Q. A proton beam enters a magnetic field of ${10}^{-4}Wb{m}^{-2}$ normally. If the specific charge of the proton is ${10}^{11}Ck{g}^{-1}$ and its velocity is ${10}^{9}m{s}^{-1}$, then the radius of the circle described will be

1. $0.1m$
2. $10m$
3. $100m$
4. $1m$

Q. The angle between the dipole moment and electric field at any point on the equatorial plane is :

1. $0^{\circ }$
2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. ${45}^{\circ }$

Q. In the circuit shown below, the ammeter and the voltmeter readings are $3A$ and $6V$ respectively. Then the value of the resistance $R$ is:

1. $2\Omega$
2. $>2\Omega$
3. $<2\Omega$
4. $\ge 2\Omega$

Q. The ratio of angular speed of a second-hand to the hour-hand of a watch is

1. $720:1$
2. $60:1$
3. $3600:1$
4. $72:1$

Q. $1$ gram of ice is mixed with $1$ gram of steam. At thermal equilibrium, the temperature of the mixture is

1. ${55}^{\circ }C$
2. ${100}^{\circ }C$
3. $0^{\circ }C$
4. ${50}^{\circ }C$

Q. The velocity - time graph for two bodies $A$ and $B$ are shown. Then the acceleration of $A$ and $B$ are in the ratio:

1. $\tan {25}^{\circ }$ to $\tan {40}^{\circ }$
2. $\tan {25}^{\circ }$ to $\tan {50}^{\circ }$
3. $\sin {25}^{\circ }$ to $\sin {50}^{\circ }$
4. $\cos {25}^{\circ }$ to $\cos {50}^{\circ }$

Q. In Wheatstones network $P=2\Omega ,Q=2\Omega ,R=2\Omega$ and $S=3\Omega$. The resistance with which $S$ is to shunted in order that the bridge may be balanced is

1. $2\Omega$
2. $1\Omega$
3. $4\Omega$
4. $6\Omega$

Q. Three point charges $3nC,6nC$ and $9nC$ are placed at the corners of an equilateral triangle of side $0.1m$. The potential energy of the system is :

1. $89100mJ$
2. $8910nJ$
3. $99100KJ$
4. $9910J$

Q. The ratio of hydraulic stress to the corresponding strain is known as

1. Compressiblity
2. Bulk modulus
3. Rigidity modulus
4. Young's modulus

Q. A spherical shell of radius $10cm$ is carrying a charge $q$. If the electric potential at distances $5cm,20cm$ and $15cm$ from the centre of the spherical shell is $V_1,V_2$ and $V_3$ respectively, then :

1. $V_1=V_2>V_3$
2. $V_1>V_2>V_3$
3. $V_1=V_2<V_3$
4. $V_2<V_3<V_1$

Q. The resistance of the bulb filament is $100\Omega$ at a temperature of ${100}^{\circ }C$. If its temperature co-efficient of resistance be $0.005$ per ${}^{\circ }C$, its resistance will become $200\Omega$ at a temperature

1. ${300}^{\circ }C$
2. ${400}^{\circ }C$
3. ${200}^{\circ }C$
4. ${500}^{\circ }C$

Q. A stretched string is vibrating in the second overtone, then the number of nodes and antinodes between the ends of the string are respectively:

1. $4$ and $3$
2. $3$ and $4$
3. $2$ and $3$
4. $3$ and $2$

Q. The kinetic energy of a body of mass $4kg$ and momentum $6Ns$ will be

1. $2.5J$
2. $3.5J$
3. $4.5J$
4. $5.5J$

Q. Three resistances $2\Omega ,3\Omega$ and $4\Omega$ are connected in parallel. The ratio of currents passing through them when a potential difference is applied across its ends will be

1. $6:3:2$
2. $5:4:3$
3. $4:3:2$
4. $6:4:3$

Q. A cyclotron is used to accelerate

1. Neutron
2. Both positively and negatively charged particles
3. Only positively charged particles
4. Only negatively charged particles

Q. Two cells of emf $E_1$ and $E_2$ are joined in opposition (such that $E_1>E_2$). If $r_1$ and $r_2$ be the internal resistance and $R$ be the external resistance, then the terminal potential difference is

1. $\frac{E_1+E_2}{r_1+r_2}\times R$
2. $\frac{E_1+E_2}{r_1+r_2+R}\times R$
3. $\frac{E_1-E_2}{r_1+r_2}\times R$
4. $\frac{E_1-E_2}{r_1+r_2+R}\times R$

Q. A particle is projected with a velocity $v$ so that its horizontal range twice the greater height attained. The horizontal range is

1. $\frac{v^2}{g}$
2. $\frac{2v^2}{3g}$
3. $\frac{4v^2}{5g}$
4. $\frac{v^2}{2g}$

Q. Two concentric coils each of radius equal to $2\pi$ cm are placed right angles to each other. If $3A$ and $4A$ are the currents flowing through the two coils respectively. The magnetic induction (in $Wb{m}^{-2})$ at the centre of the coils will be

1. $12\times {10}^{-5}$
2. ${10}^{-5}$
3. $7\times {10}^{-5}$
4. $5\times {10}^{-5}$

Q. A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are:

1. constant, decreases, decreases
2. increases, decreases, decreases
3. constant, decreases, increases
4. constant, increases, decreases

Q. Two spheres carrying charges $+6\mu C$ and $+9\mu C$ separated by a distance $d$, experiences a force of repulsion $F$. When a charge of $-3\mu C$ is given to both the sphere and kept at the same distance as before, the new force of repulsion is :

1. $F$
2. $3F$
3. $F/3$
4. $F/9$

Q. A stone of mass $0.5kg$ is thrown vertically upwards. What is the direction and magnitude of net force on the stone during its upward motion?

1. $4.9N$ vertically upward
2. $4.9N$ vertically downward
3. $0.98N$ vertically downward
4. $9.8N$ vertically downward

Q. Moment of Inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is $I$. If the same rod is bent into a ring and its moment of inertia about its diameter is $I^{\prime }$, then the ratio $\frac{I}{I^{\prime }}$ is

1. $3{\pi }^2/2$
2. $8{\pi }^2/3$
3. $2{\pi }^2/3$
4. $5{\pi }^2/3$

Q. The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

1. $3:1$
2. $4:1$
3. $2:1$
4. $8:1$

Q. Pick out the statement which is incorrect :

1. The tangent drawn to a line of force represents the direction of electric field
2. The electric field lines form closed loop
3. A negative test charge experiences a force opposite to the direction of the field
4. Field lines never intersect

Q. When two tuning forks $A$ and $B$ are sounded together, $4$ beats per second are heard. The frequency of the fork $B$ is $384Hz$. When one of the prongs of the fork $A$ is filed and sounded with $B$, then beat frequency increases, then frequency of the fork $A$ is

1. $380Hz$
2. $388Hz$
3. $379Hz$
4. $389Hz$

Q. The efficiency of a Carnot engine which operates between the two temperature $T_1=500K$ and $T_2=300K$ is

1. $50$%
2. $25$%
3. $75$%
4. $40$%

Q. Four identical cells of emf $E$ and internal resistance $r$ are to be connected in series. Suppose if one of the cell is connected wrongly, the equivalent emf and effective internal resistance of the combination is

1. $4E$ and $4r$
2. $4E$ and $2r$
3. $2E$ and $2r$
4. $2E$ and $4r$

Q. Water is heated from $0^{\circ }C$ to ${10}^{\circ }C$, then its volume

1. Decreases
2. Increases
3. Does not change
4. First decreases and then increases

Q. The ratio of the dimensions of Planck constant and that of moment of inertia has the dimensions of

1. Time
2. Frequency
3. Angular momentum
4. Velocity

Q. If the mass of a body is $M$ on the surface of the earth, the mass of the same body on the surface of the moon is :

1. $M$
2. $M/6$
3. $6M$
4. Zero