The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is \(40\,cm.\) The area of the image is \(9\,times\) that of the square. The focal length of the lens is........\(cm\)

Choose the correct option from the following options given below

Match List \(- I\) with List \(- II\)

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below:

An electric bulb rated \(50 \mathrm{~W}-200 \mathrm{~V}\) is connected across a \(100 \mathrm{~V}\) supply. The power dissipation of the bulb is _______.

The difference between threshold wavelengths for two metal surfaces \(A\) and \(B\) having work function \(\phi_A=9\,eV\) and \(\phi_{ B }=4.5\,eV\) in \(nm\) is:(Given, \(hc =1242\,eV\,nm\))

A sound wave of frequency \(245 \,Hz\) travels with the speed of \(300\, ms ^{-1}\) along the positive \(x\)-axis. Each point of the wave moves to and fro through a total distance of \(6 \,cm\). What will be the mathematical expression of this travelling wave ?

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 _______.

In a meter bridge experiment to determine the value of unknown resistance, first the resistances \(2 \Omega\) and \(3 \Omega\) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \(l cm\) from the left. Now when an unknown resistance \(x \Omega\) is connected in parallel to \(3 \Omega\) resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance \(x\) is _________ \(\Omega\).

In the Young's double slit experiment, the distance between the slits varies in time as \({d}({t})={d}_{0}+{a}_{0}\, sin\omega \,t\) ; where \({d}_{0}, \omega\) and \(a_{0}\) are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

In Young's double slit experiment, the distance between slits and the screen is \(1 .0\,\,m\) and monochromatic light of \(600\,\,nm\)  is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance \(d_0\) between the slits . If the angular resolution of the eye is \(\frac {1}{60}^o,\) the value of \(d_0\)  is close to......\(mm\)