Two particles $A, \,B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $\omega .$ At
$t= 0,$ their positions and direction of motion are shown in the figure:
$--$
The relative velocity $V_{\vec{A}}- V_{\vec{B}}$ at $t= \frac{\pi}{2\omega}$ is given by:
a.
$\omega (R_{1}+R_{2})\hat{i}$
b.
$-\omega (R_{1}+R_{2})\hat{i}$
c.
$\omega (R_{2}- R_{1})\hat{i}$
d.
$\omega (R_{1}- R_{2})\hat{i}$
Correct Answer
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Q2mcq
In a radioactive decay chain, the initial nucleus is $^{232}_{90} Th$ . At the end, there are $6\alpha$ -particles and $4\beta$ -particles
which are emitted. If the end nucleus is $^{A}_{Z} X, \,A$ and $Z$ are given by:
a.
$A= 208;Z = 82$
Correct Answer
b.
$A= 208;Z = 80$
c.
$A= 200;Z = 81$
d.
$A= 202;Z = 80$
No explanation saved for this question yet.
Q3mcq
Let $L, \,R, \,C$ and $V$ represent inductance, resistance, capacitance and voltage, respectively. The dimension of
$\frac{L}{RCV}$ in $SI$ units will be:
a.
$[LTA]$
b.
$[A^{-1}]$
Correct Answer
c.
$[LT^{2}]$
d.
$[LA^{-2}]$
No explanation saved for this question yet.
Q4mcq
A simple harmonic motion is represented by:
$y= 5(sin 3\pi t+ \sqrt{3}cos 3\pi t)\, cm$
The amplitude and time period of the motion are:
a.
$5 cm, \frac{2}{3}\,s$
b.
$10 cm, \frac{2}{3}\,s$
Correct Answer
c.
$5 cm, \frac{3}{2}\,s$
d.
$10 cm, \frac{3}{2}\,s$
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Q5mcq
In the above circuit, $C = \frac{\sqrt{3}}{2}\mu F, R_{2} = 20\,\Omega , L= \frac{\sqrt{3}}{10}H$ and $R_{1} = 10\,\Omega .$ Current in $L-R_{1}$ path is $I_{1}$ and in
$C-R_{2}$ path it is $I_{2}.$ The voltage of AC source is given by, $V = 200\sqrt{2} sin (100t)$ volts. The phase difference
between $I_{1}$ and $I_{2}$ is:
a.
$60^{o}$
b.
$0^{o}$
c.
$30^{o}$
d.
$150^{o}$
Correct Answer
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Q6mcq
The mean intensity of radiation on the surface of the Sun is about $10^{8}W/m^{2}.$ The rms value of the
corresponding magnetic field is closest to:
a.
$1T$
b.
$10^{-2}T$
c.
$10^{2}T$
d.
$10^{-4}T$
Correct Answer
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Q7mcq
An alpha- particle of mass $m$ suffers $1-$ dimensional elastic collision with a nucleus at rest of unknown mass. It
is scattered directly backwards losing $64%$ of its initial kinetic energy. The mass of the nucleus is
a.
$1.5m$
b.
$4m$
Correct Answer
c.
$3.5m$
d.
$5m$
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Q8mcq
A $10\,m$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0\,m\,s^{-1},$ at
right angles to the horizontal component of the earth's magnetic field of $0.3 \times 10^{-4}\, Wb \,m^{-2}.$ The value of
the induced emf in the wire is:
a.
$0.3 \times 10^{-3}\,V$
b.
$1.1 \times 10^{-3}\,V$
Correct Answer
c.
$2.5 \times 10^{-3}\,V$
d.
$1.5 \times 10^{-3}\,V$
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Q9mcq
A plano - convex lens (focal length $f_{2}$ , refractive index $\mu _{2},$ radius of curvature R) fits exactly into a plano -
concave lens (focal length $f_{1},$ refractive index $\mu _{1},$ radius of curvature R). Their plane surfaces are parallel to
each other. Then, the focal length of the combination will be:
a.
$\frac{R}{\mu _{2}\,-\,\mu _{1}}$
Correct Answer
b.
$f_{1}- f_{2}$
c.
$f_{1}+f_{2}$
d.
$\frac{2f_{1}f_{2}}{f_{1}+f_{2}}$
No explanation saved for this question yet.
Q10mcq
To double the covering range of a TV transmitting tower, its height should be multiplied by:
a.
$\frac{1}{\sqrt{2}}$
b.
$4$
Correct Answer
c.
$2$
d.
$\sqrt{2}$
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When a certain photosensitive surface is illuminated with a monochromatic light of frequency $ν,$ the stopping
potential of the photo current is $-\frac{V_{0}}{2} .$ When the surface is illuminated by monochromatic light of frequency
$\frac{ν}{2},$ the stopping potential is $-V_{0}.$ The threshold frequency for photoelectric emission is
a.
$\frac{5v}{3}$
b.
$\frac{3v}{2}$
c.
$\frac{4}{3}v$
d.
$2v$
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In the given circuit diagram, the currents, $I_{1} = -0.3A, I_{4} = 0.8A$ and $I_{5} = 0.4A,$ are flowing as shown. The
currents $I_{2}, I_{3}$ and $I_{6},$ respectively, are:
a.
$0.4A, 1.1A, 0.4A$
b.
$1.1A, -0.4A, 0.4A$
c.
$1.1A, 0.4A, 0.4A$
d.
$-0. 4A, 0. 4A, 1. 1A$
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In the figure, given that $V_{BB}$ supply can vary from $0$ to $5.0\,V, \,V_{CC} = 5\,V, \,\beta _{dc} = 200,R_{B} = 100\,k\Omega ,$
$R_{C} = 1k\Omega$ and $V_{BE} = 1.0V.$ The minimum base current and the input voltage at which the transistor will go
to saturation, will be, respectively:
a.
$25\,\mu A$ and $2.8\,V$
b.
$20\mu A$ and $2.8V$
c.
$25\mu A$ and $3.5V$
d.
$20\mu A$ and $3.5V$
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A load of mass $M kg$ is suspended from a steel wire of length $2m$ and radius $1.0\,mm$ in Searle's apparatus
experiment. The increase in length produced in the wire is $4.0\,mm.$ Now the load is fully immersed in a liquid
of relative density $2.$ The relative density of the material of load is $8.$ The new value of increase in length of
the steel wire is:
a.
$4.0\,mm$
b.
Zero
c.
$5.0mm$
d.
$3.0mm$
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A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible
thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is
$l_{1},$ and that below the piston is $l_{2},$ such that $l_{1} >l_{2}.$ Each part of the cylinder contains $n$ moles of an ideal gas at
equal temperature $T.$ If the piston is stationary, its mass $m$ will be given by:
( $R$ is universal gas constant and $g$ is the acceleration due to gravity)
An ideal gas is enclosed in a cylinder at pressure of $2$ atm and temperature, $300\,K.$ The mean time between
two successive collisions is $6 \times 10^{-8}s.$ If the pressure is doubled and temperature is increased to $500\,K,$ the
mean time between two successive collisions will be close to:
a.
$2 x 10^{-7}s$
b.
$3 x 10^{-6}s$
c.
$0. 5 x 10^{-8}s$
d.
$4 x 10^{-8}s$
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The moment of inertial of a solid sphere, about an axis parallel to its diameter and at a distance of $x$ from it, is
$'I(x)'.$ Which one of the graphs represents the variation of $I(x)$ with $x$ correctly?
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A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2N$ down
the inclined plane. The maximum external force up the inclined plane that does not move the block is $10N.$ The
coefficient of static friction between the block and the plane is: [Take $g= 10\,m/s^{2}$ ]
a.
$\frac{\sqrt{3}}{4}$
b.
$\frac{2}{3}$
c.
$\frac{1}{2}$
d.
$\frac{\sqrt{3}}{2}$
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A parallel plate capacitor with plates of area $1\,m^{2}$ each, are at a separation of $0.1\,m.$ If the electric field
between the plates is $100 N/C,$ the magnitude of charge on each plate is: $(Take \in _{0}= 8.85 \times 10^{-12} \frac{C^{2}}{N-m^{2}})$
a.
$8.85 x 10^{-10}C$
b.
$6.85 x 10^{-10}C$
c.
$9.85 x 10^{-10}C$
d.
$7.85 x 10^{-10}C$
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A particle of mass $20\,g$ is released with an initial velocity $5\,m\,s^{-1}$ along the curve from the point $A,$ as shown
in the figure. The point $A$ is at height $h$ from point $B.$ The particle slides along the frictionless surface. When
the particle reaches point $B,$ its angular momentum about $O$ will be: (Take $g= 10\,m\,s^{-2}$ )
a.
$3\, kg \,m^{2}\,s^{-1}$
b.
$2\, kg \,m^{2}\,s^{-1}$
c.
$6\, kg \,m^{2}\,s^{-1}$
d.
$8\, kg \,m^{2}\,s^{-1}$
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A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the
liquid rises up near the wall. If the radius of vessel is $5\,cm$ and its rotational speed is $2$ rotations per second,
then the difference in the heights between the center and the sides, in $cm,$ will be:
a.
$0.4$
b.
$2.0$
c.
$1.2$
d.
$0.1$
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A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of
sound in air. A tuning fork of frequency $512\, Hz$ produces first resonance when the tube is filled with water to a
mark $11\, cm$ below a reference mark, near the open end of the tube. The experiment is repeated with another
fork of frequency $256\, Hz$ which produces first resonance when water reaches a mark $27\, cm$ below the
reference mark. The velocity of sound in air, obtained in the experiment, is close to
a.
$335\,m\,s^{-1}$
b.
$341\,m\,s^{-1}$
c.
$322\,m\,s^{-1}$
d.
$328\,m\,s^{-1}$
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A paramagnetic material has $10^{28}\, atoms \,m^{-3}$ . Its magnetic susceptibility at temperature $350\,K$ is
$2.8$ Ã $-10^{-4}$ . Its susceptibility at $300\,K$ is
a.
$3.726 x 10^{-4}$
b.
$2.672 x 10^{-4}$
c.
$3.267 x 10^{-4}$
d.
$3.672 x 10^{-4}$
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Two satellites, $A$ and $B$ , have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius $R$ and $B$ is in a
circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $\frac{K_{A}}{K_{B}}$ is:
a.
$2$
b.
$\frac{1}{2}$
c.
$1$
d.
$\sqrt{\frac{1}{2}}$
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A soap bubble, blown by a mechanical pump at the mouth of a tube increases in volume with time at a constant
rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by:
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In a Frank - Hertz experiment, an electron of energy $5.6eV$ passes through mercury vapour and emerges with
an energy $0.7eV.$ The minimum wavelength of photons emitted by mercury atoms is close to:
a.
$250\,nm$
b.
$1700nm$
c.
$220nm$
d.
$2020nm$
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A galvanometer, whose resistance is $50\, ohm$ , has $25$ divisions in it. When a current of $4 \times 10^{-4}$ A passes
through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range $2.5\,V$
it should be connected to a resistance of:
a.
6250 ohm
b.
250 ohm
c.
6200 ohm
d.
200 ohm
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Formation of real image using a biconvex lens is shown below:
If the whole set up is immersed in water without disturbing the object and the screen positions, what will one
observe on the screen?
a.
Image disappears
b.
Magnified image
c.
Erect real image
d.
No change
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$\wedge ^{o}_{m}$ for $NaCl, HCl$ and $NaA$ are $126.4, 425.9$ and $100 .5 S cm^{2} mol^{-1}$ respectively. If the conductivity of
$0 .001 M HA$ is $5 \times 10^{-5}S cm^{-1}$ , degree of dissociation of $HA$ is
a.
$0.125$
b.
$0.75$
c.
$0.25$
d.
$0.50$
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The correct statement(s) among $I$ to $III$ with respect to potassium ions that are abundant within the cell fluids,
is/are
$I.$ They activate many enzymes.
$II.$ They participate in the oxidation of glucose to produce $ATP$ .
$III.$ Along with sodium ions, they are responsible for the transmission of nerve signals.
a.
$I , II$ and $III$
b.
$III$ only
c.
$I$ and $II$ only
d.
$I$ and $III$ only
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An open vessel at $27^{o}C$ is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the
vessel. Assuming that the volume of the vessel remains constant, the temperature to which the vessel has
heated is:
a.
$750^{o}C$
b.
$500^{o}C$
c.
$750K$
d.
$500K$
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For a reaction, consider the plot of $ln k$ versus $1/T$ given in the figure. If the rate constant of this reaction at
$400K$ is $10^{-5}s^{-1}$ , then the rate constant at $500K$ is:
a.
$10^{-4}s^{-1}$
b.
$10^{-6}s^{-1}$
c.
$2 x 10^{-4}s^{-1}$
d.
$4 x 10^{-4}s^{-1}$
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$8\,g$ of $NaOH$ is dissolved in $18g$ of $H_{2}O$ . Mole fraction of $NaOH$ in solution and molality (in $\, mol \, kg^{-1}$ ) of
the solution respectively are:
a.
$0.167, 11.11$
b.
$0.167, 22.20$
c.
$0.2, 11.11$
d.
$0.2, 22.20$
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If the de Broglie wavelength of the electron in $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5\pi a_{0} (a_{0}$ is
Bohr radius $)$ , then the value of $\frac{n}{z}$ is:
a.
$1.50$
b.
$1.0$
c.
$0.4$
d.
0.75
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Molecules of benzoic acid $(C_{6}H_{5}COOH)$ dimerise in $30 g$ of benzene. ' $w$ ' $g$ of benzoic acid shows a
depression in freezing point equal to $2\,K$ . If the percentage association of the acid to form dimer in the
solution is $80$ , then $w$ is: $($ Given that $K_{f} = 5\, Kmol^{-1}$ , molar mass of benzoic acid $= 122\, gmol^{-1})$
a.
$1.0g$
b.
$2.4g$
c.
$1.8g$
d.
$1.5g$
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If an angle between the line, $\frac{x+1}{2} = \frac{y-2}{1} = \frac{z-3}{-2}$ and the plane, $x-2y- kz= 3$ is $cos^{-1}( \frac{2\sqrt{2}}{3})$ , then a value
of $k$ is
a.
$\sqrt{\frac{5}{3}}$
b.
$\sqrt{\frac{3}{5}}$
c.
$-\frac{3}{5}$
d.
$-\frac{5}{3}$
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Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $(-\lambda ^{2}, \,1, \,1), \,(1, \, - \lambda ^{2}, \,1)$
and $(1, \,1, \, - \lambda ^{2})$ also passes through the point $(-1, \, -1, \,1)$ . Then $S$ is equal to :
a.
${\sqrt{3}}$
b.
${3, \, -3}$
c.
${1, -1}$
d.
${\sqrt{3}, - \sqrt{3}}$
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There are $m$ men and two women participating in a chess tournament. Each participant plays two games with
every other participant. If the number of games played by the men between themselves exceeds the number of
games played between the men and the women by $84$ , then the value of $m$ is :
a.
$11$
b.
$12$
c.
$7$
d.
$9$
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Let $Z$ be the set of integers. If $A={x\in Z : \,2^{(x+2)(x^{2}-5x+6)} = 1}$ and $B= {x\in Z : -3 < 2x-1 < 9}$ ,
then the number of subsets of the set $A\times B$ , is :
a.
$2^{12}$
b.
$2^{10}$
c.
$2^{18}$
d.
$2^{15}$
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If the sum of the first $15$ terms of the series $^{3}+ 1^{3}+ 2^{3}+ 33+ 3^{3} + …$ is equal to $225K$ ,
$(\frac{3}{4}) ( \frac{1}{2}) ( \frac{1}{4}) ( \frac{3}{4} )$
then $K$ is equal to :
a.
$9$
b.
$27$
c.
$54$
d.
$108$
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In a game, a man wins Rs. $100$ if he gets $5$ or $6$ on a throw of a fair die and loses Rs. $50$ for getting any other
number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three
throws, then his expected gain/loss (in rupees) is :
a.
$\frac{400}{3}$ gain
b.
$\frac{400}{9}$ gain
c.
$\frac{400}{3}$ loss
d.
$0$
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The mean and the variance of five observations are $4$ and $5.20$ , respectively. If three of the observations are
$3, 4$ and $4$ ; then the absolute value of the difference of the other two observations, is :
a.
$3$
b.
$5$
c.
$7$
d.
$1$
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If a straight line passing through the point $P(-3, \,4)$ is such that its intercepted portion between the coordinate
axes is bisected at $P$ , then its equation is :
a.
$4x+ 3y= 0$
b.
$4x-3y+ 24 = 0$
c.
$3x-4y+ 25 = 0$
d.
$x- y+ 7 = 0$
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In a class of $60$ students, $40$ opted for NCC, $30$ opted for NSS and $20$ opted for both NCC and NSS. If one of
these students is selected at random, then the probability that the student selected has opted neither for NCC
nor for NSS is :
a.
$\frac{1}{6}$
b.
$\frac{5}{6}$
c.
$\frac{1}{3}$
d.
$\frac{2}{3}$
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If the angle of elevation of a cloud from a point $P$ which is $25m$ above a lake be $30^{o}$ and the angle of
depression of reflection of the could in the lake from $P$ be $60^{o}$ , then the height of the cloud (in meters) from
the surface of the lake is :
a.
$50$
b.
$60$
c.
$45$
d.
$42$
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If the function $f$ given by $f(x) =x^{3} -3(a-2)x^{2} + 3ax+ 7$ , for some $a\in R$ is increasing in $(0, \,1]$ and
decreasing in $[1, \,5)$ , then a root of the equation, $\frac{f(x)-14}{(x-1)^{2}} = 0, \,(x\neq 1)$ is :
a.
$7$
b.
$-7$
c.
$6$
d.
$5$
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The set of all values of $\lambda$ for which the system of linear equations
$x-2y-2z=\lambda x$
$x+ 2y+z=\lambda y$
$-x- y=\lambda z$
has a non-trivial solution :
a.
is an empty set
b.
contains more than two elements
c.
is a singleton
d.
contains exactly two elements
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If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$ , then the locus
of the foot of perpendicular from $O$ on $AB$ is :
a.
$(x^{2} +y^{2})(x+y) =R^{2}xy$
b.
$(x^{2} +y^{2})^{3} = 4R^{2}x^{2}y^{2}$
c.
$(x^{2} +y^{2})^{2} = 4R^{2}x^{2}y^{2}$
d.
$(x^{2} +y^{2})^{2} = 4Rx^{2}y^{2}$
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If a curve passes through the point $(1, \, -2)$ and has slope of the tangent at any point $(x, \,y)$ on it as $\frac{x^{2}-2y}{x}$ ,
then the curve also passes through the point
a.
$(\sqrt{3}, \,0)$
b.
$(-1, 2)$
c.
$(-, 1\sqrt{2} )$
d.
$(3, 0)$
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Let $S$ and $S'$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta S'BS$ is a right
angled triangle with right angle at $B$ and area $(\Delta S'BS) = 8\, sq. units$ , then the length of a latus rectum of the
ellipse is :
a.
$2\sqrt{2}$
b.
$2$
c.
$4$
d.
$4\sqrt{2}$
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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors, out of which vectors $\vec{b}$ and $\vec{c}$ are non-parallel. If $\alpha$ and $\beta$ are the angles
which vector $\vec{a}$ makes with vectors $\vec{b}$ and $\vec{c}$ respectively and $\vec{a}\times (\vec{b}\times \vec{c})= \frac{1}{2} \vec{b}$ , then $|\alpha - \beta |$ is equal to :
a.
$90^{o}$
b.
$60^{o}$
c.
$45^{o}$
d.
$30^{o}$
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