A parallel beam of light of wavelength \(900\,nm\) and intensity \(100\,Wm ^{-2}\) is incident on a surface perpendicular to the beam. Tire number of photons crossing \(1\,cm ^{2}\) area perpendicular to the beam in one second is :

The force is given in terms of time \(t\) and displacement \(x\) by the equation \({F}={A} \cos {Bx}+{C} \sin {Dt}\) The dimensional formula of \(\frac{{AD}}{{B}}\) is -

Figure shows a rod \({AB}\), which is bent in a \(120^{\circ}\) circular arc of radius \(R\). A charge \((-Q)\) is uniformly distributed over rod \({AB}\). What is the electric field \(\overrightarrow{{E}}\) at the centre of curvature \({O}\) ?

A boy ties a stone of mass \(100 \,g\) to the end of a \(2\) \(m\) long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of \(80 \,N\). If the maximum speed with which the stone can revolve is \(\frac{ K }{\pi} rev\). / \(min\). The value of \(K\) is (Assume the string is massless and unstretchable)

The ratio for the speed of the electron in the \(3^{ rd }\) orbit of \(He ^{+}\)to the speed of the electron in the \(3^{\text {ad }}\) orbit of hydrogen atom will be

A source of sound emits sound waves at frequency \(f_0\). It is moving towards an observer with fixed speed \(v_s\) (\(v_s < v\), where \(v\) is the speed of sound in air). If the observer were to move towards the source with speed \(v_0\), one of the following two graphs (\(A\) and \(B\)) will given the correct variation of the frequency \(f\) heard by the observer as \(v_0\) is changed The variation of \(f\) with \(v_0\) is given correctly by

A cup of coffee cools from \(90^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\) in t minutes when the room temperature is \(20^{\circ} \mathrm{C}\). The time taken by the similar cup of coffee to cool from \(80^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) at the same room temperature is :

When a diode is forward biased, it has a voltage drop of \(0.5\, V.\) The safe limit of current through the diode is \(10\, mA\). If a battery of emf \(1.5\, V\) is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is\(.....\Omega\)

Choose the incorrect statement from the following

Two travelling waves produces a standing wave represented by equation, \({y}=1.0\, {mm} \cos \left(1.57 \,{cm}^{-1}\right) {x} \sin \left(78.5\, {s}^{-1}\right) {t}\) The node closest to the origin in the region \({x}>0\) will be at \({x}=\ldots \ldots \ldots\, {cm}\)

A galvanometer of resistance \(100 \Omega\) when connected in series with \(400 \Omega\) measures a voltage of upto \(10 \mathrm{~V}\). The value of resistance required to convert the galvanometer into ammeter to read upto \(10 \mathrm{~A}\) is \(\mathrm{x} \times 10^{-2} \Omega\). The value of \(\mathrm{x}\) is _______.

If \(K_{1}\) and \(K_{2}\) are the thermal conductivities \(L_{1}\) and \(L _{2}\) are the lengths and \(A _{1}\) and \(A _{2}\) are the cross sectional areas of steel and copper rods respectively such that \(\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2\). Then, for the arrangement as shown in the figure. The value of temperature \(T\) of the steel - copper junction in the steady state will be ........... \(^{\circ} C\)