A uniformly charged solid sphere of radius R has potential $V_{0}$ (measured with respect to $\infty$ ) on its surface. For
this sphere the equipotential surfaces with potential $\frac{3V_{0}}{2}, \frac{5V_{0}}{4} , \frac{3V_{0}}{4}$ and $\frac{V_{0}}{4}$ have radius $R_{1}$ , $R_{2}, \,R_{3}$ and $R_{4}$
respectively. Then
Note : This question had two option correct at the time of examination. Proper corrections are made in the
question to avoid it.
a.
$2R>R_{4}$
b.
$R_{1} = 0$ and $R_{2} > (R_{4}- R_{3})$
c.
$R_{1} \neq 0$ and $(R_{2}- R_{1}) > \,(R_{4}- R_{3})\,$
d.
$R_{1} = 0$ and $R_{2} < (R_{4}- R_{3})$
Correct Answer
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Q2mcq
A rectangular loop of sides $10\, cm$ and $5\, cm$ , carrying a current $I$ of $12\,A$ , is placed in different orientations as
shown in the figure below.
(a) (b)
(c) (d)
If there is a uniform magnetic field of $0. 3\,T$ in the positive $z$ direction, in which orientations the loop would
be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium?
a.
(b) and (c), respectively.
b.
(a) and (b), respectively.
c.
(a) and (c), respectively.
d.
(b) and (d), respectively.
Correct Answer
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Q3mcq
Assuming that the human pupil has a radius of $0. 25\, cm$ and a comfortable viewing distance of $25\, cm$ . The
minimum separation between two point objects that the human eye can resolve for the light of wavelength
$500\, nm$ is
a.
$300\,$ $\mu$ $m$
b.
$1\,$ $\mu$ $m$
c.
$30\,$ $\mu$ $m$
Correct Answer
d.
$100\,$ $\mu$ $m$
No explanation saved for this question yet.
Q4mcq
A train is moving on a straight track with speed $20\,m\,s^{-1}$ . It is blowing its whistle at the frequency of
$1000\, Hz$ . The percentage change in the frequency heard by a person standing near the track as the train passes
him is (speed of sound $= 320\,m\,s^{-1}$ ) close to:
a.
$24%$
b.
$6%$
c.
$12%$
Correct Answer
d.
$18%$
No explanation saved for this question yet.
Q5mcq
A solid body of constant heat capacity $1\,J\,($ ℃ $)^{-1}$ is being heated by keeping it in contact with reservoirs in
two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same
amount of heat. (ii) Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies the same
amount of heat. In both, cases the body is brought from initial temperature $100\,K$ to final temperature $200\,K$ .
Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since
temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to
avoid it.
a.
$2 ln 2, \,8 ln 2$
b.
$ln 2, \,4 ln 2$
c.
$ln 2, \, ln 2$
Correct Answer
d.
$ln 2, \,2 ln 2$
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Q6mcq
$-\rightarrow \rightarrow$
Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $F_{1}$ be the magnetic force on
$-$
the inner solenoid due to the outer one and $\vec{F}_{2}$ be the magnetic force on the outer solenoid due to the inner one.
Then:
$----$
a.
$\rightarrow \rightarrow$
$F_{1}$ is radially outwards and $\vec{F}_{2} = 0\,$
$\rightarrow \rightarrow$
$F_{1}$ is radially inwards and $\vec{F}_{2}$ is radially
outwards
d.
$\vec{F}_{1}$ is radially inwards and $\vec{F}_{2} = 0\,$
No explanation saved for this question yet.
Q7mcq
In the given circuit, charge $Q_{2}$ on the $2\,$ $\mu$ $F$ capacitor changes as C is varied from $1\,$ $\mu$ $F$ to $3\,$ $\mu$ $F$ . $Q_{2}$ as a
function of 'C' is given properly by: (figures are drawn schematically and are not to scale)
No explanation saved for this question yet.
Q8mcq
A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in
the lower half. The electric field lines around the cylinder will look like figure given in:
(figures are schematic and not drawn to scale)
No explanation saved for this question yet.
Q9mcq
For a simple pendulum, a graph is plotted between its kinetic energy (K.E.) and potential energy (P.E.) against
its displacement d. which one of the following represents these correctly? (graphs are schematic and not drawn
to scale)
No explanation saved for this question yet.
Q10mcq
Two long currents carrying thin wires, both with current $I$ , are held by insulating threads of length L and are in
equilibrium as shown in the figure, with threads making an angle ' $\theta$ ' with the vertical. If wires have a mass $\lambda$
per unit length then the value of $I$ is:
( $g=$ gravitational acceleration)
An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to $Q_{0}$ and then
connected to the L and R as shown below:
If a student plots graphs of the square of maximum charge $(Q^{2}_{Max})$ on the capacitor with time (t) for two
different values $L_{1}$ and $L_{2}(L_{1} >L_{2})$ of L then which of the following represents this graph correctly? (plots
are schematic and not drawn to scale)
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Given in the figure are two blocks $A$ and $B$ of weight $20\,N$ and $100\,N$ , respectively. These are being pressed
against a wall by a force $F$ and kept in equilibrium as shown. If the coefficient of friction between the blocks is
$0. 1$ and between block $B$ and the wall is $0. 15$ , the frictional force applied by the wall on block $B$ is:
a.
$150\,N$
b.
$100\,N$
c.
$80\,N$
d.
$120\,N$
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Two stones are thrown up simultaneously from the edge of a cliff $240\,m$ high with an initial speed of $10\,m\,s^{-1}$
and $40\,m\,s^{-1}$ respectively. Which of the following graph best represents the time variation of the relative
position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground
and neglect air resistance, take $g= 10\, ms^{-2}$ )(the figure are schematic and not drawn to scale)
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Distance of the centre of mass of a solid uniform cone from its vertex is $z_{0}$ . If the radius of its base is $R$ and its
height is $h$ then $z_{0}$ is equal to:
a.
$\frac{3h^{2}}{8R}$
b.
$\frac{h^{2}}{4R}$
c.
$\frac{3h}{4}$
d.
$\frac{5h}{8}$
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Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as
an ideal gas of photons with internal energy per unit volume $u= \frac{U}{V} \propto T^{4}$ and pressure $p= \frac{1}{3}(\frac{U}{V})$ . If the
shell now undergoes an adiabatic expansion the relation between T and R is:
a.
$T \propto \frac{1}{R^{3}}$
b.
$T \propto e^{-R}$
c.
$T \propto e^{-3R}$
d.
$T \propto \frac{1}{R}$
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Match list-I (Fundamental Experiment) with List-II (its conclusion) and select the correct option from the
choices given below the list:
List-I List-II
A Franck-Hertz Experiment (i) Particle nature of light
B Photo-electric experiment (ii) Discrete energy levels of the atom
C Davison-Germer Experiment (iii) Wave nature of electron
(iv) Structure of atom
a.
$A -(iv)\,; B -(iii); C -(ii)$
b.
$A -(i)\,; B -(iv); C -(iii)$
c.
$A -(ii)\,; B -(iv); C -(iii)$
d.
$A -(ii)\,; B -(i); C -(iii)$
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Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism
is $\mu$ , a ray, incident at an angle $\theta$ , on the face AB would get transmitted through the face AC of the prism
provided:
From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $(\frac{R}{2})$ is removed as shown in the
figure. Taking gravitational potential $V = 0$ at $r= \infty ,$ the potential at the centre of the cavity thus formed is (
$G=$ gravitational constant)
a.
$\frac{-2GM}{R}$
b.
$\frac{-GM}{2R}$
c.
$\frac{-GM}{R}$
d.
$\frac{-2GM}{3R}$
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Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the
average time of collision between molecules increases as $V^{q}$ , where $V$ is the volume of the gas. The value of $q$
is:
$(\gamma = \frac{C_{P}}{C_{v}})$
a.
$\frac{$\gamma$-1}{2}$
b.
$\frac{3\gamma +5}{6}$
c.
$\frac{3$\gamma$-5}{6}$
d.
$\frac{$\gamma$+1}{2}$
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A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is
added to its bob, the time period changes to $T_{M}$ . If the Young's modulus of the material of the wire is $Y$ , then
$\frac{1}{Y}$ is equal to:
( $g=$ gravitational acceleration)
a.
$2$
$[1 - (\frac{T}{T_{M}}) ]\frac{A}{Mg}$
b.
$2$
$[(\frac{T_{M}}{T} ) -1] \frac{A}{Mg}$
c.
$2$
$[(\frac{T_{M}}{T} ) -1]\frac{Mg}{A}$
d.
$2$
$[1 - (\frac{T_{M}}{T}) ]\frac{A}{Mg}$
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From a solid sphere of mass $M$ and radius $R$ , a cube of the maximum possible volume is cut. Moment of inertia
of cube about an axis passing through its centre and perpendicular to one of its faces is:
a.
$\frac{4MR^{2}}{3\sqrt{3}\pi}$
b.
$\frac{MR^{2}}{32\sqrt{2}\pi}$
c.
$\frac{MR^{2}}{16\sqrt{2}\pi}$
d.
$\frac{4MR^{2}}{9\sqrt{3}\pi}$
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The period of oscillation of a simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}. \,$ Measured value of $l$ is $20. 0\, cm$ , known to
$1\, mm$ accuracy and time for $100\,$ oscillations of the pendulum is found to be $90\,s$ using a wristwatch of $1\,s$
resolution. The accuracy in the determination of $g$ is
a.
$5%$
b.
$4%$
c.
$3%$
d.
$1%$
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A particle of mass $m$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in
the $y$ direction with speed $v.$ If the collision is perfectly inelastic, the percentage loss in the energy during the
collision is close to:
a.
$62%$
b.
$44%$
c.
$50%$
d.
$56%$
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An inductor $(L= 0.03 H)$ and a resistor $(R= 0.15\, k\Omega )$ are connected in series to a battery of $15 V$ E.M.F. in
a circuit shown below. The key $K_{1}$ has been kept closed for a long time. Then at $t= 0$ , $K_{1}$ is opened and key
$K_{2}$ is closed simultaneously. At $t= 1 ms$ , the current in the circuit will be : $(Take, \,e^{5} ≈150)$
a.
$0. 67\, mA$
b.
$100\, mA$
c.
$67\, mA$
d.
$6. 7\, mA$
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A red $LED$ emits light at $0. 1\, watt$ uniformly around it. The amplitude of the electric field of the light at a
distance of $1\,m$ from the diode is:
a.
$7. 75\,V\,m^{-1}$
b.
$1. 73\,V\,m^{-1}$
c.
$2. 45\,V\,m^{-1}$
d.
$5. 48\,V\,m^{-1}$
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When $5\,V$ potential difference is applied across a wire of length $0. 1\,m$ , the drift speed of electrons is
$2.5 \times 10^{-4}\,m\,s^{-1}$ . If the electron density in the wire is $8 \times 10^{28}\,m^{-3}$ , the resistivity of the material is close
to:
a.
$1 .56 \times 10^{-5}\,\Omega \,m$
b.
$1 .6 \times 10^{-8}\,\Omega \,m$
c.
$1 .6 \times 10^{-7}\,\Omega \,m$
d.
$1 .6 \times 10^{-6}\,\Omega \,m$
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On a hot summer night, the refractive index of air is the smallest near the ground and increases with a height
from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that
as it travels, the light beam,
a.
bends upward.
b.
becomes narrower.
c.
goes horizontally without any deflection.
d.
bends downward.
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Match the catalysts to the correct process.
Catalyst Process
A. $TiCl_{3}$ i. Wacker process
B. $PdCl_{2}$ ii. Ziegler - Natta polymerisation
C. $CuCl_{2}$ iii. Contact process`
D. $V_{2}O_{5}$ iv. Deacon’s process
The following reaction is performed at $298\,K$ .
