A \(10\,m\) long horizontal wire extends from North East to South West. It is falling with a speed of \(5.0\,ms^{-1},\) at right angles to the horizontal component of the earth’s magnetic field, of \(0.3\times 10^{-4}\,Wb/m^2\). The value of the induced \(emf\) in wire is 

The truth table for the circuit given in the fig is

Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) \(EM\) waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason \(R\) : Infrared \(EM\) waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below:

For particle \(P\) revolving round the centre \(O\) with radius of circular path \(r\) and angular velocity \(\omega\), as shown in below figure, the projection of \(OP\) on the \(x\)-axis at time \(t\) is \(.................\).

Let \(N_{\beta}\) be the number of \(\beta \) particles emitted by \(1\) gram of \(Na^{24}\) radioactive nucler (half life \(= 15\, hrs\)) in \(7.5\, hours\), \(N_{\beta}\) is close to (Avogadro number \(= 6.023\times10^{23}\,/g.\, mole\))

Unpolarized light of intensity \(I_0\) incident on surface of a block of glass at Brewster's angle. In that case, which one of ihe following statements is true ?

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) An electric fan continues to rotate for some time after the current is switched off. Reason \(R:\) Fan continuous to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below.

A thin convex lens of focal length \('f'\) is put on a plane mirror as shown in the figure. When an object is kept at a distance \('a'\) from the lens - mirror combination, its image is formed at a distance \(\frac{a}{3}\) in front of the combination. The value of \('a'\) is

In a large building, there are \(15\) bulbs of \(40\ W\), \(5\) bulbs of \(100\ W, 5\) fans of \(80\ W\) and \(1\) heater of \(1\ kW\). The voltage of electric mains is \(220\ V\). The minimum capacity of the main fuse of the building will be ................ \(A\)

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P, V, T\). Heating is started from left side until pressure changes to \(\dfrac{27P}{8}\). If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas \(C_P/C_V = 1.5\))

When one moves from a point \(16\) km below the earth's surface to a point \(16\) km above the earth's surface. The change in \(g\) is approximately \(\alpha\) %. The value of \(\alpha\) is _____.
(Take radius of the earth \(= 6400\) km.)

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A pendulum clock when taken to Mount Everest becomes fast. Reason \(R:\) The value of \(g\) (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below

A body of mass (\(2 {M}\)) splits into four masses \(\{{m}, {M}-{m}, {m}, {M}-{m}\}\), which are rearranged to form a square as shown in the figure. The ratio of \(\frac{{M}}{{m}}\) for which, the gravitational potential energy of the system becomes maximum is \({x}: 1\). The value of \(x\) is ..... .