a periodic, but not simple harmonic motion with
a period $2\pi /\omega$
b.
a periodic, but not simple harmonic motion with
a period $\pi /\omega$
c.
a simple harmonic motion with a period $2\pi /\omega$
d.
a simple harmonic motion with a period $\pi /\omega$
Correct Answer
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Q2mcq
Two voltameters one of copper and another of silver, are joined in parallel. When a total charge $q$ flows
through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper
and silver are $z_{1}$ and $z_{2}$ respectively the charge which flows through the silver voltameter is
a.
$\frac{q}{1+^{z}^{1}}$
$z2$
b.
$\frac{q}{1+^{z}^{2}}$
$z1$
Correct Answer
c.
$q \frac{z}{z_{2}}^{1}$
d.
$q\frac{z}{z_{1}}^{2}$
No explanation saved for this question yet.
Q3mcq
$A$ and $B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is contained with
them. The resultant of $A$ and $B$ after combining is displaced through a distance
a.
$\frac{2H}{A-B}$
b.
$\frac{H}{A+B}$
Correct Answer
c.
$\frac{H}{2(A+B)}$
d.
$\frac{H}{A-B}$
No explanation saved for this question yet.
Q4mcq
A gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $\frac{C_{p}}{C_{v}}$ of the mixture is
a.
$1.59$
b.
$1.62$
Correct Answer
c.
$1.4$
d.
$1.54$
No explanation saved for this question yet.
Q5mcq
Two simple harmonic motions are represented by the equation $y_{1} = 0.1 sin(100\pi t+ \frac{\pi}{3})$ and $y_{2} = 0.1 cos\pi t$ .
The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is
a.
$-\pi /6$
Correct Answer
b.
$\pi /3$
c.
$-\pi /3$
d.
$\pi /6$
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Q6mcq
Two point charges $+8q$ and $-2q$ are located at $x= 0$ and $x=L$ respectively. The location of a point on the $x$
axis at which the net electric field due to these two point charges is zero is
a.
$2\,L$
Correct Answer
b.
$L/4$
c.
$8\,L$
d.
$4\,L$
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Q7mcq
A body $A$ of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass
$1/3M$ and a body $C$ of mass $2/3M$ . The centre of mass of bodies $B$ and $C$ taken together shifts compared to
that of body $A$ towards
a.
depends on height of breaking
b.
does not shift
Correct Answer
c.
body C
d.
body B
No explanation saved for this question yet.
Q8mcq
Consider a car moving on a straight road with a speed of $100\,m/s$ . The distance at which car can be stopped is
$[\mu _{k} = 0.5]$
a.
$800\,m$
b.
$1000\,m$
Correct Answer
c.
$100\,m$
d.
$400\,m$
No explanation saved for this question yet.
Q9mcq
If $I_{0}$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its
intensity when the slit width is doubled?
a.
$2I_{0}$
b.
$4I_{0}$
c.
$I_{0}$
Correct Answer
d.
$I_{0}/2$
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Q10mcq
A particle is projected from a point $O$ with velocity $u$ at an angle of $60^{\circ }$ with the horizontal. When it is moving
in a direction at right angles to its direction at $O$ , its velocity then is given by
a.
$\frac{u}{3}$
b.
$\frac{u}{2}$
c.
$\frac{2u}{3}$
d.
$\frac{u}{\sqrt{3}}$
Correct Answer
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A $20\,cm$ long capillary tube is dipped in water. The water rises up to $8\,cm$ . If the entire arrangement is put in a
freely falling elevator the length of water column in the capillary tube will be
a.
$8\,cm$
b.
$10\,cm$
c.
$4\,cm$
d.
$20\,cm$
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When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now,
some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6 beats per seconds
are heard. If the frequency of fork 1 is $200\,Hz$ , then what was the original frequency of fork 2 ?
a.
$200\,Hz$
b.
$202\,Hz$
c.
$196\,Hz$
d.
$204\,Hz$
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A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and
voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms
needed to be connected in series with the coil will be
a.
$10^{3}$
b.
$10^{5}$
c.
99995
d.
9995
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An observer moves towards a stationary source of sound, with a velocity one fifth of the velocity of sound.
What is the percentage increase in the apparent frequency?
a.
zero
b.
$0.5%$
c.
$5%$
d.
$20%$
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A charged ball B hangs from a silk thread $S$ which makes an angle $\theta$ with a large charged conducting sheet $P$ ,
as show in the figure. The surface charge density $\sigma$ of the sheet is proportional to
a.
$cos\theta$
b.
$cot\theta$
c.
$sin\theta$
d.
$tan\theta$
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In the circuit, the galvanometer $G$ shows zero deflection. If the batteries $A$ and $B$ have negligible internal
resistance, the value of the resistor $R$ will be
a.
$200\Omega$
b.
$100\Omega$
c.
$500\Omega$
d.
$1000\Omega$
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Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f$ ' respectively. If $A$
takes $m$ sec. more than $B$ and describes ' $n$ ' units more than $B$ in acquiring the same speed then
a.
$(f- f')m^{2} =ff'n$
b.
$(f+f')m^{2} =ff'n$
c.
$\frac{1}{2}(f+f')m=ff'n^{2}$
d.
$(f' - f)n= \frac{1}{2}ff'm^{2}$
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A charged particle of mass $m$ and charge $q$ travels on a circular path of radius $r$ that is perpendicular to a
magnetic field $B$ . The time taken by the particle to complete one revolution is
a.
$\frac{2\pi mq}{B}$
b.
$\frac{2\pi q^{2}B}{m}$
c.
$\frac{2\pi qB}{m}$
d.
$\frac{2\pi m}{qB}$
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Two thin wires rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The
charges on the two rings are $+q$ and $-q$ . The potential difference between the centres of the two rings is
Two concentric coils each of radius equal to $2\pi cm$ are placed at right angles to each other. 3 Ampere and 4
ampere are the currents flowing in each coil respectively. The magnetic induction in Weber $/m^{2}$ at the centre
of the coils will be $(\mu _{0} = 4\pi \times 10^{-7}$ Wb/A-m)
a.
$12 \times 10^{-5}$
b.
$10^{-5}$
c.
$5 \times 10^{-5}$
d.
$7 \times 10^{-5}$
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The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the
emission of a photon with the most energy ?
a.
III
b.
IV
c.
I
d.
II
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The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the
plane of the disc through the centre is
a.
$\frac{1}{4}Mr^{2}$
b.
$\frac{2}{5}Mr^{2}$
c.
$Mr^{2}$
d.
$\frac{1}{2}Mr^{2}$
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An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed.
The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_{1}/F_{2}$
is
a.
$\frac{R_{2}}{R_{1}}$
b.
$2$
$(\frac{R_{1}}{R_{2}})$
c.
1
d.
$\frac{R_{1}}{R_{2}}$
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A block is kept on a frictionless inclined surface with angle of inclination $\alpha$ . The incline is given an
acceleration a to keep the block stationary. Then a is equal to
a.
$g/ tan\alpha$
b.
$g cosec\alpha$
c.
g
d.
$g tan\alpha$
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A fully charged capacitor has a capacitance ' $C$ ' it is discharged through a small coil of resistance wire
embedded in a thermally insulated block of specific heat capacity ' $s$ ' and mass ' $m$ '. If the temperature of the
block is raised by ' $\Delta T$ '. The potential difference $V$ across the capacitance is
a.
$\sqrt{\frac{2mC\Delta T}{s}}$
b.
$\frac{mC\Delta T}{s}$
c.
$\frac{ms\Delta T}{c}$
d.
$\sqrt{\frac{2ms\Delta T}{C}}$
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A car starting from rest accelerates at the rate $f$ through a distance $S$ , then continues at constant speed for time $t$
and then decelerates at the rate $f/2$ to come to rest. If the total distance traversed is $15\,S$ , then
a.
$S =ft$
b.
$S = 1/6ft^{2}$
c.
$S = 1/2ft^{2}$
d.
None of these
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Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources
are $R_{1}$ and $R_{2}(R_{2} >R_{1})$ . If the potential difference across the source having internal resistance $R_{2}$ is zero,
then
a.
$R = R_{2}\times (R_{1}+ R_{2})/R_{2}-R_{1})$
b.
$R = R_{2}-R_{1}$
c.
$R = R_{1}R_{2}/ (R_{1}+ R_{2})$
d.
$R = R_{1}R_{2}/ (R_{2}-R_{1})$
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The change in the value of $g$ at a height ' $h$ ' above the surface of the earth is the same as at a depth 'd' below
the surface of earth. When both ' $d$ ' and ' $h$ ' are much smaller than the radius of earth, then which one of the
following is correct?
a.
$d= \frac{h}{2}$
b.
$d = \frac{3\,h}{2}$
c.
$d = 2\,h$
d.
$d = \,h$
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A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$ . The instantaneous power
delivered to the body as a function time is given by
a.
$\frac{mv^{2}}{\,T^{2}} \cdot t$
b.
$\frac{mv^{2}}{T^{2}} \cdot t^{2}$
c.
$\frac{1}{2} \frac{mv^{2}}{\,T^{2}} \cdot t$
d.
$\frac{1}{2} \frac{mv^{2}}{\,T^{2}} \cdot t^{2}$
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A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $F$ is applied at the
point $P$ parallel to $AB$ , such that the object has only the translational motion without rotation. Find the
location of $P$ with respect to $C$
a.
$\frac{2}{3}\ell$
b.
$\frac{3}{2}\ell$
c.
$\frac{4}{3}\ell$
d.
$\ell$
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A system goes from $A$ to $B$ via two processes I and II as shown in the figure. If $\Delta U_{1}$ and $\Delta U_{2}$ are the changes
in internal energies in the processes I and II respectively, the
a.
$\Delta U_{1} = \Delta U_{2}$
b.
relation between $\Delta U_{1}$ and $\Delta U_{2}$ can not be
determined
c.
$\Delta U_{2} > \Delta U_{1}$
d.
$\Delta U_{2} < \Delta U_{1}$
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A photocell is illuminated by a small bright source placed $1\,m$ away. When the same source of light is placed
$\frac{1}{2}\,m$ away, the number of electrons emitted by photo cathode would
a.
decrease by a factor of 4
b.
increase by a factor of 4
c.
decrease by a factor of 2
d.
increase by a factor of 2
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A mass ' $m$ ' moves with a velocity $v$ and collides inelastically with another identical mass. After collision the
$1^{st\,}$ mass moves with velocity $v/\sqrt{3}$ in a direction perpendicular to the initial direction of motion. Find the
speed of the $2^{nd\,}$ mass after collision
a.
v
b.
$\sqrt{3}v$
c.
$2v/\sqrt{3}$
d.
$v/\sqrt{3}$
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The block of mass $M$ moving on the frictionless horizontal surface collides with a spring of spring constant $K$
and compresses it by length $L$ . The maximum momentum of the block after collision is
a.
$\sqrt{MK}L$
b.
$\frac{KL^{2}}{2M}$
c.
zero
d.
$\frac{ML^{2}}{\,K}$
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Two point white dots are $1\,mm$ apart on a black paper. They are viewed by eye of pupil diameter $3\,mm$ .
Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take
wavelength of light $= 500\,nm$ ]
a.
$5\,m$
b.
$1\,m$
c.
$6\,m$
d.
$3\,m$
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The figure shows a system of two concentric spheres of radii $r_{1}$ and $r_{2}$ and kept at temperatures $T_{1}$ and $T_{2}$
respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to
a.
$\frac{r_{2}-r_{1}}{r_{1}r_{2}}$
b.
$ln(\frac{r_{2}}{r_{1}})$
c.
$\frac{r_{1}r_{2}}{r_{2}-r_{1}}$
d.
$ln (r_{2}- r_{1})$
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A parachutist after bailing out falls $50\,m$ without friction. When parachute opens, it decelerates at $2\,m/s^{2}$ . He
reaches the ground with a speed of $3\,m/s$ . At what height, did he bail out?
a.
