Q. A power transmission line feeds input power t 2300 V to a step-down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is 90%, the output current would be :

1. 25 A
2. 35 A
3. 50 A
4. 45 A

Q. A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1,K_2,K_3,K_4$ arranged as shown in the figure. The effective dielectric constant K will be :

1. $K=\frac{(K_1+K_2)(K_3+K_4)}{2(K_1+K_2+K_3+K_4)}$
2. $K=\frac{(K_1+K_2)(K_3+K_4)}{(K_1+K_2+K_3+K_4)}$
3. $K=\frac{(K_1+K_4)(K_2+K_3)}{2(K_1+K_2+K_3+K_4)}$
4. $K=\frac{(K_1+K_3)(K_2+K_4)}{K_1+K_2+K_3+K_4}$

Q. Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of $V_o$ changes by : (assume that the Ge diode has large breakdown voltage)

1. 0.6 v
2. 0.8 V
3. 0.4 V
4. 0.2 V

Q. A series AC circuit containing an inductor (20 mH), a capacitor ($120\mu F$) and a resistor ($60\Omega$) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is :

1. $2.26\times {10}^{3}J$
2. $3.39\times {10}^{3}J$
3. $5.17\times {10}^{2}J$
4. $5.65\times {10}^{2}J$

Q. In the given circuit the internal resistance of the 18 V cell is negligible. If $R_1=400\Omega ,R_3=100\Omega$ and $R_4=500\Omega$ and the reading of an ideal voltmeter across $R_4$ is 5V, then the value $R_2$ will be :

1. $550\Omega$
2. $450\Omega$
3. $230\Omega$
4. $300\Omega$

Q. Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $\left(M_1\right)$ and parallel to the second mirror $\left(M_2\right)$ is finally reflected from the second mirror $\left(M_2\right)$ parallel to the first mirror $\left(M_1\right)$. The angle between the two mirrors will be :

1. ${90}^o$
2. ${45}^o$
3. ${60}^o$
4. ${75}^o$

Q. A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are
attached at distance ${}^{\prime }L/2^{\prime }$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio m/M is close to :

1. 0.175
2. 0.375
3. 0.775
4. 0.575

Q. A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :

1. $\frac{A}{2}$
2. $A$
3. $\frac{A}{2\sqrt{2}}$
4. $\frac{A}{\sqrt{2}}$

Q. The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is :

1. 5.740 m
2. 5.950 mm
3. 5.755 m
4. 5.725 mm

Q. Expression for time in terms of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light) is proportional to :

1. $\sqrt{\frac{Gh}{c^3}}$
2. $\sqrt{\frac{h{c}^5}{G}}$
3. $\sqrt{\frac{c^3}{Gh}}$
4. $\sqrt{\frac{Gh}{c^5}}$

Q. At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio $\frac{R_B}{R_A}$ of their activities after time t itself decays with time t as $e^{-3t}.$ If the half-life of A is $ln2$, the half-life of B is:

1. $\frac{ln2}{2}$
2. $2ln2$
3. $\frac{ln2}{4}$
4. $4ln2$

Q. One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $\left(B_L\right)$ to that at the centre of the coil $\left(B_C\right)$, i.e. R $\frac{B_L}{B_C}$ will be

1. $N^2$
2. $\frac{1}{N}$
3. $\frac{1}{N^2}$
4. $N$

Q. A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it move in a straight path, then the mass of the particle is ___?
(Given charge of electron = $1.6\times {10}^{-19}C$)

1. $1.6\times {10}^{-27}kg$
2. $9.1\times {10}^{-31}kg$
3. $2.0\times {10}^{-24}kg$
4. $1.6\times {10}^{-19}kg$

Q. A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of ${30}^o$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad $s^{-1}$) will be ($g=10m{s}^{-2}$)

1. $\sqrt{30}$
2. $\sqrt{\frac{30}{2}}$
3. $\frac{\sqrt{30}}{2}$
4. $\frac{\sqrt{20}}{3}$

Q. A force acts on a $2kg$ object so that its position is given as a function of time as $x=3t^2+5$. What is the work done by this force in first $5$ seconds ?

1. $850J$
2. $950J$
3. $900J$
4. $875J$

Q. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature ${27}^{o}C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about :

1. 10 kJ
2. 0.9 kJ
3. 6 kJ
4. 14 kJ

Q. A carbon resistance has a following colour code. What is the value of the resistance ?

1. $64k\Omega \pm 10\%$
2. $5.3M\Omega \pm 5\%$
3. $1.64M\Omega \pm 5\%$
4. $530k\Omega \pm 5\%$

Q. The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos $\omega$ t
y = a sin $\omega$ t
and z = a$\omega$t
The speed of the particle is :

1. $\sqrt{2}a\omega$
2. $a\omega$
3. $\sqrt{3}a\omega$
4. $2a\omega$

Q. The top of a water tank is open to air and its water level is maintained. It is giving out $0.74m^3$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to :

1. $9.6m$
2. $4.8m$
3. $6.0m$
4. $2.9m$

Q. A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of ${45}^o$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($g=10m{s}^2$)

1. 200 N
2. 100 N
3. 70 N
4. 140 N

Q. The energy required to take a satellite to a height ${}^{\prime }{h}^{\prime }$ above Earth surface ( radius of Earth = $6.4\times {10}^{3}km$) is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of $h$ for which $E_1$ and $E_2$ are equal, is:

1. $1.28\times {10}^{4}km$
2. $1.6\times {10}^{3}km$
3. $3.2\times {10}^{3}km$
4. $6.4\times {10}^{3}km$

Q. A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to :

1. 753 Hz
2. 500 Hz
3. 666 Hz
4. 333 Hz

Q. Two point charges $q_1\left(\sqrt{10}\mu C\right)$ and $q_2(-25\mu C)$ are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, $[take\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{,}^2{C}^{-2}]$

1. $(63\hat{i}-27\hat{j})\times {10}^2$
2. $(-63\hat{i}+27\hat{j})\times {10}^2$
3. $(-81\hat{i}+81\hat{j})\times {10}^2$
4. $(81\hat{i}-81\hat{j})\times {10}^2$

Q. The energy associate with electric field is $\left(U_E\right)$ and with magnetic field is $\left(U_B\right)$ for an electromagetic wave in free space. Then :

1. $U_E=U_B$
2. $U_E>U_B$
3. $U_E<U_B$
4. $U_E=\frac{U_B}{2}$

Q. The magnetic field associated with a light wave is given, at the origin, by $B=B_0\left[sin\right(3.14\times {10}^7)ct+sin(6.28\times {10}^7\left)ct\right]$. If this light falls on a silver plate having a work function of $4.7eV$, what will be the maximum kinetic energy of the photo electrons ?
$(c=3\times {10}^{8}m{s}^{-1}.h=6.6\times {10}^{-34}J-s)$

1. 7.72 eV
2. 8.52 eV
3. 6.82 eV
4. 12.5 eV

Q. In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda =500nm$ is incident on the slits. The total number of bright fringes that are observed in the angular range $-{30}^o\le \theta \le {30}^o$ is :

1. 320
2. 641
3. 321
4. 640

Q. Charge is distributed within a sphere of radius R with a volume charge density $\rho \left(r\right)=\frac{A}{r^2}{e}^{-2r/a}$ , where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

1. $alog(1-\frac{Q}{2\pi aA})$
2. $\frac{a}{2}log(1-\frac{Q}{2\pi aA})$
3. $alog\left(\frac{1}{1-\frac{Q}{2\pi aA}}\right)$
4. $\frac{a}{2}log\left(\frac{1}{1-\frac{Q}{2\pi aA}}\right)$

Q. Two Carrnot engines A and B are operated in series. The first one, A, receives heat at $T_1(=600K)$ and rejects to a reservoir at temperature $T_2$. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3(=400K)$. Calculate the temperature $T_2$ if the work outputs of the two engines are equal :

1. 400 K
2. 500 K
3. 300 K
4. 600 K

Q. In a car race on straight road, car A takes a times t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the car start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then 'v' is equal to

1. $\frac{a_1+a_2}{2}t$
2. $\sqrt{a_1{a}_{2}t}$
3. $\frac{2a_1{a}_2}{a_1+a_2}t$
4. $\sqrt{2a_1{a}_{2}t}$

Q. In a communication system operating at wavelength 800 nm, only one percent of the source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of bandwidth 6 MHz are (Take velocity of light $c=3\times {10}^{8}m/s,h=6.6\times {10}^{-34}J-s$)

1. $3.75\times {10}^6$
2. $4.87\times {10}^5$
3. $3.86\times {10}^6$
4. $6.25\times {10}^5$