load is 6000 N bolts in extending and retracting stroke.



Power during extension stroke and return stroke are

A capacitor of capacitance $10\mu \text{F}$ is connected to a battery of emf $4\text{V}$. Now this charged capacitor is disconnected from the battery and a dielectric slab of dielectric constant $4$ is inserted between the plates. Find the magnitude of the charge induced on the surface of the dielectric.

Which element will deflect more number of $\alpha -$particles at a scattering angle of ${25}^{\circ }$?



$Z_P=75,Z_Q=80,Z_R=85$ and $Z_S=79$

A rectangular lamina $ABCD$ has same density along side $AD$ but has increasing density along side $AB$. The density along side $AB$ is given as $\rho ={\rho }_0+kx$ where ${\rho }_0$ and $k$ are constants and $x$ is distance from the side $AD$. Find the distance of $COM$ from side $AD$.

Find the equivalent capacitance between the points $\text{A}$ and $\text{B}$ in the given circuit?

Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by 3% is