At \(40\,^oC\), a brass wire of \(1\, mm\) is hung from the ceiling. A small mass, \(M\) is hung from the free end of the wire. When the wire is cooled down from \(40\,^oC\) to \(20\,^oC\) it regains its original length of \(0.2\, m\). The value of \(M\) is close to ........\(kg\) (Coefficient of linear expansion and Young's modulus of brass are \(10^{-5}/^oC\) and \(10^{11}\, N/m^2\), respectively; \(g = 10\, ms^{-2}\))

For an ideal heat engine, the temperature of the source is \(127\,^{\circ} C\). In order to have \(60\, \%\) efficiency the temperature of the sink should be \(........\,{ }^{\circ} C\). (Round off to the Nearest Integer)

A porter lifts a heavy suitcase of mass \(80\, {kg}\) and at the destination lowers it down by a distance of \(80\, {cm}\) with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take \(g=9.8\, {ms}^{-2}\) ) (In \({J}\))

If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of

An object of mass 8 kg is hanging from one end of a uniform rod \(C D\) of mass 2 kg and length 1 m pivoted at its end \(C\) on a vertical wall as shown in figure. It is supported by a cable \(A B\) such that the system is in equilibrium. The tension in the cable is:
(Take \(g=10 m s ^{-2}\) )

The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).

In a double -slit experiment, green light \(\left( {5303\,\mathop A\limits^o } \right)\) falls on a double slit having a separation of \(19.44\,\mu m\) and a width of \(4.05\,\mu m\). The number of bright fringes between the first and the second diffraction minima is

Match List-I with List-II.

List-I (Physical Quantity)	List-II (Dimensional Formula)
(A) Coefficient of viscosity	(I) [ML0T-3]
(B) Intensity of wave	(II) [ML-2T-2]
(C) Pressure gradient	(III) [M-1LT2]
(D) Compressibility	(IV) [ML-1T-1]

Choose the correct answer from the options given below :

A solid sphere of radius \(R\) gravitationally attracts a particle placed at \(3 R\) form its centre with a force \(F _{1}\). Now a spherical cavity of radius \(\left(\frac{ R }{2}\right)\) is made in the sphere (as shown in figure) and the force becomes \(F _{2}\). The value of \(F _{1}: F _{2}\) is

Given below are two statements: Statement \(I\) : A uniform wire of resistance \(80\,\Omega\) is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be \(5\,\Omega\). Statement \(II :\) Two resistance \(2\,R\) and \(3\,R\) are connected in parallel in a electric circuit. The value of thermal energy developed in \(3\,R\) and \(2\,R\) will be in the ratio \(3:2.\) In the light of the above statements, choose the most appropriate answer from the options given below