A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is
(1) hyperbola
(2) circle
(3) straight line
(4) parabola

Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light $= 500\,\mathrm{nm}$]
(1) 5 m
(2) 1 m
(3) 6 m
(4) 3 m

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is
(1) $\frac{1}{2}\mathrm{I}_0$
(2) $\frac{1}{4}\mathrm{I}_0$
(3) zero
(4) $I_0$

If $\mathrm{I}_0$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?
(1) $2\mathrm{I}_0$
(2) $4I_0$
(3) $I_0$
(4) $I_0/2$

A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed $\frac{1}{2}\mathrm{~m}$ away, the number of electrons emitted by photo cathode would
(1) decrease by a factor of 4
(2) increase by a factor of 4
(3) decrease by a factor of 2
(4) increase by a factor of 2

If the kinetic energy of a free electron doubles. Its deBroglie wavelength changes by the factor
(1) $\frac{1}{2}$
(2) 2
(3) $\frac{1}{\sqrt{2}}$
(4) $\sqrt{2}$

The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be
(1) 6 mm
(2) 9 mm
(3) 18 mm
(4) 12 mm

Starting with a sample of pure ${}^{66}\mathrm{Cu}$, $7/8$ of it decays into Zn in 15 minutes. The corresponding half-life is
(1) 10 minutes
(2) 15 minutes
(3) 5 minutes
(4) $7\frac{1}{2}$ minutes

If radius of ${}_{13}^{27}\mathrm{Al}$ nucleus is estimated to be 3.6 Fermi then the radius ${}_{52}^{125}\mathrm{Te}$ nucleus be nearly
(1) 6 fermi
(2) 8 fermi
(3) 4 fermi
(4) 5 fermi

A nuclear transformation is denoted by $X(n,\alpha){}_{3}^{7}\mathrm{Li}$. Which of the following is the nucleus of element $X$?
(1) ${}^{12}\mathrm{C}_6$
(2) ${}_{5}^{10}\mathrm{B}$
(3) ${}_{5}^{9}\mathrm{B}$
(4) ${}_{4}^{11}\mathrm{Be}$

A wire elongates by $\ell$ mm when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in mm)
(1) $\ell/2$
(2) $\ell$
(3) $2\ell$
(4) zero

A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed $v$ ms$^{-1}$. The velocity of sound in air is $300$ ms$^{-1}$. If the person can hear frequencies upto a maximum of $10{,}000$ Hz, the maximum value of $v$ upto which he can hear the whistle is
(1) $30$ ms$^{-1}$
(2) $15\sqrt{2}$ ms$^{-1}$
(3) $15/\sqrt{2}$ ms$^{-1}$
(4) $15$ ms$^{-1}$

A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
(1) 10.5 Hz
(2) 105 Hz
(3) 1.05 Hz
(4) 1050 Hz

The flux linked with a coil at any instant '$t$' is given by $\phi = 10t^2 - 50t + 250$. The induced emf at $t = 3$ s is
(1) 190 V
(2) $-190$ V
(3) $-10$ V
(4) 10 V

In a series resonant LCR circuit, the voltage across $R$ is 100 volts and $R = 1$ k$\Omega$ with $C = 2\,\mu$F. The resonant frequency $\omega$ is $200$ rad/s. At resonance the voltage across $L$ is
(1) $4 \times 10^{-3}$ V
(2) $2.5 \times 10^{-2}$ V
(3) 40 V
(4) 250 V

An inductor ($L = 100$ mH), a resistor ($R = 100\,\Omega$) and a battery ($E = 100$ V) are initially connected in series. After a long time the battery is disconnected after short circuiting the points $A$ and $B$. The current in the circuit 1 ms after the short circuit is
(1) 1 A
(2) $1/e$ A
(3) $e$ A
(4) 0.1 A

An alpha nucleus of energy $\frac{1}{2}mv^2$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to
(1) $\frac{1}{Ze}$
(2) $v^2$
(3) $\frac{1}{m}$
(4) $\frac{1}{v^4}$

If the binding energy per nucleon in ${}_{3}^{7}\mathrm{Li}$ and ${}_{2}^{4}\mathrm{He}$ nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction $\mathrm{p} + {}_{3}^{7}\mathrm{Li} \rightarrow 2\,{}_{2}^{4}\mathrm{He}$, the energy of the proton must be
(1) 39.2 MeV
(2) 28.24 MeV
(3) 17.28 MeV
(4) 1.46 MeV

If the ratio of the concentration of electrons to that of holes in a semiconductor is $\frac{7}{5}$ and the ratio of currents is $\frac{7}{4}$, then what is the ratio of their drift velocities?
(1) $\frac{4}{7}$
(2) $\frac{5}{8}$
(3) $\frac{4}{5}$
(4) $\frac{5}{4}$

In a common base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor $(\beta)$ will be
(1) 48
(2) 49
(3) 50
(4) 51

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
(1) $200 \mathrm{~J} - 500 \mathrm{~J}$
(2) $2 \times 10 ^ { 5 } \mathrm{~J} - 3 \times 10 ^ { 5 } \mathrm{~J}$
(3) $20,000 \mathrm{~J} - 50,000 \mathrm{~J}$
(4) $2,000 \mathrm{~J} - 5,000 \mathrm{~J}$

A body of mass $m = 3.513 \mathrm{~kg}$ is moving along the $x$-axis with a speed of $5.00 \mathrm{~ms} ^ { - 1 }$. The magnitude of its momentum is recorded as
(1) $17.6 \mathrm{~kg~ms} ^ { - 1 }$
(2) $17.565 \mathrm{~kg~ms} ^ { - 1 }$
(3) $17.56 \mathrm{~kg~ms} ^ { - 1 }$
(4) $17.57 \mathrm{~kg~ms} ^ { - 1 }$

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is $11 \mathrm{~kms} ^ { - 1 }$, the escape velocity from the surface of the planet would be
(1) $1.1 \mathrm{~kms} ^ { - 1 }$
(2) $11 \mathrm{~kms} ^ { - 1 }$
(3) $110 \mathrm{~kms} ^ { - 1 }$
(4) $0.11 \mathrm{~kms} ^ { - 1 }$

This question contains Statement - 1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - I: For a mass $M$ kept at the centre of a cube of side ' $a$ ', the flux of gravitational field passing through its sides is $4\pi GM$.
Statement - II: If the direction of a field due to a point source is radial and its dependence on the distance ' $r$ ' from the source is given as $1/r^{2}$, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
(1) Statement - 1 is false, Statement - 2 is true.
(2) Statement - 1 is true, Statement - 2 is true; Statement - 2 is correct explanation for Statement-1.
(3) Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement-1.
(4) Statement - 1 is true, Statement - 2 is False.

A spherical solid ball of volume $V$ is made of a material of density $\rho _ { 1 }$. It is falling through a liquid of density $\rho _ { 2 }$ $\left( \rho _ { 2 } < \rho _ { 1 } \right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F _ { \text{viscous} } = - k v ^ { 2 }$ $(k > 0)$. The terminal speed of the ball is
(1) $\sqrt { \frac { Vg \left( \rho _ { 1 } - \rho _ { 2 } \right) } { k } }$
(2) $\frac { Vg \rho _ { 1 } } { k }$
(3) $\sqrt { \frac { V g \rho _ { 1 } } { k } }$
(4) $\frac { Vg \left( \rho _ { 1 } - \rho _ { 2 } \right) } { k }$