Q. Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane contains the circular coil and excluding the circular coil area is given by ${\Phi }_{\text{i}}$. The magnetic flux through the area of the circular coil area is given by ${\Phi }_0$
Which of the following options is correct?

1. ${\Phi }_{\text{i}}<{\Phi }_0$
2. ${\Phi }_{\text{i}}={\Phi }_0$
3. ${\Phi }_{\text{i}}>{\Phi }_0$
4. ${\Phi }_{\text{i}}=-{\Phi }_0$

Q. The radius of gyration of a uniform rod of length $l$, about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod, and perpendicular to it, is :

1. $\sqrt{\frac{7}{48}}l$
2. $\sqrt{\frac{3}{8}}l$
3. $\frac{1}{8}l$
4. $\frac{1}{4}l$

Q. Speed of a transverse wave on a straight wire (mass $6.0g$, length $60$ cm) and area of cross-section ($1.0m{m}^2$) is $90m{s}^{-1}$. If the Young's modulus of wire is $16\times {10}^{11}N{m}^{-2}$, the extension of wire over its natural length is :

1. $0.01mm$
2. $0.03mm$
3. $0.02mm$
4. $0.04mm$

Q. A litre of dry air at STP expands adiabatically to a volume of $3$ litres. If $\gamma =1.40$, the work done by air is: $(3^{1.4}=4.6555)$ [Take air to be an ideal gas]

1. $48J$
2. $100.8J$
3. $60.7J$
4. $90.5J$

Q.
Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is ${30}^0$. The electric field in the region shown between them is given by :

1. $\frac{\sigma }{2{ϵ}_0}[(1-\frac{\sqrt{3}}{2})\hat{y}-\frac{\hat{x}}{2}]$
2. $\frac{\sigma }{2{ϵ}_0}[(1+\frac{\sqrt{3}}{2})\hat{y}+\frac{\hat{x}}{2}]$
3. $\frac{\sigma }{2{ϵ}_0}[(1+\sqrt{3})\hat{y}+\frac{\hat{x}}{2}]$
4. $\frac{\sigma }{2{ϵ}_0}[(1+\sqrt{3})\hat{y}-\frac{\hat{x}}{2}]$

Q. Two moles of an ideal gas with $\frac{C_P}{C_V}=\frac{5}{3}$ are mixed with $3$ moles of another ideal gas with $\frac{C_P}{C_V}=\frac{4}{3}$. The value of $\frac{C_P}{C_V}$ for the mixture is :

1. $1.47$
2. $1.45$
3. $1.42$
4. $1.50$

Q. As shown in the figure, a bob of mass $m$ is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius $r$ and mass $m$. When released from rest the bob starts falling vertically. When it has covered a distance of $h$, the angular speed of the wheel will be :

1. $r\sqrt{\frac{3}{4gh}}$
2. $\frac{1}{r}\sqrt{\frac{4gh}{3}}$
3. $r\sqrt{\frac{3}{2gh}}$
4. $\frac{1}{r}\sqrt{\frac{2gh}{3}}$

Q. A satellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height R(R= radius of the earth), it ejects a rocket of mass $\frac{m}{10}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ($G$ is the gravitational constant; $M$ is the mass of the earth) :

1. $\frac{m}{20}(u^2+\frac{113}{200}\frac{GM}{R})$
2. $5m(u^2-\frac{119}{200}\frac{GM}{R})$
3. $\frac{m}{20}{(u-\sqrt{\frac{2GM}{3R}})}^2$
4. $\frac{3m}{8}{(u+\sqrt{\frac{5GM}{6R}})}^2$

Q. A long solenoid of radius $R$ carries a time (t)-dependent current $I\left(t\right)=I_{0}t(1-t)$. A ring of radius $2R$ is placed coaxially near its middle. During the time interval $0\le t\le 1$, the induced current $\left(I_R\right)$ and the induced $EMF\left(V_R\right)$ in the ring change as:

1. At $t=0.5$ direction of $I_R$ reverses and $V_R$ is zero.
2. Direction if $I_R$ remains unchanged and $V_R$ is zero at $t=0.25$
3. At $t=0.25$ direction of $I_R$ reverses and $V_R$ is maximum.
4. Direction of $I_R$ remains unchanged and $V_R$ is maximum at $t=0.5$

Q. The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6\times {10}^{-16}$ s. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is:

1. $5.6\times {10}^{12}$
2. $1.6\times {10}^{14}$
3. $6.2\times {10}^{15}$
4. $7.8\times {10}^{14}$

Q. If the magnetic field in a plane electromagnetic wave is given by
$\overrightarrow{B}=3\times {10}^{-8}\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{j}T$, then what will be expression for electric field?

1. $\overrightarrow{E}=3\times {10}^{-8}\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{j}V/m$
2. $\overrightarrow{E}=60\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{k}V/m$
3. $\overrightarrow{E}=9\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{k}V/m$
4. $\overrightarrow{E}=3\times {10}^{-8}\sin (1.6\times {10}^{3}x+48\times {10}^{10}t)\hat{i}V/m$

Q. If we need a magnification of $375$ from a compound microscope of tube length $150mm$ and an objective of focal length $5mm$, the focal length of the eye-piece, should be close to :

1. $2$ mm
2. $12$ mm
3. $33$ mm
4. $22$ mm

Q. Three point particles of masses $1.0kg$, $1.5kg$ and $2.5kg$ are placed at three corners of a right angle triangle of sides $4.0cm,3.0cm$ and $5.0cm$ as shown in the figure. The centre of mass of the system is at a point :

1. $1.5cm$ right and $1.2cm$ above $1kg$ mass
2. $2.0cm$ right and $0.9cm$ above $1kg$ mass
3. $0.6cm$ right and $2.0cm$ above $1kg$ mass
4. $0.9cm$ right and $2.0cm$ above $1kg$ mass

Q. Visible light of wavelength $6000\times {10}^{-8}cm$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at ${60}^0$ from the central maximum. if the first minimum is produced at ${\theta }_1$ then ${\theta }_1$ is close to :

1. ${25}^0$
2. ${30}^0$
3. ${20}^0$
4. ${45}^0$

Q. Which of the following gives a reversible operation ?

Q. A $60HP$ electric motor lifts an elevator having a maximum total load capacity of $2000kg$. If the frictional force on the elevator is $4000N$, the speed of the elevator at full load is close to : ($1$ HP=$746W$, $g=10m{s}^{-2}$)

1. $1.5m{s}^{-1}$
2. $1.9m{s}^{-1}$
3. $1.7m{s}^{-1}$
4. $2.0m{s}^{-1}$

Q. A parallel plate capacitor has plates of area 'A' separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as $k\left(x\right)=K(1+\alpha x)$ where 'x' is the distance measured from one of the plates. If $\left(\alpha d\right)<<1$, the total capacitance of the system is best by the expression:

1. $\frac{A{ϵ}_{0}K}{d}(1+{\left(\frac{\alpha d}{2}\right)}^2)$
2. $\frac{A{ϵ}_{0}K}{d}(1+\frac{{\alpha }^2{d}^2}{2})$
3. $\frac{A{ϵ}_{0}K}{d}(1+\frac{\alpha d}{2})$
4. $\frac{A{ϵ}_0}{d}(1+\alpha d)$

Q. A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be :

1. $L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b$
2. $L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}$
3. $L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m$
4. $L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b$

Q. The current $I_1$ (in A) flowing through $1\Omega$ resistor in the above circuit is :

1. $0.25$
2. $0.2$
3. $0.5$
4. $0.4$

Q. A polarizer -analyser set is adjusted such that the intensity of light coming out of the analyser is just $10\%$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is:

1. ${90}^0$
2. ${71.6}^0$
3. ${18.4}^0$
4. ${45}^0$

Q. A loop ABCDEFA of straight edges has six corner points $A(0,0,0),B(5,0,0),C(5,5,0),D(0,5,0),E(0,5,5)$ abd $F(0,0,5)$. The magnetic field in this region is $\overrightarrow{B}=(3\hat{i}+4\hat{k})T$. The quantity of flux through the loop ABCDEFA (in Wb) is ______.