$2NO(g) + O_{2}(g) \rightleftharpoons 2NO_{2}(g)$
The standard free energy of the formation of $NO(g)$ is $86. 6\, kJ \, mol^{-1}$ at $298\,K$ . What is the standard free
energy of the formation of $NO_{2}(g)$ at $298\,K$ ? $(K_{P} = 1.6 \times 10^{12})$
In the following sequence of reactions:
$---Toluene^{KMnO_{4}} A^{SOCl}\rightarrow \rightarrow^{2} B^{H}_{BaS}^{_{2}/ Pd}_{\vec{O}_{4}} C$
The Product $\vec{C}$ is:
a.
$C_{6}H_{5}CHO$
b.
$C_{6}H_{5}COOH$
c.
$C_{6}H_{5}CH_{3}$
d.
$C_{6}H_{5}CH_{2}OH$
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$3\,g$ of activated charcoal was added to $50\, mL$ of acetic acid solution $(0. 06\,N)$ in a flask. After an hour, it was
filtered and the strength of the filtrate was found to be $0. 042\,N$ . The amount of acetic acid adsorbed (per gram
of charcoal) is:
a.
$54\, mg$
b.
$18\, mg$
c.
$36\, mg$
d.
$42\, mg$
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Assertion: Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form
oxides of nitrogen.
Reason:The reaction between nitrogen and oxygen requires high temperature.
a.
Both the Assertion and Reason are incorrect.
b.
Both Assertion and Reason are correct and the
Reason is the correct explanation for the
Assertion.
c.
Both Assertion and Reason are correct, but the
Reason is not the correct explanation for the
Assertion.
d.
The Assertion is incorrect but the Reason is
correct.
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In Carius method of estimation of halogens, $250\, mg$ of an organic compound gave $141\, mg \, AgBr$ . What is
the percentage of bromine in the compound (atomic mass of $Ag = 108$ and atomic number of $Br = 80$ )?
a.
$60$
b.
$24$
c.
$36$
d.
$48$
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The standard Gibbs energy change at 300 K for the reaction $2A \rightleftharpoons B + C$ is 2494.2 J. At a given time, the
composition of the reaction mixture is $[A] = \frac{1}{2} , \,[B] = 2$ and $[C] = \frac{1}{2}$ . The reaction proceeds in the:
$[R = 8.314\,J/K -mol\,, \,\,e = 2.718 ]\,$ {Given antilog (-0.44)=0.36}
a.
Reverse direction because $Q < K_{C}$
b.
Forward direction because $Q > K_{C}$
c.
Reverse direction because $Q > K_{C}$
d.
Forward direction because $Q < K_{C}$
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The molecular formula of a commercial resin used for exchanging ions in water softening is $C_{8}H_{7}SO_{3}Na$
$(molecular \,weight = 206)$ . What would be the maximum uptake of $Ca^{2+}$ ions by the resin if expressed in
$mol$ per $gm$ ?
a.
$\frac{1}{412}$
b.
$\frac{1}{103}$
c.
$\frac{1}{206}$
d.
$\frac{2}{309}$
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The vapour pressure of acetone at $20^{o}C$ is $185\, torr$ . When $1. 2\,g$ of a non-volatile substance was dissolved in
$100\,g$ of acetone at $20^{o}C$ , its vapour pressure was $183\, torr$ . The molar mass $(g\,mol^{-1})$ of the substance is:
a.
$488$
b.
$32$
c.
$64$
d.
$128$
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A complex number $z$ is said to be unimodular if $|z| = 1$ . Let $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z_{1}-2z_{2}}{2-z_{1}z_{2}}$ is
unimodular and $z_{2}$ is not unimodular, then the point $z_{1}$ lies on a
a.
circle of radius $\sqrt{2}$
b.
straight line parallel to $x$ -axis
c.
straight line parallel to $y$ -axis
d.
circle of radius $2$
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Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2} = 8y$ . If the point $P$ divides the line segment $OQ$
internally in the ratio $1 : 3$ , then the locus of $P$ is
a.
$x^{2} = 2y$
b.
$x^{2} =y$
c.
$y^{2} =x$
d.
$y^{2} = 2x$
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$1 2 2$
$[ ]$
If $A= 2 1 -2$ is a matrix satisfying the equation $AA^{T} = 9I$ , where $I$ is $3 \times 3$ identity matrix, then the
$[ ]$
$a 2 b$
ordered pair $(a, \,b)$ is equal to
a.
