Q. Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute(rpm) to ensure proper mixing is close to : (Take the radius of the drum to be $1.25$ in and its axle to be horizontal)

1. $27.0$
2. $1.3$
3. $0.4$
4. $8.0$

Q. To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are:

1. Two
2. Four
3. Three
4. Five

Q. A hemispherical glass body of radius $10cm$ and refractive index 1.5 is silvered on its curved surface. A small air bubble is $6cm$ below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

1. $14cm$ below flat surface
2. $20cm$ below flat surface
3. $16cm$ below flat surface
4. $30cm$ below flat surface

Q. Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ${}^{\prime }{v}^{\prime }$ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities ${\sigma }_1$ and ${\sigma }_2$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :

1. ${\sigma }_1=\frac{-{ϵ}_{0}vB}{2},{\sigma }_2=\frac{{ϵ}_{0}vB}{2}$
2. ${\sigma }_1={ϵ}_{0}vB,{\sigma }_2=-{ϵ}_{0}vB$
3. ${\sigma }_1=\frac{{ϵ}_{0}vB}{2},{\sigma }_2=\frac{-{ϵ}_{0}vB}{2}$
4. ${\sigma }_1={\sigma }_2={ϵ}_{0}vB$

Q. A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as $B=B_0{e}^{-t/\tau }$, where $B_0$ and $\tau$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time $(t\to \infty )$ is

1. $\frac{{\pi }^2{r}^4{B}_0^4}{2\tau R}$
2. $\frac{{\pi }^2{r}^4{B}_0^2}{2\tau R}$
3. $\frac{{\pi }^2{r}^4{B}_0^2}{\tau R}$
4. $\frac{{\pi }^2{r}^4{B}_0^{2}R}{\tau }$

Q. Within a spherical charge distribution of charge density $\rho \left(r\right)$, N equipotential surfaces of potential $V_0,V_0+\Delta V,V_0+2\Delta V,.....,V_0+N\Delta V(\Delta V>0)$, are drawn and have increasing radii $r_0,r_1,r_2,.....r_N$, respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$ then :

1. $\rho \left(r\right)=$ constant
2. $\rho \left(r\right)\propto \frac{1}{r^2}$
3. $\rho \left(r\right)\propto \frac{1}{r}$
4. $\rho \left(r\right)\propto 1$

Q. In an engine the piston undergoes vertical simple harmonic motion with amplitude $7cm$. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :

1. $1.9Hz$
2. $0.7Hz$
3. $1.2Hz$
4. $0.1Hz$

Q. A bottle has an opening of radius $a$ and length $b$. A cork of length $b$ and radius $(a+\Delta a)$ where $(\Delta a<<a)$ is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and the frictional coefficient between the bottle and cork is $\mu$ then the force needed to push the cork into the bottle is :

1. $\left(2\pi \mu Bb\right)\Delta a$
2. $\left(\pi \mu Bb\right)a$
3. $\left(\pi \mu Bb\right)\Delta a$
4. $\left(4\pi \mu Bb\right)\Delta a$

Q. A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a common-emitter transistor configuration is :

1. 
   
2. 
   
3. 
   
4. 
   

Q. Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year $=9.46\times {10}^{15}m$) of the order of:

1. ${10}^{8}km$
2. ${10}^{10}km$
3. ${10}^{11}km$
4. ${10}^{6}km$

Q. A particle of mass $m$ is acted upon by a force $F$ given by the empirical law $F=\frac{R}{t^2}v\left(t\right)$. If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

1. $\log v\left(t\right)$ against $\frac{1}{t}$
2. $v\left(t\right)$ against $t^2$
3. $\log v\left(t\right)$ against $t$
4. $\log v\left(t\right)$ against $\frac{1}{t^2}$

Q. Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 $\mu F$ is :

1. $\frac{32}{23}\mu F$
2. $\frac{34}{23}\mu F$
3. $\frac{31}{23}\mu F$
4. $\frac{33}{23}\mu F$

Q. The resistance of an electrical toaster has a temperature dependence given by $R\left(T\right)=R_0[1+\alpha (T-T_0\left)\right]$ in its range of operation. At $T_0=300K,R_0=100\Omega$ and at $T=500K,R=120\Omega$. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is :

1. $400ln\frac{5}{6}J$
2. $200ln\frac{2}{3}J$
3. $300J$
4. $400ln\frac{1.5}{1.3}J$

Q. A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is $240m{s}^{-1}$. The earth's magnetic field over Delhi is $5\times {10}^{-5}$ T with the declination angle $\sim 0^o$ and dip of $\theta$ such that $sin\theta =\frac{2}{3}$. If the voltage developed is $V_B$ between the lower and upper side of the plane and $V_W$ between the tips of the wings then $V_B$ and $V_W$ are close to

1. $V_B=45mV;V_W=120mV$ with right side of pilot at higher voltage
2. $V_B=40mV;V_W=135mV$ with left side of pilot at higher voltage
3. $V_B=40mV;V_W=135mV$ with right side of pilot at high voltage
4. $V_B=45mV;V_W=120mV$ with left side of pilot at higher voltage

Q. A particle of mass $M$ is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^{2}R{t}^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it, is:

1. $\frac{1}{2}M{n}^2{R}^2{t}^2$
2. $M{n}^2{R}^{2}t$
3. $Mn{R}^2{t}^2$
4. $Mn{R}^{2}t$

