silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of \(10^{12}  /sec\). What is the force constant of the bonds connecting one atom with the other? ................ \(\mathrm{N/m}\)     (Mole wt. of silver \(= 108 \) andAvagadro number \(= 6.02 \times 10^{23}\) \(gm \ mole^{ -1}\) )

Two capacitors of capacitances \(C\) and \(2\, C\) are charged to potential differences \(V\) and \(2\, V\), respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is\(.....CV^2\)

A light planet is revolving around a massive star in a circular orbit of radius \(R\) with a period of revolution \(T\). If the force of attraction between planet and star is proportional to \(\mathrm{R}^{-3 / 2}\) then choose the correct option.

A bar magnet with a magnetic moment \(5.0\,Am ^2\) is placed in parallel position relative to a magnetic field of \(0.4\,T\). The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is \(.........\,J\)

In a common emitter amplifier circuit using an \(n-p-n\) transistor, the phase difference between the input and the output voltages will be.....\(^o\)

A solution containing active cobalt \({}_{27}^{60}Co\) having activity of \(0.8\,\mu Ci\) and decay constant \(\lambda \) is injected in an animal's body. If \(1 \,cm^3\) of blood is drawn from the animal's body after \(10\, hrs\) of injection, the activity found was \(300\, decays\) per minute. What is the volume of blood that is flowing in the body?..........\(litres\) ( \(ICi = 3.7 \times 10^{10}\) decay per second and at \(t = 10\, hrs\) \({e^{ - \lambda t}} = 0.84\) )

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ...........

The end correction of a resonance column is \(1\,cm.\)  If the shortest length resonating with the tuning fork is \(10\,cm,\)  the next resonating length should be ..... \(cm\)

A liquid drop having \(6\) excess electrons is kept stationary under a uniform electric field of \(25.5\, k\,Vm^{-1}\) . The density of liquid is \(1.26\times10^3\, kg\, m^{-3}\) . The radius of the drop is (neglect buoyancy)

Match List\(-I\) with List\(-II.\)

List\(-I\)	List\(-II\)
\((a)\) \(10\, km\) height over earth's surface	\((i)\) Thermosphere
\((b)\) \(70\, km\) height over earth's surface	\((ii)\) Mesosphere
\((c)\) \(180\, km\) height over earth's surface	\((iii)\) Stratosphere
\((d)\) \(270\, km\) height over earth's surface	\((iv)\) Troposphere

A ball will a speed of \(9\, m / s\) collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of \(30^{\circ}\) with the original direction. The ratio of velocities of the balls after collision is \(x : y\) where \(x\) is........

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :

Region \(I\) and \(II\) are separated by a spherical surface of radius \(25\, {cm}\). An object is kept in region \(I\) at a distance of \(40\, {cm}\) from the surface. The distance of the image from the surface is \(.....\,cm\)