$91\,m$
b.
$182\,m$
c.
$293\,m$
d.
$111\,m$
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A bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$ . How much further it will
penetrate before coming to rest assuming that it faces constant resistance to motion?
a.
$3.0\,cm$
b.
$2.0\,cm$
c.
$1.5\,cm$
d.
$1.0\,cm$
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A particle of mass $10\,g$ is kept on the surface of a uniform sphere of mass $100\,kg$ and radius $10\,cm$ . Find the
work to be done against the gravitational force between them to take the particle far away from the sphere (you
may take $G = 6.67 \times 10^{-11}Nm^{2}/kg^{2}$ )
a.
$13.34 \times 10^{-10}\,J$
b.
$3.33 \times 10^{-10}\,J$
c.
$6.67 \times 10^{-9}\,J$
d.
$6.67 \times 10^{-10}\,J$
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The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body
starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half
is given by
a.
$2 sin\phi$
b.
$2 cos\phi$
c.
$2 tan\phi$
d.
$tan\phi$
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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of
the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of
oscillation would
a.
first increase and then decrease to the original
value.
b.
first decreased then increase to the original value.
c.
remain unchanged.
d.
increase towards a saturation value.
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A particle is moving eastwards with a velocity of $5\,m/s$ in 10 seconds the velocity changes to $5\,m/s$
northwards. The average acceleration in this time is
a.
$\frac{1}{\sqrt{2}}\,m/s^{2}$ towards north-east
b.
$\frac{1}{2}\,m/s^{2}$ towards north.
c.
zero
d.
$\frac{1}{\sqrt{2}}\,m/s^{2}$ towards north-west
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In a potentiometer experiment the balancing with a cell is at length $240\,cm$ . On shunting the cell with a
resistance of $2\Omega$ the balancing length becomes $120\,cm$ . The internal resistance of the cell is
a.
$1\Omega$
b.
$0.5\Omega$
c.
$4\Omega$
d.
$2\Omega$
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A spherical ball of mass $20\,kg$ is stationary at the top of a hill of height $100\,m$ . It rolls down a smooth surface
to the ground, then climbs up another hill of height $30\,m$ and finally rolls down to a horizontal base at a height
of $20\,m$ above the ground. The velocity attained by the ball is
a.
$40\,m/s$
b.
$20\,m/s$
c.
$10\,m/s$
d.
$10\,m/s\sqrt{30}$
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A projectile can have the same range $R$ for two angles of projection. If $t_{1}$ and $t_{2}$ be the times of flights in the
two cases, then the product of the two time of flights is proportional to
a.
$R^{2}$
b.
$1/R^{2}$
c.
$1/R$
d.
$R$
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The intensity of gamma radiation from a given source is I. On passing through $36\,mm$ of lead, it is reduced to
$\frac{I}{8}$ . The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be
a.
$6\,mm$
b.
$9\,mm$
c.
$18\,mm$
d.
$12\,mm$
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The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of
$100\,W$ and $200\,V$ lamp when not in use?
a.
$40\Omega$
b.
$20\Omega$
c.
$400\Omega$
d.
$200\Omega$
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A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the
capacitance between any two adjacent plates is C then the resultant capacitance is
a.
$(n-1)C$
b.
$(n+ 1)C$
c.
$C$
d.
$nC$
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A particle of mass $0.3\,kg$ is subjected to a force $F = -kx$ with $k= 15\,N/m$ . What will be its initial
acceleration if it is released from a point $20\,cm$ away from the origin?
a.
$3\,m/s^{2}$
b.
$15\,m/s^{2}$
c.
$5\,m/s^{2}$
d.
$10\,m/s^{2}$
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A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If
an electron is projected along the direction of the fields with a certain velocity then
a.
its velocity will decrease.
b.
its velocity will increase.
c.
it will turn towards right of direction of motion.
d.
it will turn towards left of direction of motion
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The self inductance of the motor of an electric fan is $10H$ . In order to impart maximum power at $50\,Hz$ , it
should be connected to a capacitance of
a.
$C = 4\mu F$
b.
$C = 8\mu F$
c.
$C = 1\mu F$
d.
$C = 2\mu F$
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A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive
index of water is $4/3$ and the fish is $12\,cm$ below the surface, the radius of this circle in $cm$ is
a.
$36\sqrt{7}$
b.
$36/\sqrt{7}$
c.
$36\sqrt{5}$
d.
$4\sqrt{5}$
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A smooth block is released at rest on a $45^{\circ }$ incline and then slides a distance d. The time taken to slide is $n$
times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
a.
$\mu _{k} = 1 - \frac{1}{n^{2}}$
b.
$\mu _{k} =\sqrt{1} - \frac{1}{n^{2}}$
c.
$\mu _{s} = 1 - \frac{1}{n^{2}}$
d.
$\mu _{s} =\sqrt{1} - \frac{1}{n^{2}}$
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One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the
tubes. The magnetic field $B$ is perpendicular to the plane of the figure. if each tube moves towards the other at
a constant speed V, then the emf induced in the circuit in terms of $B, \ell$ and $V$ where $\ell$ is the width of each tube
will be
a.
$B\ell V$
b.
$-B\ell V$
c.
zero
d.
$2B\ell V$
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Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first
solution + 520 mL of 1.2 M second solution. What is the molarity of the final mixture?
a.
1.20 M
b.
1.50 M
c.
1.344 M
d.
2.70 M
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If we consider that $\frac{1}{6}$ , in place of $\frac{1}{12}$ ; mass of carbon atom is taken to be the relative atomic mass unit, the
mass of one mole of a substance will
a.
Decrease twice
b.
Increase two fold
c.
Remain unchanged
d.
Be a function of the molecular mass of the
substance
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An organic compound having molecular mass 60 is found to contain $C = 20%, H = 6.67%$ and $N = 46.67%$
while rest is oxygen. On heating it gives $NH_{3}$ alongwith a solid residue. The solid residue give violet colour
with alkaline copper sulphate solution. The compound is
a.
$CH_{3}NCO$
b.
$CH_{3}CONH_{2}$
c.
$(NH_{2})_{2}CO$
d.
$CH_{3}CH_{2}CONH_{2}$
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Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a
compound if water during the reaction is continuously removed. The compound formed is generally known as
a.
a Schiff’s base
b.
an enamine
c.
an imine
d.
an amine
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Calculate $\wedge ^{\infty }_{HOAc}$ Using appropriate molar conductances of the electrolytes listed above at infinite dilution in
$H_{2}O$ at $25^{\circ }C$
a.
517.2
b.
552.7
c.
390.7
d.
217.5
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An amount of solid $NH_{4}HS$ is placed in a flask already containing ammonia gas at a certain temperature and
$0.50\,atm$ . Pressure. Ammonium hydrogen sulphide decomposes to yield $NH_{3}$ and $H_{2}\,S$ gases in the flask.
When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to $0.84\,atm$ . The
equilibrium constant for $NH_{4}HS$ decomposition at this temperature is
a.
$0.30$
b.
$0.18$
c.
$0.17$
d.
$0.11$
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Consider the reaction: $N_{2}+ 3H_{2} \longrightarrow 2NH_{3}$ carried out at constant temperature and pressure. If $\Delta H$ and $\Delta U$
are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?
a.
$\Delta H = 0$
b.
$\Delta H = \Delta U$
c.
$\Delta H < \Delta U$
d.
$\Delta H > \Delta U$
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Aluminium oxide may be electrolysed at $1000^{\circ }C$ to furnish aluminium metal (Atomic mass $= 27$ amu; 1
Faraday $= 96, 500$ Coulombs). The cathode reaction is $Al^{3+} + 3e^{-} \longrightarrow Al^{\circ }$ To prepare $5.12\,kg$ of
aluminium metal by this method would require
a.
$5.49 \times 10^{7}C$ of electricity
b.
$1.83 \times 10^{7}$ C of electricity
c.
$5.49 \times 10^{4}C$ of electricity
d.
$5.49 \times 10^{1}C$ of electricity
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If the bond dissociation energies of $XY,X_{2}$ and $Y_{2}$ (all diatomic molecules) are in the ratio of 1:1:0.5 and
$\Delta _{t}H$ for the formation of $XY$ is $-200\,kJ\,mole^{-1}$ . The bond dissociation energy of $X_{2}$ will be
a.
$100\,kJ\,mol^{-1}$
b.
$200\,kJ\,mol^{-1}$
c.
$300\,kJ\,mol^{-1}$
d.
None of these
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The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged,
respectively, which of the following statements is NOT correct?
a.
magnesium chloride solution coagulates, the
gold sol more readily than the iron (III)
hydroxide sol.
b.
sodium sulphate solution causes coagulation in
both sols
c.
mixing the sols has no effect
d.
coagulation in both sols can be brought about by
electrophoresis
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The exothermic formation of $ClF_{3}$ is represented by the equation:
$Cl_{2(g)}+ 3\,F_{2(g)} \rightleftharpoons 2ClF_{3(g)}; \Delta rH = -329\,kJ$
Which of the following will increase the quantity of $ClF_{3}$ in an equilibrium mixture of $Cl_{2}, \,F_{2}$ and $ClF_{3}$ ?
a.
Increasing the temperature
b.
Removing $Cl_{2}$
c.
Increasing the volume of the container
d.
Adding $F_{2}$
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Consider an endothermic reaction, $X \longrightarrow Y$ with the activation energies $E_{b}$ and $E_{f}$ for the backward and
forward reactions, respectively. In general
a.
$E_{b} < E_{f}$
b.
$E_{b} >E_{f}$
c.
$E_{b} =E_{f}$
d.
There is no definite relation between $E_{b}$ and $E_{f}$
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An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of
the faces of the cube. The empirical formula for this compound would be
a.
$A\,B$
b.
$A_{2}\,B$
c.
$A\,B_{3}$
d.
$A_{3}\,B$
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$t_{1/4}$ can be taken as the time taken for the concentration of a reactant to drop to $\frac{3}{4}$ of its initial value. If the
rate constant for a first order reaction is $K$ , the $t_{1/4}$ can be written as
a.
$0.10/K$
b.
$0.29/K$
c.
$0.69/K$
d.
$0.75/K$
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In a multi - electron atom, which of the following orbitals described by the three quantum numbers will have
the same energy in the absence of magnetic acid and electric fields? (a) $n= 1,l= 0,m= 0$ (b)
$n= 2,l= 0,m= 0$ (c) $n= 2,l= 1,m= 1$ (d) $n= 3,l= 2,m= 1$ (e) $n= 3,l= 2,m= 0$
a.
(a) and (b)
b.
(b) and (c)
c.
(c) and (d)
d.
(d) and (e)
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For the reaction
$2NO_{2(\,g)} \rightleftharpoons 2NO_{(g)}+ O_{2(\,g)},\,$
$(K_{c} = 1.8 \times 10^{-6}at\,184C)$
$(R = 0.0831\,kJ/(mol. K)$
When $K_{p}$ and $K_{c}$ are compared at $184^{\circ }C$ , it is found that
a.
$K_{p}$ is greater than $K_{c}$
b.
$K_{p}$ is less than $K_{c}$
c.
$K_{p} = K_{c}$
d.
Whether $K_{p}$ is greater than, less than or equal to
$K_{c}$ depends upon the total gas pressure
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p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to
form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the
carboxylic acid is
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The solubility product of a salt having general formula $MX_{2}$ , in water is: $4 \times 10^{-12}$ . The concentration of
$M^{2+}$ ions in the aqueous solution of the salt is
a.
$2.0 \times 10^{-6}M$
b.
$1.0 \times 10^{-4}M$
c.
$1.6 \times 10^{-4}M$
d.
$4.0 \times 10^{-10}M$
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The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter
than $2480\,nm$ is incident on it. The band gap in (eV) for the semiconductor is
a.
$1.1eV$
b.
$2.5eV$
c.
$0.5eV$
d.
$0.7eV$
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Benzene and toluene form nearly ideal solutions. At $20^{\circ }C$ , the vapour pressure of benzene is 75 torr and that of
toluene is 22 torr. The partial vapour pressure of benzene at $20^{\circ }C$ for a solution containing $78\,g$ of benzene
and $46\,g$ of toluene in torr is
a.
50
b.
25
c.
37.5
d.
53.5
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$loga_{n} loga_{n+1} loga_{n+2}$
If $a_{1},a_{2},a_{3}, … ,a_{n}, …$ are in G.P., then the determinant $\Delta = loga_{n+3} loga_{n+4} loga_{n+5}$ is equal to
$loga_{n+6} loga_{n+7} loga_{n+8}$
a.
1
b.
0
c.
4
d.
2
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The locus of a point $P(\alpha ,\beta )$ moving under the condition that the line $y=\alpha x+\beta$ is a tangent to the
hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is
a.
an ellipse
b.
a circle
c.
a parabola
d.
a hyperbola
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If the plane $2ax-3ay+ 4az+ 6 = 0$ passes through the midpoint of the line joining the centres of the
spheres
$x^{2} +y^{2} +z^{2} + 6x-8y-2z= 13\,and\,$
$x^{2} +y^{2} +z^{2} -10x+ 4y-2z= 8$ , then a equals
a.
-1
b.
1
c.
-2
d.
2
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A spherical iron ball $10\,cm$ in radius is coated with a layer of ice of uniform thickness than melts at a rate of
$50\,cm^{3}/min$ . When the thickness of ice is $5\,cm$ , then the rate at which the thickness of ice decreases, is
a.
$\frac{1}{36\pi}cm/min$
b.
$\frac{1}{18\pi}cm/min$
c.
$\frac{1}{54\pi}cm/min$
d.
$\frac{5}{6\pi}cm/ min$
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Let $\alpha$ and $\beta$ be the distinct roots of $ax^{2} +bx+c= 0$ , then $lim_{x\rightarrow \rightarrow \alpha } \frac{1-cos(ax^{2}+bx+c)}{(x-\alpha )^{2}}$ is equal to
a.
$\frac{a^{2}}{2}(\alpha - \beta )^{2}$
b.
0
c.
$-\frac{a^{2}}{2}(\alpha - \beta )^{2}$
d.
$\frac{1}{2}(\alpha - \beta )^{2}$
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A real valued function $f(x)$ satisfies the functional equation $f(x- y) =f(x)f(y) - f(a- x)f(a+y)$
where $a$ is a given constant and $f(0) = 1,f(2a- x)$ is equal to
a.
$-f(x)$
b.
$f(x)$
c.
$f(a) +f(a- x)$
d.
$f(-x)$
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Let $x_{1}, x_{2}, … , x_{n}$ be $n$ observations such that $\sum x^{2}_{i} = 400$ and $\sum x_{i} = 80$ . Then a possible value of $n$ among
the following is
a.
15
b.
18
c.
9
d.
12
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If the equation $a_{n}x^{n} +a_{n-1}x^{n-1} + … … +a_{1}x= 0,a_{1} \neq 0,n\geq 2$ , has a positive root $x=\alpha$ , then the
equation $na_{n}x^{n-1} + (n-1)a_{n-1}x^{n-2} + … . . +a_{1} = 0$ has a positive root, which is
a.
greater than $\alpha$
b.
smaller than $\alpha$
c.
greater than or equal to $\alpha$
d.
equal to $\alpha$
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Let $f(x)$ be a non-negative continuous function such that the area bounded by the curve $y=f(x),x$ -axis and
the ordinates $x= \frac{\pi}{4}$ and $x=\beta > \frac{\pi}{4}$ is $(\beta sin\beta + \frac{\pi}{4} cos\beta + \sqrt{2}\beta )$ . Then $f(\frac{\pi}{2})$ is
a.
