Q. For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram?

Q. A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

1. Towards the wire
2. Away from the wire
3. Parallel to the wire along the current
4. Parallel to the wire opposite to the current

Q. The electric field component of a monochromatic radiation is given by
$\overrightarrow{E}=2E_0\hat{i}coskzcos\omega t$
Its magnetic field $\overrightarrow{B}$ is then given by :

1. $\frac{2E_0}{c}\hat{j}\sin kz\cos \omega t$
2. $-\frac{2E_0}{c}\hat{j}\sin kz\sin \omega t$
3. $\frac{2E_0}{c}\hat{j}\cos kz\cos \omega t$
4. $\frac{2E_0}{c}\hat{j}\sin kz\sin \omega t$

Q. The current gain of a common emitter amplifier is $69$. If the emitter current is $7.0mA$, collector current is:

1. $9.6mA$
2. $0.69mA$
3. $6.9mA$
4. $69mA$

Q. In an experiment to determine the period of a simple pendulum of length $1m,$ it is attached to different spherical bobs of radii $r_1$ and $r_2$. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be $5\times {10}^{-4}s$, the difference in radii, $|r_1-r_2|$ is best given by :

1. $1cm$
2. $0.01cm$
3. $0.1cm$
4. $0.5cm$

Q. ${}^{\prime }{N}^{\prime }$ moles of a diatomic gas in a cylinder are at a temperature ${}^{\prime }{T}^{\prime }$. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas gets converted into monatomic gas. What is the change in the total kinetic energy of the gas ?

1. $\frac{5}{2}nRT$
2. $\frac{1}{2}nRT$
3. $0$
4. $\frac{3}{2}nRT$

Q. A uniform wire of length $l$ and radius $r$ has a resistance of $100\Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of new 2 wire will be :

1. $100\Omega$
2. $1600\Omega$
3. $200\Omega$
4. $400\Omega$

Q. In an experiment a convex lens of focal length $15cm$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5cm$ from it. It is found that an object and its image coincide, if the object is placed at a distance of $20cm$ from the lens. The focal length of the convex mirror is:

1. $27.5cm$
2. $25.0cm$
3. $30.5cm$
4. $20.0cm$

Q. The mass density of a spherical body is given by $\rho \left(r\right)=\frac{k}{r}$ for $r\le R$ and $\rho \left(r\right)=0$ for $r>R$, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by
$y(x,t)=0.5sin\left(\frac{5\pi }{4}x\right)cos\left(200\pi t\right)$.
What is the speed of the travelling wave moving in the positive x direction ?
($x$ and t are in meter and second, respectively.)

1. $90m/s$
2. $180m/s$
3. $120m/s$
4. $160m/s$

Q. Four closed surface and corresponding charges distributions are shown below:
Let the respective electric fluxes through the surfaces be ${\Phi }_1$, ${\Phi }_2$, ${\Phi }_3$ and ${\Phi }_4$. Then :

1. ${\Phi }_1>{\Phi }_3;{\Phi }_2<{\Phi }_4$
2. ${\Phi }_1<{\Phi }_2={\Phi }_3>{\Phi }_4$
3. ${\Phi }_1>{\Phi }_2>{\Phi }_3>{\Phi }_4$
4. ${\Phi }_1={\Phi }_2={\Phi }_3={\Phi }_4$

Q. A circular hole of radius $\frac{R}{4}$ is made in a thin uniform disc having mass $M$ and radius $R$, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point $O$ and perpendicular to the plane of the disc is :

1. $\frac{197M{R}^2}{256}$
2. $\frac{219M{R}^2}{256}$
3. $\frac{237M{R}^2}{512}$
4. $\frac{19M{R}^2}{512}$

Q. Two tubes of radii $r_1$ and $r_2$, and lengths $l_1$ and $l_2$, respectively, are connected in series and a liquid flows through each of them in stream line conditions. $P_1$ and $P_2$ are pressure differences across the two tubes. If $P_2$ is $4P_1$ and $l_2$ is $\frac{l_1}{4}$, then the radius $r_2$ will be equal to :

1. $2r_1$
2. $4r_1$
3. $r_1$
4. $\frac{r_1}{2}$

Q. A Laser light of wavelength $660nm$ is used to weld Retina detachment. If a Laser pulse of width $60ms$ and power $0.5kW$ is used, the approximate number of photons in the pulse are:
[Take Planck's constant $h=6.62\times {10}^{-34}Js$]

1. ${10}^{22}$
2. ${10}^{19}$
3. ${10}^{20}$
4. ${10}^{18}$

Q. In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P=4\Omega$ and the neutral point $N$ is at $60cm$ from $A$. Now an unknown resistance $R$ is connected in series to $P$ and the new position of the neutral point is at $80cm$ from $A$. The value of unknown resistance $R$ is :

1. $7\Omega$
2. $\frac{20}{3}\Omega$
3. $6\Omega$
4. $\frac{33}{5}\Omega$

Q. A sinusoidal voltage of peak value $283V$ and angular frequency $320/s$ is applied to a series LCR circuit. Given that $R=5\Omega ,L=25mH$ and $C=1000\mu F$. The total impedance, and phase difference between the voltage across the source and the current will respectively be:

1. $7\Omega$ and ${45}^o$
2. $10\Omega$ and ${\tan }^{-1}\left(\frac{8}{3}\right)$
3. $10\Omega$ and ${\tan }^{-1}\left(\frac{5}{3}\right)$
4. $7\Omega$ and ${\tan }^{-1}\left(\frac{5}{3}\right)$

Q. The machine as shown has $2$ rods of length $1m$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a $2kg$ weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

1. Increasing speed speed which is $\frac{3}{4}th$ of the
2. Roller when weight is $0.4m$ above the ground
3. Constant speed
4. Decreasing speed

Q. Imagine that a reactor converts all given mass into energy and that it operates at a power level of ${10}^{9}W$. The mass of the fuel consumed per hour in the reactor will be (velocity of light, c is $3\times {10}^{8}m/s$)

1. $0.8gm$
2. $0.96gm$
3. $4\times {10}^{-2}gm$
4. $6.6\times {10}^{-5}gm$

Q. A car is standing $200m$ behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2m/s^2$ and the car has acceleration $4m/s^2$. The car will catch up with the bus after a time of :

1. $10\sqrt{2}s$
2. $\sqrt{110}s$
3. $\sqrt{120}s$
4. $15s$

Q. A signal is to be transmitted through a wave of wavelength $\lambda$, using a linear antenna. The length $l$ of the antenna and effective power radiated $P_{eff}$ will be given respectively as :
(K is a constant of proportionality)

1. $\frac{\lambda }{16},P_{eff}=K{\left(\frac{1}{\lambda }\right)}^3$
2. $\frac{\lambda }{5},P_{eff}=K{\left(\frac{1}{\lambda }\right)}^{\frac{1}{2}}$
3. $\frac{\lambda }{8},P_{eff}=K\left(\frac{1}{\lambda }\right)$
4. $\lambda ,P_{eff}=K{\left(\frac{1}{\lambda }\right)}^2$

Q. Two particles A and B of equal mass M are moving with the same speed $\upsilon$ as shown in the figure. They collide completely inelastically and move as a single particle C. The angle $\theta$ that the path of C makes with the X-axis is given by :

1. $tan\theta =\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}$
2. $tan\theta =\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}$
3. $tan\theta =\frac{1-\sqrt{3}}{1+\sqrt{2}}$
4. $tan\theta =\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}$

Q. A combination of parallel plate capacitors is maintained at a certain potential difference. When a $3mm$ thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by $2.4mm$. Find the dielectric constant of the slab.

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

Q. The acceleration of an electron in the first orbit of the hydrogen atom $(n=1)$ is :

1. $\frac{h^2}{{\pi }^2{m}^2{r}^3}$
2. $\frac{h^2}{8{\pi }^2{m}^2{r}^3}$
3. $\frac{2{\pi }^{2}km{e}^{2}Z}{\eta h}$
4. $\frac{h^2}{4\pi m^2{r}^3}$

Q. A block of mass $0.1kg$ is connected to an elastic spring of spring constant $640N{m}^{-1}$ and oscillates in a damping medium of damping constant ${10}^{-2}kg{s}^{-1}$. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to:

1. $7s$
2. $5s$
3. $3.5s$
4. $2s$

Q. A uniform magnetic field $B$ of $0.3T$ is along the positive Z-direction. A rectangular loop (abed) of sides $10cm\times 5cm$ carries a current $I$ of $12A$. Out of the following different orientations which one corresponds to stable equilibrium ?

1. 
   
2. 
   
3. 
   
4. 
   

Q. The figure shows three circuits I, II and III which are connected to a $3V$ battery. If the powers dissipated by the configurations $I,II$ and $III$ are $P_1,P_2$ and $P_3$ respectively, then :

1. $P_2>P_1>P_3$
2. $P_1>P_3>P_2$
3. $P_1>P_2>P_3$
4. $P_3>P_2>P_1$

Q. A single slit of width $0.1mm$ is illuminated by a parallel beam of light of wavelength $6000\mathring{A}$ and diffraction bands are observed on a screen $0.5m$ from the slit. The distance of the third dark band from the central bright band is :

1. $3mm$
2. $4.5mm$
3. $1.5mm$
4. $9mm$

Q. A conical pendulum of length $1m$ makes an angle $\theta ={45}^o$ w.r.t. Z-axis and moves in a circle in the $XY$ plane. The radius of the circle is $0.4m$ and its center is vertically below $O$. The speed of the pendulum, in its circular path, will be : (Take $g=10m{s}^{-2}$)

1. $0.4m/s$
2. $4m/s$
3. $2m/s$
4. $0.2m/s$

Q. A steel rail of length 5 m and area of cross section $40c{m}^2$ is prevented from expanding along its length while the temperature rises by ${10}^{o}C$. If coefficient of linear expansion and Young's modulus of steel are $1.2\times {10}^{-5}{K}^{-1}$ and $2\times {10}^{11}N{m}^{-2}$ respectively, the force developed in the rail is approximately :

1. $2\times {10}^{7}N$
2. $3\times {10}^{-5}N$
3. $1\times {10}^{5}N$
4. $2\times {10}^{9}N$

Q. A physical quantity $P$ is described by the relation $p=a^{1/2}{b}^2{c}^3{d}^{-4}$
If the relative errors in the measurement of $a,b,c$ and $d$ respectively, are $2,1,3$ and $5$, then the relative error in $P$ will be :

1. $8\%$
2. $25\%$
3. $12\%$
4. $32\%$