In a hydrogen like atom, when an electron jumps from the \(M -\) shell to the \(L-\) shell the wavelength of emitted radiation is \(\lambda \). If an electron jumps from \(N-\) shell to the \(L-\) shell the wavelength of emitted radiation will be

When \(100\,g\) of a liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of a liquid \(B\) at temperature \(75\,^oC\), the temperature of the mixture becomes \(90\,^oC\). The temperature of the mixture, if \(100\,g\) of liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of liquid \(B\) at \(50\,^oC\), will be ........\(^oC\)

Match the List-I with List-II

	List-I		List-II
A	Radio-wave	I	is produced by Magnetron value
B	Micro-wave	II	Due to change in the vibrational modes of atoms
C	Infrared-wave	II	Due to inner shell electrons moving from higher energy level to lower energy level
D	X-ray	IV	Due to rapid acceleration of electrons

Choose the correct answer from the options given below:

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, \(5 cm\). If the tube is dipped in a similar manner in another liquid \(B\) of surface tension and density double the values of liquid \(A\), the height of liquid column raised in liquid \(B\) would be \(........m\).

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

A thin uniform bar of length \(L\) and mass \(8\,m\) lies on a smooth horizontal table. Two point masses \(m\) and \(2\,m\) moving in the same horizontal plane from opposite sides of the bar with speeds \(2v\) and \(v\) respectively. The masses stick to the bar after collision at a distance \(\frac{L}{3}\) and \(\frac{L}{6}\) respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be

A convex lens is put \(10\, cm\) from a light source and it makes a sharp image on a screen, kept \(10\, cm\) from the lens. Now a glass block (refractive index \(1.5\)) of \(1.5\, cm\) thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance \(d\). Then \(d\) is

A ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees.

A 4 kg mass moves under the influence of a force \(\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right) N\) where \(t\) is the time in second. If mass starts from origin at \(t=0\), the velocity and position after \(t=2 s\) will be :

The Young's modulus of steel wire of radius \(r\) and length \(L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\)

A liquid column of height \(0.04 \mathrm{~cm}\) balances excess pressure of soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}\) and surface tension of soap solution is \(0.28 \mathrm{Nm}^{-1}\), then diameter of the soap bubble is _______ \(\mathrm{cm}\). \(\text { (if } g=10 \mathrm{~ms}^{-2} \text { ) }\)

To find the spring constant \((k)\) of a spring experimentally, a student commits \(2 \%\) positive error in the measurement of time and \(1 \%\) negative error in measurement of mass. The percentage error in determining value of \(\mathrm{k}\) is _______.