A particle of mass \(M\) is moving in a circle of fixed radius \(R\) in such a way that its centripetal acceleration at time \(t\) is given by \(n^2Rt^2\) where \(n\) is a constant. The Power delivered to the particle by the force acting on it, is

Which of the following statements are correct? \((A)\) Electric monopoles do not exist whereas magnetic monopoles exist. \((B)\) Magnetic field lines due to a solenoid at its ends and outside cannot be completely
straight and confined. \((C)\) Magnetic field lines are completely confined within a toroid. \((D)\) Magnetic field lines inside a bar magnet are not parallel. \((E)\) \(\chi=-1\) is the condition for a perfect diamagnetic material, where \(\chi\) is its
magnetic susceptibility. Choose the correct answer from the options given below:

A simple pendulum is being used to determine the value of gravitational acceleration \(\mathrm{g}\) at a certain place. The length of the pendulum is \(25.0\; \mathrm{cm}\) and a stop watch with \(1\; \mathrm{s}\) resolution measures the time taken for \(40\) oscillations to be \(50\; s\). The accuracy in \(g\) is  ....... \(\%\)

Two capacitors having capacitance \(C _{1}\) and \(C _{2}\) respectively are connected as shown in figure. Initially, capacitor \(C _{1}\) is charged to a potential difference \(V\) volt by a battery. The battery is then removed and the charged capacitor \(C_{1}\) is now connected to uncharged capacitor \(C _{2}\) by closing the switch \(S\). The amount of charge on the capacitor \(C _{2}\), after equilibrium is

Ratio of thermal energy released in two resistor \(R\) and \(3 R\) connected in parallel in an electric circuit is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of \(H_2\) and \(O_2\) molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of \(H_2\) and \(O_2\) molecules are same at same temperature.

Choose the correct answer from the options given below

A parallel plate capacitor has \(1\,\mu F\) capacitance. One of its two plates is given \(+2\,\mu C\) charge and the other plate, \(+4\,\mu C\) charge. The potential difference developed across the capacitor is......\(V\)

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

\(Sl\). \(No\).	\(R\, (\Omega )\)	\(l\, (cm)\)
\(1\).	\(1000\)	\(60\)
\(2\).	\(100\)	\(13\)
\(3\).	\(10\)	\(1.5\)
\(4\).	\(1\)	\(1.0\)

Which of the readings is inconsistent ?

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from \(\mathrm{T}_1\) to \(\mathrm{T}_2\) is proportional to \(\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
Choose the correct answer from the options given below :

Under isothermal condition, the pressure of a gas is given by \(P = aV ^{-3}\), where \(a\) is a constant and \(V\) is the volume of the gas. The bulk modulus at constant temperature is equal to \(..........\,P\)

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at \(A\) and \(B\) are \(6 cm^2\) and \(3 cm^2\) respectively.
The rate of flow will be ___________ \(cm ^3 / s\). (take \(g =10 m / s ^2\) )

A wire of resistance \(R\) is bent to form a square \(ABCD\) as shown in the figure. The effective resistance between \(E\) and \(C\) is ( \(E\) is mid-point of arm \(CD\) )

A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )