Q. An electromagnetic wave in vacuum has the electric and magnetic field $\overrightarrow{E}$ and $\overrightarrow{B}$, which are always perpendicular to each other. If the direction of polarization is given by $\overrightarrow{X}$ and that of wave propagation by $\overrightarrow{k}$. then:

1. $\overrightarrow{X}\parallel \overrightarrow{B}$ and $\overrightarrow{k}\parallel \overrightarrow{B}\times \overrightarrow{E}$
2. $\overrightarrow{X}\parallel \overrightarrow{E}$ and $\overrightarrow{k}||\overrightarrow{B}\times \overrightarrow{E}$
3. $\overrightarrow{X}\parallel \overrightarrow{B}$ and $\overrightarrow{k}\parallel \overrightarrow{E}\times \overrightarrow{B}$
4. $\overrightarrow{X}\parallel \overrightarrow{E}$ and $\overrightarrow{k}||\overrightarrow{E}\times \overrightarrow{B}$

Q. A boy can throw a stone up to a maximum height of $10m$. The maximum horizontal distance that the boy can throw the same stone up to will be:

1. $20\sqrt{2}m$
2. $10m$
3. $10\sqrt{2}m$
4. $20m$

Q. The resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and voltage are each $3$% respectively, the maximum percentage error in measurement of resistance is:
( $R=\frac{V}{I}$ )

1. $3$%
2. $1$%
3. $6$%
4. $zero$

Q. Proton, denteron and alpha particles of the same kinetic energy and moving in circular trajectories in a constant magnetic field. The radii of proton, denteron and alpha particles are respectively $r_p,r_d$ and $r_{\alpha }.$ Which one of the following relations is correct ?

1. $r_{\alpha }=r_p=r_d$
2. $r_{\alpha }=r_p<r_d$
3. $r_{\alpha }>r_d>r_p$
4. $r_{\alpha }=r_d>r_p$

Q. A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree, Vernier scale reading : 9 divisions. Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data:

1. $58.59degree$
2. $58.77degree$
3. $58.65degree$
4. $59degree$

Q. Carnot engine, whose efficiency is $40$% takes in heat from a source maintained at a temperature of $500K$. It is desired to have an engine of efficiency $60$ %. Then the intake temperature for the same exhaust (sink) temperature must be :

1. Efficiency of carnot engine cannot be made larger than $50$%
2. $1200K$
3. $600K$
4. $750K$

Q. A radar has a power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mountain top, of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth is:
(Radius of earth $=6.4\times {10}^{6}m$)

1. 80 km
2. 40 km
3. 64 km
4. 16 km

Q. An object $2.4m$ in front of a lens forms a sharp image on a film $12cm$ behind the lens. A glass plate $1cm$ thick of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?

1. $7.2m$
2. $2.4m$
3. $3.2m$
4. $5.6m$

Q. A thin liquid film formed between a $U$-shaped wire and light slider supports a weight of $1.5\times {10}^{-2}N$ (see figure). If the length of the slider $30cm$ and its weight negligible, then the surface tension of the liquid film is:

1. $0.05N{m}^{-1}$
2. $0.025N{m}^{-1}$
3. $0.0125N{m}^{-1}$
4. $0.1N{m}^{-1}$

Q. Helium gas goes through a cycle $ABC$ (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

1. $15.4\%$
2. $9.1\%$
3. $10.5\%$
4. $12.5\%$

Q. A liquid in a beaker has temperature $\theta$ at time $t$ and ${\theta }_0$ is temperature of surroundings, then according to Newton's law of cooling, correct graph between ${\log }_e(\theta -{\theta }_0)$ and $t$ is :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F\left(t\right)=F_0{e}^{-bt}$ in the $x$ direction. Its speed $v\left(t\right)$ is depicted by which of the following curves ?

1. 
   
2. 
   
3. 
   
4. 
   

Q. Truth table for system of four NAND gates as shown in figure is :

1. 
   
2. 
   
3. 
   
4. 
   

Q. Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4$. Then the number of spectral lines in the emission spectra will be.

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

Q. A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating and it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

1. induction of electrical charge on the plate
2. development of air current when the plate is placed
3. electromagnetic induction in the aluminium plate giving rise to electromagnetic damping
4. shielding of magnetic lines of force as aluminium is a paramagnetic material

Q. The figure shows an experimental plot for discharging of a capacitor in an RC circuit. The time constant $\tau$ of this circuit lies between :

1. 150 sec and 200 sec
2. 50 sec and 100 sec
3. 0 and 50 sec
4. 100 sec and 150 sec

Q. Two electric bulbs marked 25W-220V and 100W-220V are connected in series to a 440V supply. Which of the bulbs will fuse ?

1. Both
2. 100W
3. 25W
4. neither

Q. The wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of metal strip of cross sectional area $S$ and length L. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel it is heated so that its temperature rises by $\Delta T$ and just steps over the wheel. As it cools down to the surrounding temperature it presses the semicircular part together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is

1. $2\pi SY\alpha \Delta T$
2. $\pi SY\alpha \Delta T$
3. $SY\alpha \Delta T$
4. $2SY\alpha \Delta T$

Q. Assume that a neutron breaks into a proton and an electron. The energy released during this process is
(Mass of neutron $=1.6725\times {10}^{-27}kg$, Mass of proton $=1.6725\times {10}^{-27}kg$ , Mass of electron $=9\times {10}^{-31}kg$)

1. $0.50625$$MeV$
2. $7.10$ $MeV$
3. $6.30$ $MeV$
4. $5.40$ $MeV$

Q. A cylindrical tube, open at both ends, has a fundamental frequency, v, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column now is

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

Q. This question has statement 1 and statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius R has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.
Statement-1 : When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by $\frac{q\rho }{3{ϵ}_0}$
Statement-2 : The electric field at a distance r(r<R) from the centre of the sphere is $\frac{\rho r}{3{ϵ}_0}$

1. Statement-1 is true, Statement 2 is true, statement-2 is not the correct explanation of Statement-1
2. Statement-1 is true statement-2 is false
3. Statement-1 is true, Statement-2 is true, Statement-2 is the correct explanation of Statement-1
4. Statement-1 is false, Statement-2 is true

Q. A charge Q is uniformly distributed over the surface of non-conducting disc of the radius R.The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity . As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc if we keep both the amount of charge placed on the disk and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure :

1. 
   
2. 
   
3. 
   
4. 
   

Q. In a uniformly charged sphere of total charge Q and radius R the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be:

1. 
   
2. 
   
3. 
   
4. 
   

Q. This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
If two springs $S_1$ and $S_2$ of the force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement-l : When stretched by the same amount, work done on $S_1$, will be more than that of $S_2$
Statement-2: $k_1<k_2$.

1. Statement-1 is false, statement-2 is true
2. Statement-1 is true, statement-2 is true, statement 2 is the correct explanation of statement- 1
3. Statement-1 is true, statement-2 is false
4. Statement-1 is true, statement-2 is true, statement-2 is not the correct explanation of Statement-1

Q. Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal acceleration is :

1. $m_1$ : $m_2$
2. $m_1{r}_1$ : $m_2{r}_2$
3. $r_1$ : $r_2$
4. 1 : 1

Q. If a simple pendulum has significant amplitude (up to a factor of $1/e$ of original) only in the period between $t=0s$ to $t=\tau s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with $b$' as the constant proportionality, the average life time of the pendulum in seconds (assuming damping is small) in second :-

1. $\frac{0.693}{b}$
2. $\frac{1}{b}$
3. $\frac{2}{b}$
4. $b$

Q. The mass of a spaceship is $1000kg$. It is to be launched from the earths surface out into free space. The value of $g$ and $R$ (radius of earth) are $10m/s$ and $6400km$ respectively. The required energy for this work will be :

1. $6.4\times {10}^{8}J$
2. $6.4\times {10}^{11}J$
3. $6.4\times {10}^{9}J$
4. $6.4\times {10}^{10}J$

Q. A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum, its energy will be given by ($n$ is an integer)

1. $\frac{(m_1+m_2{)}^2{n}^2{h}^2}{2m_1^2{m}_2^2{r}^2}$
2. $\frac{n^2{h}^2}{2(m_1+m_2)r^2}$
3. $\frac{2n^2{h}^2}{(m_1+m_2)r^2}$
4. $\frac{(m_1+m_2)n^2{h}^2}{2m_1{m}_2{r}^2}$

Q. This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : Davisson- Germer experiment established the wave nature of electrons.
Statement-2 : If electrons have wave nature, they can interfere and show diffraction.

1. Statement-1 is false, Statement 2 is true
2. Statement-1 is true, statement-2 is true, Statement-2 is not the correct explanation of Statement-1
3. Statement-1 is true, Statement-2 is false
4. Statement-1 is true, statement-2 is true, Statement-2 is correct explanation for Statement-1

Q. In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit double of that from other slit. If $I_m$ be the maximum intensity, the resultant intensity I. When they interfere at phase difference $\varphi$ is given by

1. $\frac{I_m}{9}(4+5\cos \varphi )$
2. $\frac{I_m}{3}(1+2{\cos }^2\frac{\varphi }{2})$
3. $\frac{I_m}{5}(1+4{\cos }^2\frac{\varphi }{2})$
4. $\frac{I_m}{9}(1+8{\cos }^2\frac{\varphi }{2})$