The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is: [Take $\mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm { NA } ^ { - 2 }$ ]
(1) $3 \mu \mathrm {~T}$
(2) $1 \mu \mathrm {~T}$
(3) $18 \mu \mathrm {~T}$
(4) $9 \mu \mathrm {~T}$

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of $5 \mathrm {~m} / \mathrm { s }$ the speed and direction of the image will be
(1) $2.26 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ away from the lens
(2) $0.92 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ away from the lens
(3) $3.22 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ towards the lens
(4) $1.16 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$ towards the lens

A coil of self inductance 10 mH and resistance of $0.1 \Omega$ is connected through a switch to a battery of internal resistance $0.9 \Omega$. After the switch is closed, the time taken for the current to attain $80\%$ of the saturation value is: $[\ln 5 = 1.6]$
(1) 0.103 s
(2) 0.002 s
(3) 0.324 s
(4) 0.016 s

The graph shows how the magnification $m$ produced by a thin lens varies with image distance $v$. The focal length of the lens used is
(1) $\frac { b } { c }$
(2) $\frac { a } { c }$
(3) $\frac { b ^ { 2 } c } { a }$
(4) $\frac { b ^ { 2 } } { a c }$

In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $\frac { 1 } { 8 }$th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:
(1) 0.74
(2) 0.85
(3) 0.94
(4) 0.8

A particle A of mass $m$ and charge $q$ is accelerated by a potential difference of 50 V. Another particle B of mass $4 m$ and charge $q$ is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $\frac { \lambda _ { A } } { \lambda _ { B } }$ is close to:
(1) 0.07
(2) 10.00
(3) 4.47
(4) 14.14

In a double-slit experiment, green light $( 5303 \mathrm {~\AA} )$ falls on a double slit having a separation of $19.44 \mu \mathrm {~m}$ and a width of $4.05 \mu \mathrm {~m}$. The number of bright fringes between the first and the second diffraction minima is
(1) 10
(2) 5
(3) 4
(4) 9

In a Young's double-slit experiment, the ratio of the slit's width is $4 : 1$. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be
(1) $25 : 9$
(2) $9 : 1$
(3) $\left(\sqrt { 3 } + 1\right) ^ { 4 } : 16$
(4) $4 : 1$

If the deBroglie wavelength of an electron is equal to $10^{-3}$ times the wavelength of a photon of frequency $6 \times 10 ^ { 14 } \mathrm {~Hz}$, then the speed of electron is equal to: (Speed of light $= 3 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$, Planck's constant $= 6.63 \times 10 ^ { - 34 } \mathrm { J.s }$, Mass of electron $= 9.1 \times 10 ^ { - 31 } \mathrm {~kg}$)
(1) $1.1 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
(2) $1.7 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
(3) $1.8 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
(4) $1.45 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$

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) $\frac { 1 } { 4 \lambda }$