Q. A galvanometer has a $50$ division scale. Battery has no internal resistance. It is found that there is deflection of $40$ divisions when $R=2400\Omega$. Deflection becomes $20$ divisions when resistance taken from resistance box is $4900\Omega$. Then we can conclude:

1. resistance of galvanometer is $200\Omega$
2. current sensitivity of galvanometer is $20\mu A/$division
3. resistance required on $R.B.$ for a deflection of $10$ divisions is $9800\Omega$.
4. full scale deflection current is $2m.A$.
5. Not Solvable

Q. In the figure shown $ABC$ is a uniform wire. If centre of mass of wire lies vertically below point $A$, then $\frac{BC}{AB}$ is close to:

1. $1.85$
2. $1.5$
3. $1.37$
4. $3$

Q. Which of the following shows the correct relationship between the pressure ${}^{\prime }{P}^{\prime }$ and density $\rho$ of an ideal gas at constant temperature ?

1. 
   
2. 
   
3. 
   
4. 
   

Q. A neutron moving with a speed ${}^{\prime }{v}^{\prime }$ makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is:

1. $20.4eV$
2. $10.2eV$
3. $12.1eV$
4. $16.8eV$

Q. Velocity-time graph for a body of mass $10kg$ is shown in figure. Work-done on the body in first two seconds of the motion is :

1. $12000J$
2. $-9300J$
3. $-12000J$
4. $-4500J$

Q. The ratio (R) of output resistance $r_0$, and and the input resistance $r_i$ in measurements of input and output characteristics of a transistor is typically in the range :

1. $R\sim {10}^2-{10}^3$
2. $R\sim 1-10$
3. $R\sim 0.1-0.01$
4. $R\sim 0.1-1.0$

Q. A thin 1 m long rod has a radius of 5 mm.1 A force of 50 $\pi kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?

1. The maximum value of Y that can be determined is ${10}^{14}N/m^2$.
2. $\frac{\Delta Y}{Y}$ gets minimum contribution . from the uncertainty in the length.
3. $\frac{\Delta Y}{Y}$ gets its maximum contribution from the uncertainty in strain
4. The figure of merit is the largest for the length of the rod.

Q. A Carnot freezer takes heat from water at $0^{o}C$ inside it and rejects it to the room at a temperature of ${27}^{o}C$ The latent heat of ice is $336\times {10}^{3}Jk{g}^{-1}$. If $5kg$ of water at $0^{o}C$ is converted into ice at $0^{o}C$ by the freezer, then the energy consumed by the freezer is close to:

1. $1.71\times {10}^{7}J$
2. $1.67\times {10}^{5}J$
3. $1.51\times {10}^{5}J$
4. $1.68\times {10}^{6}J$

Q. To get an output of 1. from the circuit shown in figure the input must be

1. $a=0,b=1,c=0$
2. $a=1,b=0,c=0$
3. $a=1,b=0,c=1$
4. $a=0,b=0,c=1$

Q. A modulated signal $C_m\left(t\right)$ has the form $C_m\left(t\right)=30sin300\pi t+10(cos200\pi t-cos400\pi t)$. The carrier frequency $f_c^{\prime }$ the modulating frequency (message frequency) $f_{{\omega }^{\prime }}$ and the modulation index $\mu$ are respectively given by

1. $f_c=200Hz;f_{\omega }=50Hz;\mu =\frac{1}{2}$
2. $f_c=150Hz;f_{\omega }=30Hz;\mu =\frac{1}{3}$
3. $f_c=200Hz;f_{\omega }=30Hz;\mu =\frac{1}{2}$
4. $f_c=150Hz;f_{\omega }=50Hz;\mu =\frac{2}{3}$

Q. Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

1. For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}-\hat{z})$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}+\hat{z})$
2. For an electromagnetic wave propagating in +y direction the 1 A electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)\hat{z}$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{B}_z(x,t)\hat{y}$
3. For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(y,z,t)(\hat{y}+\hat{z})$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{E}_{yz}(y,z,t)(\hat{y}+\hat{z})$
4. For an electromagnetic wave propagating in +y direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)\hat{y}$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{B}_z(x,t)\hat{z}$

Q. A photoelectric surface is illuminated successively by monochromatic light of wavelengths $\lambda$ and $\frac{\lambda }{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

1. $\frac{hc}{\lambda }$
2. $\frac{hc}{2\lambda }$
3. $\frac{hc}{3\lambda }$
4. $\frac{3hc}{\lambda }$

Q. A, B, C and D are four different physical quantifies having different dimensions. None of them is dimensionless. But we know that the equation $AD=Cln\left(BD\right)$ holds true. Then which of the combination is not a meaningful quantity

1. $\frac{C}{BD}-\frac{A{D}^2}{C}$
2. $A^2-B^2{C}^2$
3. $\frac{A}{B}-C$
4. $\frac{(A-C)}{D}$

Q. An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth's surface. The radius of the earth is R, while its mass is M. The gravitational pull $F_G$ on the astronaut is:

1. zero since astronaut feels weightless
2. $0<F_G<\frac{GMm}{R^2}$
3. 
   
4. $F_G=\frac{GMm}{(R+h{)}^2}$

Q. A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to:

1. 680 Hz
2. 510 Hz
3. 340 Hz
4. 170 Hz