Q. Two resistors $400\Omega$ and $800\Omega$ are connected in series with a 6 V battery. the potential difference measured by voltmeter across $400\Omega$ resistor is:

1. $2V$
2. $1.95V$
3. $3.8V$
4. $4V$

Q. A ship of mass $3\times {10}^7$ kg, initially at rest, is pulled by a force of $5\times {10}^{4}N$ through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

1. $1.5m/s$
2. $60m/s$
3. $0.1m/s$
4. $5m/s$

Q. Find the dimensions of electricity permittivity.

1. $\left[A^2{M}^{-1}{L}^{-3}{T}^4\right]$
2. $\left[A{M}^{-1}{L}^{-3}{T}^4\right]$
3. $\left[A^2{M}^{-1}{L}^{-3}{T}^0\right]$
4. $\left[A^2{M}^0{L}^{-3}{T}^4\right]$

Q. A square of side $3cm$ all is located at a distance $25cm$ from a concave mirror of focal length $10cm$. The centre of square is at the axis of the mirror and the plane is normal to rods of mirror. The area enclosed by the image of the square is

1. $16c{m}^2$
2. $4c{m}^2$
3. $36c{m}^2$
4. $6c{m}^2$

Q. Two simple pendulums first $\left(A\right)$ of bob mass $M$ and length $L_1$, second $\left(B\right)$ of bob mass $M_1$ and length $L_2$. $M_1=M_2$ and $L_1=2L_2$. If the vibrational energy of both is same. Then which of the following is correct ?

1. Amplitude of $B$ is greater than that of $A$
2. Amplitude of $B$ is smaller than that of $A$
3. Amplitude will be same
4. None of the above

Q. Light of two different frequencies whose photons have energies 1eV and 2.5eV successively illuminate a metal of work function 0.5 eV.The ratio of the maximum speeds of the emitted electrons will he

1. 1 : 4
2. 1 : 5
3. 1 : 2
4. 1 : 1

Q. Find the lifting force of $4kg$ crock life belt in sea water, if the densities of crock and sea water are $0.2\times {10}^{3}kg/m^3$ and $1.03\times {10}^{3}kg/m^3$ respectively.

1. $163N$
2. $273N$
3. $119N$
4. $298N$

Q. A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to :

1. $+\frac{Q}{2}$
2. $+\frac{Q}{4}$
3. $-\frac{Q}{4}$
4. $-\frac{Q}{2}$

Q. An object is placed on the surface of a smooth inclined plane of inclination $\theta$. It takes timer to reach the bottom. If the same object h allowed to slide down a rough inclined plane of inclination $\theta$, it takes time nt to reach the bottom, where n is a number greater than 1. The coefficient of friction $\mu$ is given by

1. $\mu =tan\theta (1-\frac{1}{n^2})$
2. $\mu =cos\theta \sqrt{1-\frac{1}{n^2}}$
3. $\mu =cos\theta (1-\frac{1}{n^2})$
4. $\mu =tan\theta \sqrt{1-\frac{1}{n^2}}$

Q. The numerical value of charge on either plate of capacitor C shown in figure:

1. $CE$
2. $\frac{CER}{R_1+r}$
3. $\frac{CE{R}_1}{R_1+r}$
4. $\frac{CER}{R_2+r}$

Q. A force $\overrightarrow{F}=\alpha \hat{i}+3\hat{j}+6\hat{k}$ is acting at a point $\overrightarrow{r}=2\hat{i}-6j-12\hat{k}$. The value of $\alpha$ for which angular momentum about origin is conserved is

1. $-1$
2. $2$
3. $0$
4. $1$

Q. A wooden block is floating in a liquid 50% of volume inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration a=g/3 is

1. $30$%
2. $60$%
3. $67$%
4. $50$%

Q. The figure shows an equiconvex lens of focal length f. If the lens is cut along PQ, the focal length of each half will be :

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

Q. An electron Jumps from the first excited state to the ground state of the hydrogen atom.What will be the percentage change in the speed of electron?

