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A sample of an ideal gas in taken through the cyclic process $abca$ as shown in figure. The change in the internal energy of the gas along the path $ca$ is $-180\text{J}$. The gas absorbs $250\text{J}$ of heat along the path $ab$ and $60\text{J}$ along the path $bc$. The work done by the gas along the $abc$ is

A 50-turn circular coil of radius 2.0 cm carrying a current of 5.0 A is rotated in a magnetic field of strength 0.20 T. (a) What is the maximum torque that acts on the coil ? (b) In a particular position of the coil, the torque acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil ?

There are two separate long cylindrical wires having uniform current density. The radius of one of the wires is twice that of the other. The figure shows the plot of magnitude of magnetic field intensity versus radial distance $\left(r\right)$ from their axis. If the curved parts of the two graphs are overlapping , then which of the following options is/are correct



$[$ Note $:-j$ is the current density which is equal to $\frac{I}{A}]$

Two balls are thrown with the same speed but making complementary angle with the horizontal. If the angle of projection of one is ${30}^{\circ }$ and its maximum height is $h$, then the maximum height of the other will be

A uniform disc of mass 'm' and radius R is rolling down a fixed inclined plane without slipping. The angular acceleration of the disc is

1. 0.506

A body weighs $200N$ on the surface of the earth. How much will it weight halfway down to the centre of the earth ?

Answer the
following as true or false.

(i)
andare
collinear.

(ii) Two
collinear vectors are always equal in magnitude.

(iii) Two
vectors having same magnitude are collinear.

(iv) Two
collinear vectors having the same magnitude are equal.

Figure shows two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are $p_A,T_A$, V in the vessel A and $p_B,T_B$, V in the vessel B. The vessels are now connected through a small tube. Show that the pressure p and the temperature T satisfy $\frac{p}{T}=\frac{1}{2}(\frac{p_A}{T_A}+\frac{p_B}{T_B})$ when equilibrium is achieved.

Two scooters starting from rest accelerate uniformly at the same rate. The time taken by the second scooter ($s_2$) to travel is twice the time taken by the first scooter ($s_1$). What is the relation between the distance covered by $s_1$ to that of $s_2$?

Find the volumetric strain of the spherical ball of radius $10\text{cm}$ whose volume changes by $4.18\times {10}^{-6}{\text{m}}^3$ under the application of bulk stresses.

Which of the following options represents incorrect ray diagram for a concave mirror?

The velocity of the liquid coming out of a small hole of a large vessel containing two different liquids of densities $2\rho$ and $\rho$ as shown in the figure is:

A student working with a spring mass systems finds the values of mass, spring constant and damping constant in CGS unit as $90,4.5\times {10}^{+3}$ and $180$ respectively. What will be the time period of the spring mass system?

An electric motor exerts a constant torque $10\text{N-m}$ on a grind stone mounted on a shaft. MOI of the grind stone about the shaft is $2{\text{kg m}}^2$. If the system starts from rest find the work done in $8\text{s}$.

A ring of radius $R$ is made out of a thin metallic wire of area of cross section $A$. The ring has a uniform charge $Q$ distributed on it. A charge $q_0$ is placed at the centre of the ring. If $\text{Y}$ is the young`s modules for the material of the ring and $\Delta R$ is the change is the radius of the ring then find $\Delta R.$

Which of the following expressions represents an oscillatory motion ?

Find the charges on the capacitor assembly as shown in the figure below

Primary circuit of potentiometer is shown in figure. Determine the maximum potential which we can measure by the given potentiometer.

A boy of mass $20\text{kg}$ is standing on a $80\text{kg}$ free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing $25\text{m}$ from a wall. If he walks $10\text{m}$ on the cart towards the wall, then the final distance of the boy from the wall will be

In $\text{YDSE}$, dichromatic light of wavelengths $400\text{nm}$ and $560\text{nm}$ are used. The distance between the slits is $0.1\text{mm}$ and the distance between the plane of the slits and the screen is $1\text{m}$. The minimum distance between two successive regions of complete darkness is

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration 'a' (relative to car) vertically. The tension in the string is equal to

A car starts form rest and accelerates uniformly over a time of $5$ seconds for a distance of $110\text{m}$. The acceleration of the car will be

A uniform sphere of mass m is positioned between two horizontal planks A and B of mass 2 m and m respectively as shown. Ground surface is smooth and friction between planks and sphere is sufficient so that no slipping takes place. Horizontal forces $F_1$ and $F_2$ are applied on plank so that acceleration of sphere is zero. Plank B is moving towards right with acceleration $a$. Which of the following is/are correct?