The length of a wire of a potentiometer is $100\,cm$ , and the e.m.f. of its standard cell is $E$ volt. It is employed to
measure the e.m.f of a battery whose internal resistance is $0.5\Omega$ . If the balance point is obtained at $l = 30 cm$
from the positive end, the e.m.f. of the battery is
a.
$\frac{30E}{100.5}$
b.
$\frac{30E}{(100-0.5)}$
c.
$\frac{30(E-0.5i)}{100}$ , where $i$ is the current in the
potentiometer wire
d.
$\frac{30E}{100}$
Correct Answer
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Q2mcq
A horizontal force of $10\,N$ is necessary to just hold a block stationary against a wall. The co-efficient of
friction between the block and the wall is $0.2$ . The weight of the block is
a.
$20\,N$
b.
$50\,N$
c.
$100\,N$
d.
$2\,N$
Correct Answer
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Q3mcq
A thin rectangular magnet suspended freely has a period of oscillation equal to $T$ . Now it is broken into two
equal halves (each having half of the original length) and one piece is made to oscillate freely in the same
field. If its period of oscillation is $T'$ , the ratio $\frac{T^{'}}{T}$ is
a.
$\frac{1}{2\sqrt{2}}$
b.
$\frac{1}{2}$
Correct Answer
c.
2
d.
$\frac{1}{4}$
No explanation saved for this question yet.
Q4mcq
The core of any transformer is laminated so as to
a.
reduce the energy loss due to eddy currents
Correct Answer
b.
make it light weight
c.
make it robust and strong
d.
increase the secondary voltage
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Q5mcq
Curie temperature is the temperature above which
a.
a ferromagnetic material becomes paramagnetic
Correct Answer
b.
a paramagnetic material becomes diamagnetic
c.
a ferromagnetic material becomes diamagnetic
d.
a paramagnetic material becomes ferromagnetic
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Q6mcq
A 220 volt, 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will be
a.
$750watt$
b.
$500watt$
c.
$250watt$
Correct Answer
d.
$1000watt$
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Q7mcq
In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the
energy is stored equally between the electric and magnetic field is
a.
$\frac{Q}{2}$
b.
$\frac{Q}{\sqrt{3}}$
c.
$\frac{Q}{\sqrt{2}}$
Correct Answer
d.
$Q$
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Q8mcq
A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$ . If a force $P$ is applied
at the free end of the rope, the force exerted by the rope on the block is
a.
$\frac{Pm}{M+m}$
b.
$\frac{Pm}{M-m}$
c.
$P$
d.
$\frac{PM}{M+m}$
Correct Answer
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Q9mcq
A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After $5\,min-$
utes, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is
a.
$0.4 ln 2$
b.
$0.2 ln 2$
c.
$0.1 ln 2$
d.
None of these
Correct Answer
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Q10mcq
A body is moved along a straight line by a machine delivering a constant power. The distance moved by the
body in time ' $t$ ' is proportional to
a.
$t^{3/4}$
b.
$t^{3/2}$
Correct Answer
c.
$t^{1/4}$
d.
$t^{1/2}$
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A Carnot engine takes $3 \times 10^{6}cal$ . of heat from a reservoir at $627^{\circ }C$ , and gives it to a sink at $27^{\circ }C$ . The work
done by the engine is
a.
$4.2 \times 10^{6}\,J$
b.
$8.4 \times 10^{6}\,J$
c.
$16.8 \times 10^{6}\,J$
d.
Zero
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A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$ , and another disc $Y$ of radius $4R$ is
made from an iron plate of thickness $\frac{t}{4}$ . Then the relation between the moment of inertia $I_{X}$ and $I_{Y}$ is
a.
$I_{Y} = 32I_{x}$
b.
$I_{Y} = 16I_{x}$
c.
$I_{Y} = I_{X}$
d.
$I_{Y} = 64I_{X}$
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A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that
the mass executes SHM of time period T. If the mass is increased by $m$ , the time period becomes $\frac{5\,T}{3}$ . Then the
ratio of $\frac{m}{M}$ is
a.
$\frac{3}{5}$
b.
$\frac{25}{9}$
c.
$\frac{16}{9}$
d.
$\frac{5}{3}$
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A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through $60^{\circ }$ . The
torque needed to maintain the needle in this position will be
a.
$\sqrt{3}\,W$
b.
W
c.
$\frac{\sqrt{3}}{2} \,W$
d.
$2\,W$
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Two identical photocathodes receive light of frequencies $f_{1}$ and $f_{2}$ . If the velocities of the photo electrons (of
mass $m$ ) coming out are respectively $v_{1}$ and $v_{2}$ , then
The negative $Zn$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by
$0.13\,g$ in 30 minutes. If the electrochemical equivalent of $Zn$ and $Cu$ are $32.5$ and $31.5$ respectively, the
increase in the mass of the positive Cu pole in this time is
a.
$0.180\,g$
b.
$0.141\,g$
c.
$0.126\,g$
d.
$0.242\,g$
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A metal wire of linear mass density of $9.8\,g/m$ is stretched with a tension of $10\,kg$ -wt between two rigid
supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it
vibrates in resonance when carrying an alternating current of frequency $n$ . The frequency $n$ of the alternating
source is
a.
$50\,Hz$
b.
$100\,Hz$
c.
$200\,Hz$
d.
$25\,Hz$
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A tuning fork of known frequency $256\,Hz$ makes 5 beats per second with the vibrating string of a piano. The
beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The
frequency of the piano string before increasing the tension was
a.
$256 + 2\,Hz$
b.
$256 -2\,Hz$
c.
$256 -5\,Hz$
d.
$256 + 5\,Hz$
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A rocket with a lift-off mass $3.5 \times 10^{4}\,kg$ is blasted upwards with an initial acceleration of $10\,m/s^{2}$ . Then the
initial thrust of the blast is
a.
$3.5 \times 10^{5}\,N$
b.
$7.0 \times 10^{5}\,N$
c.
$14.0 \times 10^{5}\,N$
d.
$1.75 \times 10^{5}\,N$
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A boy playing on the roof of a $10\,m$ high building throws a ball with a speed of $10\,m/s$ at an angle of $30^{\circ }$ with
the horizontal. How far from the throwing point will the ball be at the height of $10\,m$ from the ground?
$[g = 10\,m/s^{2}, sin 30^{\circ } = \frac{1}{2} , cos 30^{\circ } = \frac{\sqrt{3}}{2}]$
a.
$5.20\,m$
b.
$4.33\,m$
c.
$2.60\,m$
d.
$8.66\,m$
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A thin spherical conducting shell of radius $R$ has a charge $q$ . Another charge $Q$ is placed at the centre of the
shell. The electrostatic potential at a point $P$ a distance $\frac{R}{2}$ from the centre of the shell is
A car, moving with a speed of $50\,km/hr$ , can be stopped by brakes after at least $6\,m$ . If the same car is moving
at a speed of $100\,km/hr$ , the minimum stopping distance is
a.
$12\,m$
b.
$18\,m$
c.
$24\,m$
d.
$6\,m$
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If the binding energy of the electron in a hydrogen atom is $13.6eV$ , the energy required to remove the electron
from the first excited state of $Li^{++}$ is
a.
$30.6eV$
b.
$13.6eV$
c.
$3.4eV$
d.
$122.4eV$
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A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49
$N$ , when the lift is stationary. If the lift moves downward with an acceleration of $5\,m/s^{2}$ , the reading of the
spring balance will be
a.
$24\,N$
b.
$74\,N$
c.
$15\,N$
d.
$49\,N$
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Two particles start simultaneously from the same point and move along two straight lines, one with uniform
velocity $\vec{u}$ and the other from rest with uniform acceleration $\vec{f}$ . Let $\alpha$ be the angle between their directions of
motion. The relative velocity of the second particle w.r.t. the first is least after a time.
a.
$\frac{ucos\alpha}{f}$
b.
$\frac{usin\alpha}{f}$
c.
$\frac{f cos\alpha}{u}$
d.
u $sin\alpha$ .
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During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute
temperature. The ratio $C_{p}/C_{v}$ for the gas is
a.
$\frac{4}{3}$
b.
2
c.
$\frac{5}{3}$
d.
$\frac{3}{2}$
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A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it
moves with constant acceleration $f$ and in the second part with constant retardation $r$ . The value of $t$ is given by
a.
$\sqrt{2s}(\frac{1}{f} + \frac{1}{r} )$
b.
$2s(\frac{1}{f} + \frac{1}{r} )$
c.
$\frac{2\,s}{^{1}+^{1}}$
$f r$
d.
$\sqrt{2s(f+r)}$
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The length of a simple pendulum executing simple harmonic motion is increased by $21%$ . The percentage
increase in the time period of the pendulum of increased length is
a.
$11%$
b.
$21%$
c.
$42%$
d.
$10%$
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A particle of charge $-16 \times 10^{-18}$ coulomb moving with velocity $10\,ms^{-1}$ along the $x$ -axis enters a region
where a magnetic field of induction $B$ is along the $y$ -axis, and an electric field of magnitude $10^{4}\,V/m$ is along
the negative z-axis. If the charged particle continues moving along the $x$ -axis, the magnitude of $B$ is
a.
$10^{3}\,Wb/m^{2}$
b.
$10^{5}\,Wb/m^{2}$
c.
$10^{16}\,Wb/m^{2}$
d.
$10^{-3}\,Wb/m^{2}$
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Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constant $k_{1}$ and $k_{2}$ ,
respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is
a.
$\sqrt{\,} \frac{k_{1}}{k_{2}}$
b.
$\frac{k}{k_{1}}^{2}$
c.
$\sqrt{\,} \frac{k}{k_{1}}^{2}$
d.
$\frac{k_{1}}{k_{2}}$
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The thermo e.m.f. of a thermo-couple is $25\mu V/^{\circ }C$ at room temperature. A galvanometer of 40 ohm resistance,
capable of detecting current as low as $10^{-5}\,A$ , is connected with the thermo couple. The smallest temperature
difference that can be detected by this sytem is
a.
$16^{\circ }C$
b.
$12^{\circ }C$
c.
$8^{0}C$
d.
$20^{\circ }C$
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When the current changes from $+2\,A$ to $-2\,A$ in $0.05$ second, an e.m.f. of $8\,V$ is induced in a coil. The
coefficient of self-induction of the coil is
a.
$0.2H$
b.
$0.4H$
c.
$0.8H$
d.
$0.1H$
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According to Newton's law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta )^{n}$ , where $\Delta \theta$ is the
difference of the temperature of the body and the surroundings, and $n$ is equal to
a.
two
b.
three
c.
four
d.
one
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A spring of spring constant $5 \times 10^{3}\,N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the
work required to stretch it further by another $5\,cm$ is
a.
$12.50\,N -m$
b.
$18.75\,N -m$
c.
$25.00\,N -m$
d.
$6.25\,N -m$
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A nucleus with $Z = 92$ emits the following in a sequence: $\alpha ,\beta ^{-},\beta ^{-}\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,\beta ^{-},\beta ^{-},\alpha ,\beta ^{+},\beta ^{+},\alpha$ . Then $Z$
of the resulting nucleus is
a.
$76$
b.
$78$
c.
$82$
d.
$74$
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A particle of mass $M$ and charge Q moving with velocity $\vec{v}$ describe a circular path of radius $R$ when subjected
to a uniform transverse magnetic field of induction $B$ . The work done by the field when the particle completes
one full circle is
a.
$(\frac{Mv^{2}}{R})2\pi R$
b.
Zero
c.
$BQ2\pi R$
d.
$BQ$ v $2\pi R$
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Two spherical bodies of mass $M$ and $5M&$ radii $R&2R$ respectively are released in free space with initial
separation between their centres equal to $12R$ . If they attract each other due to gravitational force only, then
the distance covered by the smaller body just before collision is
a.
$2.5R$
b.
$4.5R$
c.
$7.5R$
d.
$1.5R$
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The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^{3}$ and $y=\beta t^{3}$ . The speed of the
particle at time ' $t$ ' is given by
a.
$3t\sqrt{\alpha ^{2}+\beta ^{2}}$
b.
$3t^{2}\sqrt{\alpha ^{2}+\beta ^{2}}$
c.
$t^{2}\sqrt{\alpha ^{2}+\beta ^{2}}$
d.
$\sqrt{\alpha ^{2}+\beta ^{2}}$
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The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is
increased to 4 times the previous value, the new time period will become
a.
10 hours
b.
80 hours
c.
40 hours
d.
20 hours
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A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\,N$ to the lower end.
The weight stretches the wire by $1\,mm$ . Then the elastic energy stored in the wire is
a.
$0.2\,J$
b.
$10\,J$
c.
$20\,J$
d.
$0.1\,J$
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In the nuclear fusion reaction $^{2}_{1}H +^{3}_{1}H \rightarrow \rightarrow^{4}_{2}He + n$ given that the repulsive potential energy between the two
nuclei is $\sim 7.7 \times 10^{-14}\,J$ , the temperature at which the gases must be heated to initiate the reaction is nearly
[Boltzmann's Constant $k = 1.38 \times 10^{-23}\,J/K$ ]
a.
$10^{7}\,K$
b.
$10^{5}\,K$
c.
$10^{3}\,K$
d.
$10^{9}\,K$
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Three forces start acting simultaneously on a particle moving with velocity, $\vec{v}$ . These forces are represented in
magnitude and direction by the three sides of a triangle $ABC$ . The particle will now move with velocity
a.
less than $\vec{v}$
b.
greater than $\vec{v}$
c.
$|v|$ in the direction of the largest force $BC$
d.
$\vec{v}$ , remaining unchanged
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The escape velocity for a body projected vertically upwards from the surface of earth is $11\,km/s$ . If the body
is projected at an angle of $45^{\circ }$ with the vertical, the escape velocity will be
a.
