A wire of length \(L,\) area of cross section \(A\) is hanging from a fixed support. The length of the wire changes to \({L}_1\) when mass \(M\) is suspended from its free end. The expression for Young's modulus is:

 In a guitar, two strings \(A\) and \(B\) made of same material are slightly out of tune and produce beats of frequency \(6~\text{Hz}\). When tension in \(B\) is slightly decreased, the beat frequency increases to \(7~\text{Hz}\).  If the frequency of \(A\) is \(530~\text{Hz}\), the original frequency of \(B\) will be:

A ball is thrown vertically downwards with a velocity of \(20\) m/s from the top of a tower. It hits the ground after some time with the velocity of \(80\) m/s . The height of the tower is: (assuming \(g = 10~\text{m/s}^2)\)

An electron is accelerated from rest through a potential difference of \(V\) volt. If the de Broglie wavelength of an electron is $\mathrm{}$\(1.227\times10^{-2}~\text{nm}.\) What will be its potential difference?

For the logic circuit shown, the truth table is:

A short electric dipole has a dipole moment of \(16 \times 10^{-9} ~\text{C-}\text{m}. \) The electric potential due to the dipole at a point at a distance of \(0.6~\text{m}\) from the centre of the dipole situated on a line making an angle of \(60^{\circ}\) with the dipole axis is:
\(\left( \dfrac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2 \right) \)

An iron rod of susceptibility \(599\) is subjected to a magnetizing field of \(1200~\text{A m}^{-1}.\) The permeability of the material of the rod is:
\((\mu_0 = 4 \pi\times 10^{-7}~\text{T mA}^{-1})\)
1. \(8.0\times 10^{-5}~\text{T mA}^{-1}\)
2. \(2.4\pi\times 10^{-5}~\text{T mA}^{-1}\)
3. \(2.4\pi\times 10^{-7}~\text{T mA}^{-1}\)
4. \(2.4\pi\times 10^{-4}~\text{T mA}^{-1}\)

The increase in the width of the depletion region in a \(\mathrm{p\text{-}n}\) junction diode is due to:
1. reverse bias only
2. both forward bias and reverse bias
3. increase in forwarding current
4. forward bias only

A capillary tube of radius \(r\) is immersed in water and water rises in it to a height \(h.\) The mass of the water in the capillary is \(5\) g. Another capillary tube of radius \(2r\) is immersed in water. The mass of water that will rise in this tube is: