A particle of mass $m$ moves in a circular orbit in a central potential field $U ( r ) = \frac { 1 } { 2 } k r ^ { 2 }$. If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number $n$ as:
(1) $r _ { n } \propto n ^ { 2 } , E _ { n } \propto \frac { 1 } { n ^ { 2 } }$
(2) $r _ { n } \propto \sqrt { n } , E _ { n } \propto n$
(3) $r _ { n } \propto n , E _ { n } \propto n$
(4) $r _ { n } \propto \sqrt { n } , E _ { n } \propto \frac { 1 } { n }$

In a double slit experiment, when a thin film of thickness $t$ having refractive index $\mu$ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of $t$ is ($\lambda$ is the wavelength of the light used):
(1) $\frac{\lambda}{2(\mu-1)}$
(2) $\frac{\lambda}{(2\mu-1)}$
(3) $\frac{2\lambda}{(\mu-1)}$
(4) $\frac{\lambda}{(\mu-1)}$

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: $\left( \frac { \mathrm { hc } } { \mathrm { e } } = 1240 \mathrm {~nm} - \mathrm { V } \right)$
(1) 0.5 V
(2) 1.5 V
(3) 1.0 V
(4) 2.0 V

In a photoelectric effect experiment, the threshold wavelength of light is 380 nm. If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be Given $\mathrm { E } ($ in $\mathrm { eV } ) = \frac { 1237 } { \lambda ( \mathrm { in } \mathrm { nm } ) }$
(1) 4.5 eV
(2) 3.0 eV
(3) 1.5 eV
(4) 15.1 eV

Light is incident normally on a completely absorbing surface with an energy flux of $25 \mathrm {~W} \mathrm {~cm} ^ { - 2 }$. If the surface has an area of $25 \mathrm {~cm} ^ { 2 }$, the momentum transferred to the surface in 40 min time duration will be:
(1) $6.3 \times 10 ^ { - 4 } \mathrm {~N} \mathrm {~s}$
(2) $5.0 \times 10 ^ { - 3 } \mathrm {~N} \mathrm {~s}$
(3) $3.5 \times 10 ^ { - 6 } \mathrm {~N} \mathrm {~s}$
(4) $1.4 \times 10 ^ { - 6 } \mathrm {~N} \mathrm {~s}$

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:
(1) $25 : 9$
(2) $16 : 9$
(3) $5 : 3$
(4) $4 : 1$

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:
(1) $\frac { 27 } { 20 } \lambda$
(2) $\frac { 16 } { 25 } \lambda$
(3) $\frac { 25 } { 16 } \lambda$
(4) $\frac { 20 } { 27 } \lambda$

Two radioactive materials A and B have decay constants $10 \lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:
(1) $\frac { 1 } { 10 \lambda }$
(2) $\frac { 1 } { 9 \lambda }$
(3) $\frac { 1 } { 11 \lambda }$
(4) $\frac { 11 } { 10 \lambda }$

A 2 mW laser operates at a wavelength of 500 nm . The number of photons that will be emitted per second is: [Given Planck's constant $\mathrm { h } = 6.6 \times 10 ^ { - 34 } \mathrm {~J} \mathrm {~s}$, speed of light $\mathrm { c } = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ ]
(1) $1.5 \times 10 ^ { 16 }$
(2) $5 \times 10 ^ { 15 }$
(3) $2 \times 10 ^ { 16 }$
(4) $1 \times 10 ^ { 16 }$

An NPN transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance is $100 \Omega$ and the output load resistance is $10 \mathrm { k } \Omega$. The common emitter current gain $\beta$ is:
(1) $6 \times 10 ^ { 2 }$
(2) $10 ^ { 2 }$
(3) $10 ^ { 4 }$
(4) 60

In $\mathrm { Li } ^ { + + }$, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. When the ion gets de-excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $\lambda$? (Given: $h = 6.63 \times 10 ^ { - 34 } \mathrm {~J}$ s ; $c = 3 \times 10 ^ { 8 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ )
(1) 10.8 nm
(2) 9.4 nm
(3) 11.4 nm
(4) 12.3 nm

An amplitude modulated signal is given by $\mathrm { V } ( \mathrm { t } ) = 10 \left[ 1 + 0.3 \cos \left( 2.2 \times 10 ^ { 4 } \mathrm { t } \right) \right] \sin \left( 5.5 \times 10 ^ { 5 } \mathrm { t } \right)$. Here t is in seconds. The sideband frequencies (in kHz) are, [Given $\pi = 22/7$]
(1) 1785 and 1715
(2) 178.5 and 171.5
(3) 89.25 and 85.75
(4) 892.5 and 857.5

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure $5 \mu \mathrm {~m}$ diameter of a wire is:
(1) 50
(2) 100
(3) 500
(4) 200

The surface of certain metal is first illuminated with light of wavelength $\lambda _ { 1 } = 350 \mathrm {~nm}$ and then, by a light of wavelength $\lambda _ { 2 } = 540 \mathrm {~nm}$. It is found that the maximum speed of the photoelectrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to (Energy of photon $= \frac { 1240 } { \lambda \mathrm{ in nm} } \mathrm { eV }$)
(1) 2.5
(2) 1.8
(3) 5.6
(4) 1.4

A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are:
(1) $4 ; 2 \times 10 ^ { 8 } \mathrm {~Hz}$
(2) $0.25 ; 2 \times 10 ^ { 8 } \mathrm {~Hz}$
(3) $4 ; 1 \times 10 ^ { 8 } \mathrm {~Hz}$
(4) $0.25 ; 1 \times 10 ^ { 8 } \mathrm {~Hz}$

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $\frac { 1 } { e ^ { 2 } }$ will be
(1) $\frac { 1 } { \lambda }$
(2) $\frac { 1 } { 2 \lambda }$
(3) $\frac { 2 } { \lambda }$
(4) $\frac { 1 } { 4 \lambda }$

The resistance of the meter bridge AB in given figure is $4 \Omega$. With a cell of emf $\varepsilon = 0.5 \mathrm {~V}$ and rheostat resistance $\mathrm { R } _ { \mathrm { h } } = 2 \Omega$ the null point is obtained at some point J. When the cell is replaced by another one of emf $\varepsilon = \varepsilon _ { 2 }$ the same null point J is found for $\mathrm { R } _ { \mathrm { h } } = 6 \Omega$. The emf $\varepsilon _ { 2 }$ is:
(1) 0.4 V
(2) 0.3 V
(3) 0.6 V
(4) 0.5 V

In a meter bridge, the wire of length $1 m$ has a non-uniform cross-section such that, the variation $\frac { d R } { d l }$ of its resistance $R$ with length $l$ is $\frac { d R } { d l } \propto \frac { 1 } { \sqrt { l } }$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point $P$. What is the length $AP$?
(1) 0.2 m
(2) 0.35 m
(3) 0.3 m
(4) $0.25 m$

A Sample of radioactive material $A$, that has an activity of $10 \mathrm{ mCi}$ ($1 \mathrm{ Ci} = 3.7 \times 10 ^ { 10 }$ decays $\mathrm { s } ^ { - 1 }$), has twice the number of nuclei as another sample of a different radioactive material $B$ which has an activity of $20 \mathrm{ mCi}$. The correct choices for half-lives of $A$ and $B$ would then be, respectively:
(1) 5 days and 10 days
(2) 10 days and 40 days
(3) 20 days and 10 days
(4) 20 days and 5 days

For emission line of atomic hydrogen from $n _ { i } = 8$ to $n _ { f } = n$, the plot of wave number $\bar { v }$ against $\frac { 1 } { n ^ { 2 } }$ will be: (The Rydberg constant, $\mathrm { R } _ { \mathrm { H } }$ is in wave number unit)
(1) Linear with slope $- R _ { H }$
(2) Non linear
(3) Linear with slope $R _ { H }$
(4) Linear with intercept $- \mathrm { R } _ { \mathrm { H } }$

The ground state energy of a hydrogen atom is $-13.6$ eV. The energy of second excited state of $\mathrm { He } ^ { + }$ ion in eV is:
(1) $-27.2$
(2) $-6.04$
(3) $-3.4$
(4) $-54.4$

The de Broglie wavelength $( \lambda )$ associated with a photoelectron varies with the frequency $( v )$ of the incident radiation as, [$v _ { 0 }$ is threshold frequency]:
(1) $\lambda \propto \frac { 1 } { \left( v - v _ { 0 } \right) }$
(2) $\lambda \propto \frac { 1 } { \left( v - v _ { 0 } \right) ^ { \frac { 1 } { 4 } } }$
(3) $\lambda \propto \frac { 1 } { \left( v - v _ { 0 } \right) ^ { \frac { 3 } { 2 } } }$
(4) $\lambda \propto \frac { 1 } { \left( v - v _ { 0 } \right) ^ { \frac { 1 } { 2 } } }$

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are:
(1) Paschen and Pfund
(2) Balmer and Brackett
(3) Lyman and Paschen
(4) Brackett and Pfund

An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:
(1) $+10.0$
(2) $-2.0$
(3) $-0.9$
(4) $-9.0$

0.5 moles of gas $A$ and $x$ moles of gas $B$ exert a pressure of 200 Pa in a container of volume $10 \mathrm {~m} ^ { 3 }$ at 1000 K. Given, R is the gas constant in $\mathrm { JK } ^ { - 1 } \mathrm {~mol} ^ { - 1 }$, $x$ is:
(1) $\frac { 4 + R } { 2 R }$
(2) $\frac { 2 R } { 4 + 2R }$
(3) $\frac { 4 - R } { 2 R }$
(4) $\frac { 2 R } { 4 - R }$