$11\sqrt{2}\,km/s$
b.
$22\,km/s$
c.
$11\,km/s$
d.
$\frac{11}{\sqrt{2}}\,km/s$
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Two stones are projected from the top of a cliff $h$ metres high, with the same speed $u$ , so as to hit the ground at
the same spot. If one of the stones is projected at an angle $\theta$ to the horizontal then the $\theta$ equals
a.
$u\sqrt{\frac{2}{gh}}$
b.
$\sqrt{\frac{2u}{gh}}$
c.
$2\,g\sqrt{\frac{u}{h}}$
d.
$2\,h\sqrt{\frac{u}{g}}$
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The displacement $y$ of a wave travelling in the $x$ -direction is given by $y= 10^{-4} sin(600t-2x+ \frac{\pi}{3} )$ metres
where $x$ is expressed in metres and $t$ in seconds. The speed of the wave-motion, in $ms^{-1}$ , is
a.
$300$
b.
$600$
c.
$1200$
d.
$200$
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The length of a given cylindrical wire is increased by $100%$ . Due to the consequent decrease in diameter the
change in the resistance of the wire will be
a.
$200%$
b.
$100%$
c.
$50%$
d.
$300%$
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If the electric flux entering and leaving an enclosed surface respectively is $\phi _{1}$ and $\phi _{2}$ , the electric charge inside
the surface will be
a.
$(\phi _{2}- \phi _{1})\epsilon _{0}$
b.
$(\phi _{1}+\phi _{2})/\epsilon _{0}$
c.
$(\phi _{2}- \phi _{1})/\epsilon _{0}$
d.
$(\phi _{1}+\phi _{2})\epsilon _{0}$
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A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy
(T.E) are measured as a function of displacement $x$ . Which of the following statements is true?
a.
K.E. is maximum when $x= 0$
b.
T.E is zero when $x= 0$
c.
K.E is maximum when $x$ is maximum
d.
P.E. is maximum when $x= 0$
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A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs
from the former one. Then the true statement about the scale reading is
a.
Both the scales read $Mkg$ each
b.
The scale of the lower one reads $Mkg$ and of the
upper one zero
c.
The reading of the two scales can be anything but
the sum of the reading will be $Mkg$
d.
Both the scales read $M/2\,kg$ each
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Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The
explanation for it is that
a.
oxygen in air reacts with the emitted HCI gas to
form a cloud of chlorine gas
b.
strong affinity of HCI gas for miosture in air
results in forming of droplets of liquid solution
which appears like a cloudy smoke.
c.
due to strong affinity for water, concentrated
hydrochloric acid pulls moisture of air towards it
self. This moisture forms droplets of water and
hence the cloud.
d.
concentrated hydrochloric acid emits strongly
smelling HCI gas all the time.
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$25ml$ of a solution of barrium hydroxide on titration with a $0.1$ molar solution of hydrochloric acid gave a litre
value of $35ml$ . The molarity of barium hydroxide solution was
a.
$0.14$
b.
$0.28$
c.
$0.35$
d.
$0.07$
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Bottles containing $C_{6}H_{5}$ l and $C_{6}H_{5}CH_{2}I$ lost their original labels. They were labelled $A$ and $B$ for testing $A$
and $B$ were separately taken in test tubes and boiled with $NaOH$ solution. The end solution in each tube was
made acidic with dilute $HNO_{3}$ and then some $AgNO_{3}$ solution was added. Substance B gave a yellow
precipitate. Which one of the following statements is true for this experiment?
a.
A and $C_{6}H_{5}CH_{2}I$
b.
$B$ and $C_{6}H_{5}I$
c.
Addition of $HNO_{3}$ was unnecessary
d.
A was $C_{6}H_{5}I$
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For the reaction equilibrium $N_{2}O_{4}(\,g)\rightleftharpoons 2NO_{2}(\,g)$ the concentrations of $N_{2}O_{4}$ and $NO_{2}$ at equilibrium are
$4.8 \times 10^{-2}$ and $1.2 \times 10^{-2}\,mol\,L^{-1}$ respectively. The value of $K_{c}$ for the reaction is
a.
$3 \times 10^{-1}\,mol\,L^{-1}$
b.
$3 \times 10^{-3}\,mol\,L^{-1}$
c.
$3 \times 10^{3}\,mol\,L^{-1}$
d.
$3.3 \times 10^{2}\,mol\,L^{-1}$
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In the anion $HCOO^{-}$ the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?
(1) The $C = O$ bond is weaker than the $C -O$ bond (2) The anion $HCOO^{-}$ has two resonating structures
(3) The anion is obtained by removal of a proton (4) Electronic orbitals of carbon atom are hybridised
from the acid molecule
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In a $0.2$ molal aqueous solution of a weak acid $HX$ the degree of ionization is $0.3$ . Taking $k_{f}$ for water as $1.85$
, the freezing point of the solution will be nearest to
a.
$-0.360^{\circ }C$
b.
$-0.260^{\circ }C$
c.
$+0.480^{\circ }C$
d.
$-0.480^{\circ }C$
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The radius of $La^{3+}$ (Atomic number of $La = 57$ ) is $1.06$ Å. Which one of the following given values will be
closest to the radius of $Lu^{3+}$ (Atomic number of $Lu = 71$ )?
a.
$1.40$ Å
b.
$1.06$ Å
c.
$0.85$ Å
d.
$1.60$ Å
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The rate law for a reaction between the substances $A$ and $B$ is given by Rate $= k[A]^{n}[B]^{m}$ On doubling the
concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of the
reaction will be as
a.
$(m+n)$
b.
$(n- m)$
c.
$2^{(n-m)}$
d.
$\frac{1}{2^{(m+n)}}$
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For the reaction system: $2NO(g) + O_{2}(\,g) \rightarrow 2NO\rightarrow_{2}(\,g)$ volume is suddenly reduce to half its value by
increasing the pressure on it. If the reaction is of first order with respect to $O_{2}$ and second order with respect
to $NO$ , the rate of reaction will
a.
diminish to one-eighth of its initial value
b.
increase to eight times of its initial value
c.
increase to four times of its initial value
d.
diminish to one-fourth of its initial value
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In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the
following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen
a.
$5 \rightarrow 2\rightarrow$
b.
$4 \rightarrow 1\rightarrow$
c.
$2 \rightarrow 5\rightarrow$
d.
$3 \rightarrow 2\rightarrow$
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The internal energy change when a system goes from state $A$ to $B$ is $40\,kJ/mole$ . If the system goes from $A$ to
$B$ by a reversible path and retums to state $A$ by an irreversible path what would be the net change in
internalenergy?
a.
$> 40\,kJ$
b.
$< 40\,kJ$
c.
Zero
d.
$40\,kJ$
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Consider the reaction equilibrium $2SO_{2}(\,g) + O_{2}(\,g)\rightleftharpoons 2SO_{3}(\,g); \Delta H^{0} = -198\,kJ$ . On the basis of Le
Chatelier's principle, the condition favourable for the forward reaction is
a.
increasing temperature as well as pressure
b.
lowering the temperature and increasing the
pressure
c.
any value of temperature and pressure
d.
lowering of temperature as well as pressure
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The atomic numbers of vanadium $(V)$ , Chromium $(Cr)$ , manganese $(Mn)$ and iron $(Fe)$ are respectively 23 ,
24,25 and 26 . Which one of these may be expected to have the highest second ionization enthalpy?
a.
$Cr$
b.
$Mn$
c.
$Fe$
d.
$V$
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If at $298\,K$ the bond energies of $C -H, C -C, C = C$ and $H -H$ bonds are respectively $414, 347, 615$ and
$435\,kJ mol^{-1}$ , the value of enthalpy change for the reaction $H_{2}C = CH_{2}(\,g) + H_{2}(\,g) \rightarrow H\rightarrow_{3}C -CH_{3}(\,g)$ at
$298\,K$ will be
a.
$-250\,kJ$
b.
$+125\,kJ$
c.
$-125\,kJ$
d.
$+250\,kJ$
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For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass
over a liquid metal which does not solidify before glass. The metal used can be
a.
tin
b.
sodium
c.
magnesium
d.
mercury
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For the redox reaction $Zn(s) + Cu^{2+}(0.1M) \rightarrow Zn\rightarrow^{2+}(1M) + Cu(s)$ taking place in a cell, $E^{0}_{cell\,}$ is $1.10$ volt.
$E^{\circ }$ for the cell will be $(2.303\frac{RT}{F} = 0.0591)$
a.
$1.80$ volt
b.
$1.07$ volt
c.
$0.82$ volt
d.
$2.14$ volt
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One mole of the complex compound $Co(NH_{3})_{5}Cl_{3}$ , gives 3 moles of ions on dissolution in water. One mole
of the same complex reacts with two moles of $AgNO_{3}$ solution to yield two moles of $AgCl$ (s). The structure
of the complex is
a.
$[Co(NH_{3})_{3}Cl_{3}] \cdot 2NH_{3}$
b.
$[Co(NH_{3})_{4}Cl_{2}]Cl. NH_{3}$
c.
$[Co(NH_{3})_{4}Cl]Cl_{2}. NH_{3}$
d.
$[Co(NH_{3})_{5}Cl]Cl_{2}$
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The radionucleide $^{234}_{90} Th$ undergoes two successive $\beta$ -decays followed by one $\alpha$ -decay. The atomic number
and the mass number respectively of the resulting radionucleide are
a.
94 and 230
b.
90 and 230
c.
92 and 230
d.
92 and 234
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For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be $0.295\,V$ at
$25^{\circ }C$ . The equilibrium constant of the reaction at $25^{\circ }C$ will be
a.
$29.5 \times 10^{-2}$
b.
10
c.
$1 \times 10^{10}$
d.
$1 \times 10^{-10}$
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A red solid is insoluble in water. However it becomes soluble if some $KI$ is added to water. Heating the red
solid in a test tube results in liberation of some violet coloured fumes and droplets of a metal appear on the
cooler parts of the test tube. The red solid is
a.
$HgI_{2}$
b.
$HgO$
c.
$Pb_{3}O_{4}$
d.
$(NH_{4})_{2}Cr_{2}O_{7}$
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When during electrolysis of a solution of $AgNO_{3}9650$ coulombs of charge pass through the electroplating
bath, the mass of silver deposited on the cathode will be
a.
$10.8\,g$
b.
$21.6\,g$
c.
$108\,g$
d.
$1.08\,g$
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In an irreversible process taking place at constant $T$ and $P$ and in which only pressure-volume work is being
done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria
a.
$(dS)_{V,E} > 0, (dG)_{T,P} < 0$
b.
$(dS)_{V:E} = 0, (dG)_{TPP} = 0$
c.
$(dS)_{V,E} = 0, (dG)_{T,P} > 0$
d.
$(dS)_{V,E} < 0, (dG)_{T,P} < 0$
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The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were $256\,g$ , the mass of it
remaining undecayed after 18 hours would be
a.
$8.0\,g$
b.
$12.0\,g$
c.
$16.0\,g$
d.
$4.0\,g$
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What volume of hydrogen gas, at $273\,K$ and $1\,atm$ , pressure will be consumed in obtaining $21.6\,g$ of
elemental boron (atomic mass $= 10.8$ ) from the reducti on of boron trichloride by hydrogen?
a.
$67.2\,L$
b.
$44.8\,L$
c.
$22.4\,L$
d.
$89.6\,L$
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The orbital angular momentum for an electron revolving in an orbit is given by $\sqrt{l(l+ 1)}\cdot \frac{h}{2\pi}$ . This
momentum for an s-electron will be given by
a.
zero
b.
$\frac{h}{2\pi}$
c.
$\sqrt{2}\cdot \frac{h}{2\pi}$
d.
$+ \frac{1}{2} \cdot \frac{h}{2\pi}$
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The median of a set of 9 distinct observations is $20.5$ . If each of the largest 4 observations of the set is
increased by 2 , then median of the new set
a.
remains the same as that of the original set
b.
is increased by 2
c.
is decreased by 2
d.
is two times the original median
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Let $\frac{d}{dx} F(x) =( \frac{e^{sinx\,}}{x})x> 0$ . If $\int _{1}^{4} \frac{3}{x}e^{sin\,^{3}}dx=F(k) - F(1)$ then one of the possible values of $k$ , is
a.
64
b.
15
c.
16
d.
63
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If $x_{1}, x_{2}, x_{3}$ and $y_{1}, y_{2}, y_{3}$ are both in G.P. with the same common ratio, then the points $(x_{1}, y_{1}), (x_{2}, y_{2})$ and
$(x_{3}$ , $y_{3}$ )
a.
are vertices of a triangle
b.
lie on a straight line
c.
lie on an ellipse
d.
lie on a circle
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If $\vec{u}, \vec{v}$ and $\vec{w}$ are three non-coplanar vectors, then $(\vec{u}+ \vec{v}- \vec{w}). (\vec{u}- \vec{v}) \times (\vec{v}- \vec{w})$ equals
a.
$3\vec{u}. \vec{v}\times \vec{w}$
b.
0
c.
$\vec{u}\cdot \vec{v}\times \vec{w}$
d.
$\vec{u}\cdot \vec{w}\times \vec{v}$
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If $f(x) =x^{n}$ , then the value of $f(1) - \frac{f^{'}(1)}{1} + \frac{f^{''}(1)}{2!} - \frac{f^{''}(1)}{3!} + … … … … . \frac{(-1)^{n}f^{''}(1)}{n!}$ is
a.
1
b.
$2^{n}$
c.
$2^{n} -1$
d.
0
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$\frac{n-1}{2} , when\,n\,isodd\,$
A function $f$ from the set of natural numbers to integers defined by $f(n) ={$ is
$\frac{n}{2}, when\,n\,is even\,$
a.
neither one-one nor onto
b.
one-one but not onto
c.
onto but not one-one
d.
one-one and onto both.
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Let $f(x)$ be a function satisfying $f'(x) =f(x)$ with $f(0) = 1$ and $g(x)$ be a function that satisfies
$f(x) +g(x) =x^{2}$ . Then the value of the integral $\int _{0}^{1} f(x)g(x)dx$ , is
a.
$e + \frac{e^{2}}{2} + \frac{5}{2}$
b.
$e - \frac{e^{2}}{2} - \frac{5}{2}$
c.
$e + \frac{e^{2}}{2} - \frac{3}{2}$
d.
$e - \frac{e^{2}}{2} - \frac{3}{2}$
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$| |$
If the function $f(x) = 2x^{2} -9ax^{2} + 12a^{2}x + 1$ , where $a > 0$ , attains its maximum and minimum at $p$ and $q$
respectively such that $p^{2} = q$ , then a equals
a.
$\frac{1}{2}$
b.
3
c.
1
d.
2
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If $z$ and $\omega$ are two non-zero complex numbers such that $|z\omega | = 1$ and $Arg(z) -Arg(\omega ) = \frac{\pi}{2}$ , then $z\omega -$ is equal
to
a.
$-i$
b.
1
c.
$-1$
d.
i.
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Consider points A, B, C and D with position vectors $7\hat{i}-4\hat{j}+ 7\hat{k}, \hat{i}-6\hat{j}+ 10\hat{k}, -\hat{i}-3\hat{j}+ 4\hat{k}$ and $5\hat{i}- \hat{j}+ 5\hat{k}$
respectively. Then $ABCD$ is a
a.
parallelogram but not a rhombus
b.
square
c.
rhombus
d.
rectangle
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Let $f(a) = g(a) = k$ and their $n$ th derivatives $f^{n}(a), g^{n}(a)$ exist and are not equal for some $n$ . Further if
$lim_{x\rightarrow \rightarrow a} \frac{f(a)g(x)-f(a)-g(a)f(x)+f(a)}{g(x)-f(x)} = 4$ then the value of $k$ is
a.
0
b.
4
c.
2
d.
1
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Let $Z_{1}$ and $Z_{2}$ be two roots of the equation $x^{2} +aZ+b= 0$ being complex. Further, assume that the origin,
$Z_{1}$ and $Z_{2}$ form an equilateral triangle. Then
a.
$a^{2} = 4b$
b.
$a^{2} =b$
c.
$a^{2} = 2b$
d.
$a^{2} = 3b$
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$1 \omega ^{n} \omega ^{2n}$
If $1,\omega ,\omega ^{2}$ are the cube roots of unity, then $\Delta = \omega ^{n} \omega ^{2n} 1$ is equal to
$\omega ^{2n} 1 \omega ^{n}$
a.
$\omega ^{2}$
b.
0
c.
1
d.
$\omega$
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Let $R_{1}$ and $R_{2}$ respectively be the maximum ranges up and down an inclined plane and $R$ be the maximum
range on the horizontal plane. Then $R_{1}, R, R_{2}$ are in
a.
Н.P
b.
A.G.P
c.
A.P
d.
G.P.
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The foci of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{b^{2}} = 1$ and the hyperbola $\frac{x^{2}}{144} - \frac{y^{2}}{81} = \frac{1}{25}$ coincide. Then the value of $b^{2}$ is
a.
9
b.
1
c.
5
d.
7
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If the sum of the roots of the quadratic equation $ax^{2} +bx+c= 0$ is equal to the sum of the squares of their
reciprocals, then $\frac{a}{c}, \frac{b}{a}$ and $\frac{c}{b}$ are in
a.
Arithmetic - Geometric Progression
b.
Arithmetic Progression
c.
Geometric Progression
d.
Harmonic Progression
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The upper $\frac{3}{4}$ th portion of a vertical pole subtends an angle $tan^{-1} \frac{3}{5}$ at a point in the horizontal plane through
its foot and at a distance $40\,m$ from the foot.
a.
$80\,m$
b.
$20\,m$
c.
$40\,m$
d.
$80\,m$
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The resultant of forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ . If $\vec{Q}$ is doubled then $\vec{R}$ is doubled. If the direction of $\vec{Q}$ is reversed, then
$\vec{R}$ is again doubled. Then $P^{2} : Q^{2} : R^{2}$ is
a.
$2 : 3 : 1$
b.
$3 : 1 : 1$
c.
$2 : 3 : 2$
d.
