The vertical component of the earth's magnetic field is \(6 \times 10^{-5} T\) at any place where the angle of dip is \(37^{\circ}\). The earth's resultant magnetic field at that place will be \(\left(\right.\) Given \(\left.\tan 37^{\circ}=\frac{3}{4}\right)\)

Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of \(\mu_{A}\) to \(\mu_{B}\) is \(1: 2\). Then the thickness of material, in meter is: (Given \(v_{A}\) and \(v_{B}\) are velocities of light in \(A\) and \(B\) materials respectively).

Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.

One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is

The diameter of the objective lens of microscope makes an angle \(\beta \) at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index \(n\). Then the resolving power of the microscope

The resistance of a conductor at \(15^{\circ} {C}\) is \(16\, \Omega\) and at \(100\, {C}\) is \(20\, \Omega\). What will be the temperature coefficient of resistance of the conductor?

A water heater of power \(2000\,W\) is used to heat water. The specific heat capacity of water is \(4200\,J\,kg ^{-1}\, K ^{-1}\). The efficiency of heater is \(70 \%\). Time required to heat \(2\,kg\) of water from \(10^{\circ}\,C\) to \(60^{\circ}\,C\) is \(..........s\). (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

In a Young’s double slit experiment the ratio of the slit’s width is \(4 : 1.\) The ratio of the intensity of maxima to minima, close to central fringe on the screen will be

Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below:

The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point , \(P\), located as shown, would be (nearly)