An electron accelerated through a potential difference \(V_1\) has a de-Broglie wavelength of \(\lambda\). When the potential is changed to \(V _2\), its de-Broglie wavelength increases by \(50 \%\). The value of \(\left(\frac{ V _1}{ V _2}\right)\) is equal to :

A convex lens of refractive index 1.5 and focal length \(f=18 cm\) is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is \(\alpha \times f\). The value of \(\alpha\) is ___________.
(refractive index of water \(=4 / 3\) )

A simple pendulum made of a bob of mass \(m\) and a metallic wire of negligible mass has time period \(2s\) at  \(T = 0\,^oC\) . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope \(S\). If the coefficient of linear expansion of metal is \(\alpha \) then the value of  \(S\) is

A wire of length \(30\,cm\), stretched between rigid supports, has it's \(n^{\text {th}}\) and \((n+1)^{\text {th}}\) harmonics at \(400\,Hz\) and \(450\; Hz\), respectively. If tension in the string is \(2700\,N\), it's linear mass density is.........\(kg/m\).

A potential \(V_0\) is applied across a uniform wire of resistance \(R\). The power dissipation is \(P_1\). The wire is then cut into two equal halves and a potential of \(V _0\) is applied across the length of each half. The total power dissipation across two wires is \(P_2\). The ratio \(P_2: P_1\) is \(\sqrt{x}: 1\). The value of \(x\) is \(.............\).

A metal rod of length \(L\) rotates about one end at origin with a uniform angular velocity \(\omega\). The magnetic field radially falls off as \(B(r) = B_0 e^{-\lambda r}\); \(\lambda\) being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

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

List\(-I\)	List\(-II\)
\((a)\) Magnetic Induction	\((i)\) \({ML}^{2} {T}^{-2} {A}^{-1}\)
\((b)\) Magnetic Flux	\((ii)\) \({M}^{0} {L}^{-1} {A}\)
\((c)\) Magnetic Permeability	\((iii)\) \({MT}^{-2} {A}^{-1}\)
\((d)\) Magnetization	\((iv)\) \({MLT}^{-2} {A}^{-2}\)

Choose the most appropriate answer from the options given below:

A deviation of \(2^{\circ}\) is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are \(0.02\) and \(0.03\) respectively and refractive index for yellow light for these glasses are \(1.5\) and \(1.6\) respectively. The refracting angles for crown glass prism will be \(........\,^{\circ}\) (in degree) (Round off to the Nearest Integer)

A laser beam has intensity of \( 4.0\times10^{14} W/m^{2} \). The amplitude of magnetic field associated with beam is__________ T. (Take \( \epsilon_{0}=8.85\times10^{-12} C^{2}/Nm^{2} \) and \( c=3\times10^{8} m/s \))

Given the masses of various atomic particles \(m _{ p }=1.0072 u , m _{ n }=1.0087 u\) \(m _{ e }=0.000548 u , m _{ v }=0, m _{ d }=2.0141 u\) where \(p \equiv\) proton, \(n \equiv\) neutron, \(e \equiv\) electron, \(\overline{ v } \equiv\) antineutrino and \(d \equiv\) deuteron. Which of the following process is allowed by momentum and energy conservation \(?\)