$(-2, \, -1)$
b.
$(2, \, -1)$
c.
$(-2, \,1)$
d.
$(2, \,1)$
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Let $\alpha$ and $\beta$ be the roots of equation $x^{2} -6x-2 = 0$ . If $a_{n} =\alpha ^{n} - \beta ^{n}, \,\forall \,n\geq 1,$ then the value of $\frac{a_{10}-2a_{8}}{2a_{9}}$ is
equal to
a.
$-3$
b.
$6$
c.
$-6$
d.
$3$
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If the angles of elevation of the top of a tower from three collinear points $A, \,B$ and $C$ on a line leading to the
foot of the tower are $30^{\circ}, \,45^{\circ}$ and $60^{\circ}$ respectively, then the ratio $AB:BC$ , is
a.
$2 : 3$
b.
$\sqrt{3}: 1$
c.
$\sqrt{3\,}: \sqrt{2}$
d.
$1 : \sqrt{3}$
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The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latus ractum to the
ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1,$ is
a.
$27$
b.
$\frac{27}{4}$
c.
$18$
d.
$\frac{27}{2}$
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The mean of a data set comprising of $16$ observations is $16$ . If one of the observation value $16$ is deleted and
three new observations valued $3 , 4$ and $5$ are added to the data, then the mean of the resultant data is
a.
$14 .0$
b.
$16 .8$
c.
$16 .0$
d.
$15 .8$
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Let $f(x)$ be a polynomial of degree four and having its extreme values at $x= 1$ and $x= 2$ . If
$_{x}lim_{\rightarrow 0\,\rightarrow } [1 + \frac{f(x)}{x^{2}}]= 3$ , then $f(2)$ is equal to
a.
$4$
b.
$-8$
c.
$-4$
d.
$0$
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The distance of the point $(1, \,0, \,2)$ from the point of intersection of the line $\frac{x-2}{3} = \frac{y+1}{4} = \frac{z-2}{12}$ and the plane
$x- y+z=16$ , is
a.
$13$
b.
$2\sqrt{14}$
c.
$8$
d.
$3\sqrt{21}$
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If $m$ is the $A.M. \,$ of two distinct real numbers $I$ and $n(I, \,n> 1)$ and $G_{1}, \,G_{2}\,and\,G_{3}$ are three geometric
means between $I\,and\,n$ , then $G^{4}_{1} + 2G^{4}_{2} +G^{4}_{3}$ equals
a.
$4l^{2}m^{2\,}n^{2}$
b.
$4\,l^{2}mn$
c.
$4\,lm^{2\,}n$
d.
$4lmn^{2}$
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The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices
$(0, \,0), \,(0, \,41)$ and $(41, \,0)$ is
a.
$780$
b.
$901$
c.
$861$
d.
$820$
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The set of all values of $\lambda$ for which the system of linear equations:
$2x_{1}-2x_{2}+x_{3} =\lambda x_{1}$
$2x_{1}-3x_{2}+ 2x_{3} =\lambda x_{2}$
$-x_{1}+ 2x_{2} =\lambda x_{3}$
has a non-trivial solution,
a.
Contains more than two elements.
b.
Is an empty set.
c.
Is a singleton.
d.
Contains two elements.
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Let $A$ and $B$ be two sets containing four and two elements respectively. Then the number of subsets of the set
$A\times B$ , each having at least three elements is
a.
$510$
b.
$219$
c.
$256$
d.
$275$
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Let $\vec{a}, \,\vec{b}\,\,and\,\,\vec{c}$ be three non - zero vectors such that no two of them are collinear and
$(\vec{a}\times \vec{b})\times \vec{c}= \frac{1}{3} \vec{b} \vec{c} \vec{a}$ . If $\theta$ is the angle between vectors $\vec{b}\,and\,\vec{c}$ , then a value of $sin\theta$ is
a.
$\frac{-2\sqrt{3}}{3}$
b.
$\frac{2\sqrt{2}}{3}$
c.
$\frac{-\sqrt{2}}{3}$
d.
$\frac{2}{3}$
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