$1 : 2 : 3$
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A particle acted on by constant forces $4\hat{i}+ \hat{j}-3\hat{k}$ and $3\hat{i}+ \hat{j}- \hat{k}$ to the point $5\hat{i}+ 4\hat{j}- \hat{k}$ . The total work
done by the forces is
a.
50 units
b.
20 units
c.
30 units
d.
40 units
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$--$
The vectors $A\vec{B}= 3\hat{i}+ 4\hat{k}&A\vec{C}= 5\hat{i}-2\hat{j}+ 4\hat{k}$ are the sides of a triangle $ABC$ . The length of the median
through $A$ is
a.
$\sqrt{288}$
b.
$\sqrt{18}$
c.
$\sqrt{72}$
d.
$\sqrt{33}$
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In a triangle $ABC$ , medians $AD$ and $BE$ are drawn. If $AD = 4, \angle DAB = \frac{\pi}{6}$ and $\angle ABE = \frac{\pi}{3}$ , then the area
of the $\triangle ABC$ is
a.
$\frac{64}{3}$
b.
$\frac{8}{3}$
c.
$\frac{16}{3}$
d.
None of these
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A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the
first five questions. The number of choices available to him is
a.
346
b.
140
c.
196
d.
280
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$a a^{2} 1 +a^{3}$
If $b b^{2} 1 +b^{3} = 0$ and vectors $(1,a,a^{2}),(a,b,b^{2})$ and $(a,c,c^{2})$ are non-coplanar, then the product abc
$c c^{2} 1 +c^{3}$
equals
a.
0
b.
2
c.
$-1$
d.
1
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$\vec{a}, \vec{b}, \vec{c}$ are 3 vectors, such that $\vec{a}+ \vec{b}+ \vec{c}= 0, |\vec{a}| = 1, |\vec{b}| = 2 | \vec{a}$ then $\vec{a}\cdot \vec{b}+ \vec{b}\cdot \vec{c}+ \vec{c}\cdot \vec{a}$ is equal to
a.
1
b.
0
c.
$-7$
d.
7
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If the pair of straight lines $x^{2} -2pxy- y^{2} = 0$ and $x^{2} -2pxy- y^{2} = 0$ be such that each pair bisects the
angle between the other pair, then
a.
$pq= -1$
b.
$p = q$
c.
$p= -q$
d.
$pq = 1$
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Let $\vec{u}= \hat{i}+ \hat{j}, \vec{v}= \hat{i}- \hat{j}$ and $\vec{w}= \hat{i}+ 2\hat{j}+ 3\hat{k}$ . If $\hat{n}$ is a unit vector such that $\vec{u}\cdot \hat{n}= 0$ and $\vec{v}\cdot \hat{n}= 0$ , then
$|\vec{w}\cdot \hat{n}|$ is equal to
a.
3
b.
0
c.
1
d.
2
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In an experiment with 15 observations on $x$ , the following results were available: $\Sigma x^{2} = 2830, \Sigma x= 170$
One observation that was 20 was found to be wrong and was replaced by the correct value 30 . The corrected
variance is
a.
$8.33$
b.
$78.00$
c.
$188.66$
d.
$177.33$
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A couple is of moment $\vec{G}$ and the force forming the couple is $\vec{P}$ . If $\vec{P}$ is turned through a right angle the
moment of the couple thus formed is $\vec{H}$ . If instead, the force $\vec{P}$ are turned through an angle $\alpha$ , then the
moment of couple becomes
a.
$\vec{H}sin\alpha - \vec{G}cos\alpha$
b.
$\vec{G}sin\alpha - \vec{H}cos\alpha$
c.
$\vec{H}sin\alpha + \vec{G}cos\alpha$
d.
$\vec{G}sin\alpha + \vec{H}cos\alpha$
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Events $A, B, C$ are mutually exclusive events such that $P(A) = \frac{3x+1}{3}, P(B) = \frac{x-1}{4}$ and $P(C) = \frac{1-2x}{4}$ . The
set of possible values of $x$ are in the interval.
a.
$[0, 1]$
b.
$[\frac{1}{3}, \frac{1}{2} ]$
c.
$[\frac{1}{3}, \frac{2}{3} ]$
d.
$[\frac{1}{3}, \frac{13}{3}]$
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If the equation of the locus of a point equidistant from the point $(a_{1},b_{1})$ and $(a_{2},b_{2})$ is
$(a_{1}- b_{2})x+ (a_{1}- b_{2})y+c= 0$ , then the value of 'c' is
A square of side a lies above the $x$ -axis and has one vertex at the origin. The side passing through the origin
makes an angle $\alpha (0 <\alpha < \frac{\pi}{4})$ with the positive direction of $x$ -axis. The equation of its diagonal not passing
through the origin is