1. 25%
2. 50%
3. 100%
4. 200%

Q. The mutual inductance of a pair of coils, each of N turn, be M henry. If a current of i ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt will be

1. $\frac{Mi}{t}$
2. $\frac{MN}{it}$
3. $\frac{NMi}{t}$
4. $\frac{Mi}{Nt}$

Q. The temperature at which the velocity of oxygen will be half that of hydrogen at NTP is

1. ${899}^{o}C$
2. ${1492}^{o}C$
3. $273K$
4. ${819}^{o}C$

Q. A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to (1/4) as compared to intensity due to direct beam alone. The resultant intensity will be:

1. (1/4) fold
2. (5/4) fold
3. (3/4) fold
4. (9/4) fold

Q. The work done in turning a magnet of magnetic moment M by an angle of ${90}^o$ from the meridian is n times the corresponding work done to turn it through an angle of ${60}^o$

1. $n=\frac{1}{2}$
2. $n=2$
3. $n=\frac{1}{4}$
4. $n=1$

Q. An astronomical telescope in normal adjustment receives light from a distant source S the tube length is now decreased slightly, then

1. A large, real image of S will be formed behind the eyepiece, far away from It
2. A small, teal image of S will be formed behind the eyepiece dose to It
3. No image will be formed
4. A virtual image of S will be formed at a finite distance

Q. A 500kg horse pulls a caw of mass 1500kg along a level road with an acceleration of $1m/s^2$. If the coefficient of sliding friction is 0.2 then the horizontal force exerted by the earth on the horse is

1. 300 kg-wt
2. 400 kg-wt
3. 500 kg-wt
4. 600 kg-wt

Q. Nitrogen $\left(N_2\right)$ is in equilibrium state at $T=421K$. The value of most probable speed, $v_{mp}$ is

1. 421 m/s
2. 400 m/s
3. 600 m/s
4. 500 m/s

Q. A body falls from rest. In the last second of its fall n coven half of the total distance. If g is $9.8m/s^2$, then the total time of its fall is (in second)

1. $2+\sqrt{2}$
2. $2$
3. $2\pm \sqrt{2}$
4. $2-\sqrt{2}$

Q. A spring is held compressed so that its stored energy is 2.4 J. Its ends are in contact with masses 1 g and 48 g placed on frictionless table. When the spring is released, the heavier mass will acquired a speed of

1. $\frac{2.4}{49}m{s}^{-1}$
2. $\frac{2.4\times 48}{49}m{s}^{-1}$
3. $\frac{10}{7}cm{s}^{-1}$
4. $\frac{10}{7}m{s}^{-1}$

Q. An inductor of 1 H is connected across a 220 V, 50 Hz supply. The peak value of the current is approximately

1. 0.5 A
2. 1 A
3. 0.7 A
4. 14 A

Q. Two sound waves, each of amplitude A and frequency $\omega$, superpose at a point with phase difference of $\frac{\pi }{2}$. The amplitude and frequency of the resultant wave are respectively

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

Q. A proton enters a magnetic field of flux density $1.5Wb/m^2$ with a speed of $2\times {10}^7$ m/s at angle of ${30}^o$ with the field. The force on a proton will be

1. $0.44\times {10}^{-12}N$
2. $2.4\times {10}^{-12}N$
3. $24\times {10}^{-12}N$
4. $0.024\times {10}^{-12}N$

Q. An inductive coil has a resistance of 100 When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by ${45}^o$. The inductance of the coil is

1. $\frac{1}{10\pi }$
2. $\frac{1}{20\pi }$
3. $\frac{1}{60\pi }$
4. $\frac{1}{40\pi }$

Q. A body of mass $m$ is situated on the earth in the gravitational field of sun. For the body to escape from the gravitation pull of the solar system the body must be imparted an escape velocity of (assume earth to be stationary)

1. 11.2 km/s
2. 22.4 km/s
3. 42 km/s
4. 33.6 km/s

Q. If the external forces acting on a system have zero resultant, the cenrre of mass

1. May move but not accelerate
2. May accelerate
3. Must not move
4. None of the above

Q. Two long straight wires are set parallel to each other at separation $r$ and each carries a current $i$ in the same direction. The strength of the magnetic field at any point midway between the two wires is

1. $\frac{2{\mu }_{0}i}{\pi r}$
2. Zero
3. $\frac{{\mu }_{0}i}{2\pi r}$
4. $\frac{{\mu }_{0}i}{\pi r}$