Match List - I with List - II.

List - I	List - II
(A) Magnetic induction	(I) Ampere meter2
(B) Magnetic intensity	(II) Weber
(C) Magnetic flux	(III) Gauss
(D) Magnetic moment	(IV) Ampere meter

Choose the correct answer from the options given below :

A uniform thin rope of length \(12\, m\) and mass \(6\, kg\) hangs vertically from a rigid support and a block of mass \(2\, kg\) is attached to its free end. A transverse short wavetrain of wavelength \(6\, cm\) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \(cm\) ) when it reaches the top of the rope \(?\)

Two objects of equal masses placed at certain distance from each other attracts each other with a force of \(F\). If one-third mass of one object is transferred to the other object, then the new force will be

Given below are two statements:
Statement I: The hot water flows faster than cold water.
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the options given below.

As shown in the figure. a configuration of two equal point charges \(\left( q _0=+2 \mu C \right)\) is placed on an inclined plane. Mass of each point charge is \(20\,g\). Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \(h = x \times 10^{-3}\,m\) The value of \(x\) is \(..........\).(Take \(\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)\)

In the given circuit below inductance values of \(L_1\), \(L_2\) and \(L_3\) are same. The magnetic energy stored in the entire circuit is \((U_t)\) and that stored in the \(L_2\) inductor is \((U_l)\). \(U_t / U_l\) is __________.
(Ignore the mutual inductance if any)

The temperature of an ideal gas in \(3-\)dimensions is \(300\, {K}\). The corresponding de-Broglie wavelength of the electron approximately at \(300\,{K}\), is \(....\,nm\) \(\left\lfloor{m}_{e}=\text { mass of electron }=9 \times 10^{-31} \,{kg}\right.\) \({h}=\text { Planck constant }=6.6 \times 10^{-34} {Js}\) \(\left.{k}_{{B}}=\text { Boltzmann constant }=1.38 \times 10^{-23}\, {JK}^{-1}\right]\)

Read the following statements: \(A.\) When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. \(B.\) Two bodies \(P\) and \(Q\) having equal surface areas are maintained at temperature \(10^{\circ}\,C\) and \(20^{\circ}\,C\). The thermal radiation emitted in a given time by \(P\) and \(Q\) are in the ratio \(1: 1.15\) \(C.\) A carnot Engine working between \(100\,K\) and \(400\,K\) has an efficiency of \(75 \%\) \(D.\) When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega \). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be

A \(NCC\) parade is going at a uniform speed of \(9\,km / h\) under a mango tree on which a monkey is sitting at a height of \(19.6\,m\). At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is \(...m\) (Given \(g=9.8\,m / s ^{2}\) )