Q. The actual value of resistance R, shown in the b figure is $30\Omega$. This is measured in an experiment as shown using the standard Formula $R=\frac{v}{1}$, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is:

1. $400\Omega$
2. $570\Omega$
3. $350\Omega$
4. $600\Omega$

Q. Two Forces P and Q of magnitude 2F and 3F, respectively, are at an angle $\theta$ with each other. If the forces Q is doubled, then their resultant also gets doubled. Then, the angle is

1. ${30}^o$
2. ${60}^o$
3. ${90}^o$
4. ${120}^o$

Q. A hoop and a solid cylinder of same cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. they are placed in a uniform magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are $T_{h}and{T}_c$ respectively, then:

1. $T_h=0.5T_c$
2. $T_h=2T_c$
3. $T_h=T_c$
4. $T_h=1.5T_c$

Q. Consider the nuclear fission, $N{e}^{20}\to 2H{e}^4+C^{12}$
Given that the binding energy/nucleon of $N{e}^{20}$, $H{e}^4$ and $C^{12}$ are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement:

1. 8.3 MeV energy will be released
2. energy of 12.4 MeV will be supplied
3. energy of 3.6 MeV has to be supplied
4. none of the above

Q. Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:

1. $\frac{137}{15}M{R}^2$
2. $\frac{209}{15}M{R}^2$
3. $\frac{17}{15}M{R}^2$
4. $\frac{152}{15}M{R}^2$

Q. At some location on earth the horizontal components of earth's magnetic field is $18\times {10}^{-}6T.$ At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes ${45}^0$ angle with horizontal in equilibrium to keep this needle horizontal, the vertical force that should be applied at one of its ends is:

1. $1.3\times {10}^{-}5N$
2. $1.8\times {10}^{-}5N$
3. $3.6\times {10}^{-}5N$
4. $6.5\times {10}^{-}5N$

Q. Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from ${20}^{o}C$ to ${90}^{o}C$. Work done by gas close to : (Gas constant R = 8.31 J / mol. K)

1. 73 J
2. 291 J
3. 581 J
4. 146 J

Q. A particle executes simple harmonic motion with an amplitude of 5 cm. when the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. then, its periodic time in second is:

1. $\frac{7}{3}\pi$
2. $\frac{4\pi }{3}$
3. $\frac{3}{8}\pi$
4. $\frac{8\pi }{3}$

Q. The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A is 1 s, the change in the energy of the inductance is :

1. 540 J
2. 437.5 J
3. 637.5 J
4. 740 J

Q. A particle starts from the origin at time t = 0 and moves along the positive x - axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s?

1. 6 m
2. 9 m
3. 3 m
4. 10 m

Q. Charge -q and +q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences and electrostatic force F. If Q is now moved along the equatorial line to P' such that $O{P}^{\prime }=\left(\frac{y}{3}\right)$ the force on Q will be close to L : $(\frac{y}{3}>>2a)$

1. 3F
2. 27 F
3. 9F
4. $\frac{F}{3}$

Q. The Wheatstone bridge shown in Fig. here, getsbalanced when the carbon resistor used as R1has the colour code ( Orange, Red, Brown).The resistors R2 and R4 are 80 and 40respectively.Assuming that the colour code for the carbonresistors gives their accurate values, the colour codefor the carbon resistor, used as R3, would be

1. Brown, Blue, Brown
2. Grey, Black, Brown
3. Brown, Blue, Black
4. Red, Green, Brown

Q. A rigid massless rod of length 3$l$ has two masses attached art each end as shown in the figure. The rod is pivoted at point P on the horizontal position, its instantaneous angular acceleration will be:

1. $\frac{g}{2l}$
2. $\frac{7g}{3l}$
3. $\frac{g}{13l}$
4. $\frac{g}{3l}$

Q. Two stars of masses $3\times {10}^{31}kg$ each, and at distance $2\times {10}^{11}m$ rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is : (take Gravitational constant $G=6.67\times {10}^{11}N{m}^{2}k{g}^{-2}$)

1. $3.8\times {10}^{4}m/s$
2. $24\times {10}^{4}m/s$
3. $1.4\times {10}^{5}m/s$
4. $2.8\times {10}^{5}m/s$

Q. For the circuit show below, the current through the zener diode is :

1. 5 mA
2. Zero
3. 14 mA
4. 9 mA

Q. The modulation frequency Of an AM radio station is 250 KHz, which is 10% of the carrier wave. If another AM station approaches you for licence what broadcast frequency will you allot?

1. 2750 KHz
2. 2250 KHz
3. 2900 KHz
4. 2000 KHz

Q. Two vectors $\overrightarrow{A}and\overrightarrow{B}$ have equal magnitude. The magnitude of $(\overrightarrow{A}+\overrightarrow{B})$ is 'n' times the magnitude of $(\overrightarrow{A}+\overrightarrow{B})$. The angle between $\overrightarrow{A}+\overrightarrow{B}$ is '

1. $co{s}^{-1}\left[\frac{n^2-1}{n^2+1}\right]$
2. $si{n}^{-1}\left[\frac{n-1}{n+1}\right]$
3. $si{n}^{-1}\left[\frac{n^2-1}{n^2+1}\right]$
4. $co{s}^{-1}\left[\frac{n-1}{n+1}\right]$

Q. A cylindrical plastic bottel of negligible mass is filled with 310 ml of water and left floating in a pound with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is 2.5 cm, then $\omega$ close to (density of water = ${10}^{3}kg/m^3)$

1. $7.95rad{s}^{-1}$
2. $5.00rad{s}^{-1}$
3. $1.25rad{s}^{-1}$
4. $3.75rad{s}^{-1}$

Q. The diameter and height of a cylinder are measured by a meter scale to be 12.6 + 0.1 cm and 34.2 + 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?

1. $4260+80c{m}^2$
2. $4300+80c{m}^3$
3. $4264+81.0c{m}^3$
4. $4264+81c{m}^3$

Q. A metal plate of area $1\times {10}^{-4}{m}^2$ is illuminated by a radiation of intensity $16mW/m^2$.The work function of the metal is 5eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be :
$[1eV=1.6\times {10}^{-19}]$

1. ${10}^{10}$ and 5 eV
2. ${10}^{12}$ and 5 eV
3. ${10}^{14}$ and 10 eV
4. ${10}^{11}$ and 5 eV

Q. Two kg of a monoatomic gas is at a pressure of $4\times {10}^{4}N/m^2$ . The density of the gas is $8kg/m^3$. What is the order of energy of the gas due to its thermal motion ?

1. ${10}^{3}J$
2. ${10}^{6}J$
3. ${10}^{5}J$
4. ${10}^{4}J$

Q. The eye can be regarded as a single refracting surface. The radius of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

1. 2 cm
2. 1 cm
3. 4.0 cm
4. 3.1 cm

Q. For equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work required to put a fifth Q at the origin of the coordinate system will be:

1. $\frac{Q^2}{4\pi {\epsilon }_o}(1+\frac{1}{\sqrt{5}})$
2. $\frac{Q^2}{4\pi {\epsilon }_o}$
3. $\frac{Q^2}{4\pi {\epsilon }_o}(1+\frac{1}{\sqrt{3}})$
4. $\frac{Q^2}{2\sqrt{2}\pi {\epsilon }_o}$

Q. A closed organ pipe has a fundamental frequency of 1.5 Khz. The number of overtones that can be distinctly heard by a person with this organ pipe will be : ( Assume that the highest frequency a person can hear is 20, 000 Hz)

1. 5
2. 6
3. 7
4. 4

Q. The electric field of a plane polarized electromagnetic Wave in free space at time t = 0 i given by an expression
$\overrightarrow{E}(x,y)=10\hat{j}cos\left[\right(6x+8z\left)\right]$
The magenetic field $\overrightarrow{B}$ (x, z, t) is given by ; (c is the velocity of light will be:

1. $\frac{1}{c}(4\hat{k}+8\hat{i})cos\left[\right(2x-8z+20ct\left)\right]$
2. $\frac{1}{c}(6\hat{k}-8\hat{i})cos\left[\right(6x+8z-10ct\left)\right]$
3. $\frac{1}{c}(5\hat{k}+8\hat{i})cos\left[\right(6x+8z-80ct\left)\right]$
4. $\frac{1}{c}(4\hat{k}-8\hat{i})cos\left[\right(6x+8z+70ct\left)\right]$

Q. A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates the work done by the capacitor on the slab is :

1. 560 pJ
2. 600pJ
3. 508 pJ
4. 692 pJ

Q. Consider a young's doluble slit experiment as shown in figure. What should be the slit seperation d in term of wavelength $\lambda$ such that the first minima occurs directly in front of the slit $\left(S_1\right)$ ?

1. $\frac{\lambda }{2(\sqrt{5}-2)}$
2. $\frac{\lambda }{(\sqrt{5}-2)}$
3. $\frac{\lambda }{2(5-\sqrt{2})}$
4. $\frac{\lambda }{(5-\sqrt{2})}$

Q. A particle which is experiencing a force, given by $\overrightarrow{F}=3\overrightarrow{i}-12\overrightarrow{j}$, undergoes a displacement of $\overrightarrow{d}=4\overrightarrow{i}$. If particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?

1. 10 J
2. 9 J
3. 12 J
4. 15 J

Q. A current of 2mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11V is connected across it is :

1. $11\times {10}^{-5}W$
2. $11\times {10}^{-4}W$
3. $11\times {10}^{5}W$
4. $11\times {10}^{-3}W$

Q. An unknown metal of mass 192 g heated to a temperature of ${100}^{o}c$ was immersed into a brass calorimeter of mass 128g containing 240 g of water a temperature of ${8.4}^{o}C$ calculate the specific heat of the unknown metal if water temperature stabilizes at ${21.5}^{o}c$ (specific heat of brass is $394jK{g}^{-1}{k}^{-1}$

1. 458 J $k{g}^{-1}{K}^{-1}$
2. 654 J $k{g}^{-1}{K}^{-1}$
3. 916 J $k{g}^{-1}{K}^{-1}$
4. 1232 J $k{g}^{-1}{K}^{-1}$