Q. In the following reactions, products (A) and (B), respectively, are:
$\underset{(hotandconc.)}{NaOH+}C{l}_2\to \left(A\right)+\text{side products}$

1. $NaOCl$ and $Ca(Cl{O}_3{)}_2$
2. $NaCl{O}_3$ and $Ca(Cl{O}_3{)}_2$
3. $NaCl{O}_3$ and $Ca(OCl{)}_2$
4. $NaOCl$ and $Ca(OCl{)}_2$

Q. A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times {10}^{-5}{/}^{o}C$ along the x-axis and $5\times {10}^{-6}{/}^{o}C$ along the $y$ and the z-axis. If the coefficient of volume expansion of the solid is $C\times {10}^{-6}{/}^{o}C$ then the value of $C$ is ______.

Q. A carnot engine operates between two reservoirs of temperature $900K$ and $300K$. The engine performs $1200J$ of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is_________ .

Q. Consider the following reactions:
Which of these reactions are possible ?

1. (b) and (d)
2. (b), (c) and (d)
3. (a) and (d)
4. (a) and (b)

Q. Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non volatile solute are together sealed in a container. Over time:

1. The volume of the solution does not change and the volume of the solvent decreases
2. the volume of the solution deceases and the volume of the solvent increases
3. the volume of the solution and the solvent does not change
4. the volume of the solution increases and the volume of the solvent decreases

Q. A beam of electromagnetic radiation of intensity $6.4\times {10}^{-5}W/c{m}^2$ is comprised of wavelength, $\lambda =310nm$. It falls normally on a metal (work function $\phi =2eV$) of surface area of $1c{m}^2$. If one in ${10}^3$ photons ejects an electron, total number of electrons ejected in $1$ s is ${10}^x$.
$(hc=1240eVnm,1eV=1.6\times {10}^{-19}J),$ then $x$ is ______.

Q. Which of the following statements is correct ?

1. Gluconic acid is a partial oxidation product of glucose
2. Gluconic acid is a dicarboxylic acid
3. Gluconic acid is obtained by oxidation of glucose with $HN{O}_3$
4. Gluconic acid can form cyclic (acetal/ hemiacetal) structure

Q. A particle $(m=1kg)$ slides down a frictionless rack (AOC) starting from rest at a point $A$ (height $2m$). After reaching $C$, the particle continuous to move freely in air as a projectile. When it reaching its highest point $P$ (height $1m$), the kinetic energy of the particle (in J) is : (Figure drawn is schematic and not to scale; take $g=10m{s}^{-2})$______.

Q. Among the statements (a)-(d), the incorrect ones are:
(a) Octahedral $Co\left(III\right)$ complexes with strong field ligands have very high magnetic moments
(b) When ${\Delta }_0<P,$ the d-electron configuration of $Co\left(III\right)$ in an octahedral complex is $t_{eg}^4{e}_g^2$
(c) Wavelength of light absorbed by $\left[Co\right(en{)}_3{]}^{3+}$ is lower than that of $[Co{F}_6{]}^{3-}$
(d) If the ${\Delta }_0$ for an octahedral complex of $Co\left(III\right)$ is $18,000c{m}^{-1}$, the ${\Delta }_t$ for its tetrahedral complex with the same ligand will be $16,000c{m}^{-1}$

1. (b) and (c) only
2. (a) and (d) only
3. (a) and (b) only
4. (c) and (d) only