$(\frac{\pi}{4} + -1\sqrt{2} )$
b.
$(\frac{\pi}{4} - + 1\sqrt{2} )$
c.
$(1 - \frac{\pi}{4} - \sqrt{2})$
d.
$(1 - \frac{\pi}{4} + \sqrt{2})$
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If the letters of word SACHIN are arranged in all possible ways and these words are written out as in
dictionary, then the word SACHIN appears at serial number
a.
601
b.
600
c.
603
d.
602
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If a vertex of a triangle is $(1, 1)$ and the mid-points of two sides through this vertex are $(-1, 2)$ and $(3, 2)$ ,
then the centroid of the triangle is
a.
$(-1, \frac{7}{3})$
b.
$(\frac{-1}{3}, \frac{7}{3})$
c.
$(1, \frac{7}{3} )$
d.
$(\frac{1}{3} , \frac{7}{3})$
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Three houses are available in a locality. Three persons apply for the houses. Each applies for one house
without consulting others. The probability that all the three apply for the same house is
a.
$\frac{2}{9}$
b.
$\frac{1}{9}$
c.
$\frac{8}{9}$
d.
$\frac{7}{9}$
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In a triangle $ABC$ , let $\angle C = \frac{\pi}{2}$ . If $r$ is the inradius and $R$ is the circumradius of the the triangle $ABC$ , then
$2(r+R)$ equals
a.
$b+c$
b.
$a+b$
c.
$a+b+c$
d.
$c+a$
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If $x=\sum ^{\infty }_{n=0} a^{n},y=\sum ^{\infty }_{n=0} b^{n},z=\sum ^{\infty }_{n=0} c^{n}$ where $a,b,c$ are in A.P. and $|a| < 1, |b| < 1, |c| < 1$ , then $x,y,z$
are in
a.
G.P.
b.
A.P.
c.
Arithmetic - Geometric Progression
d.
H.P.
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Let $f : (-1, 1) \rightarrow \rightarrow B$ , be a function defined by $f(x) = tan^{-1} \frac{2x}{1-x^{2}}$ , then $f$ is both one-one and onto when $B$
is the interval
a.
$(0, \frac{\pi}{2})$
b.
$[0, \frac{\pi}{2} )$
c.
$[-\frac{\pi}{2}, \frac{\pi}{2}]$
d.
$(\frac{\pi}{2}, \frac{\pi}{2})$
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The differential equation representing the family of curves $y^{2} = 2c(x+ \sqrt{c})$ , where $c> 0$ , is a parameter, is
of order and degree as follows:
a.
order 1 , degree 2
b.
order 1, degree 1
c.
order 1, degree 3
d.
order 2, degree 2
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The distance between the line $\vec{r}= 2\hat{i}-2\hat{j}+ 3\hat{k}+\lambda (\hat{i}- \hat{j}+ 4\hat{k})$ and the plane $\vec{r}\cdot (\hat{i}+ 5\hat{j}+ \hat{k}) = 5$ is
a.
$\frac{10}{9}$
b.
$\frac{10}{3\sqrt{3}}$
c.
$\frac{3}{10}$
d.
$\frac{10}{3}$
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If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$ , then
$------_{(1)}_{(2)}$
$P\vec{A}+ P\vec{B}= 2P\vec{C} P\vec{A}+ P\vec{B}+ 2P\vec{C}= 0$
$---_{(3)}_{(4) None of these}$
$P\vec{A}+ P\vec{B}+ P\vec{C}= 0$
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If the coefficients of $r$ th, $(r+ 1)$ th and $(r+ 2)$ th terms in the binomial expansion of $(1+y)^{m}$ are in A.P.,
then $m$ and $r$ satisfy the equation
a.
$m^{2} - m(4r-1) + 4r^{2} -2 = 0$
b.
$m^{2} - m(4r+ 1) + 4r^{2} + 2 = 0$
c.
$m^{2} - m(4r+ 1) + 4r^{2} -2 = 0$
d.
$m^{2} - m(4r-1) + 4r^{2} + 2 = 0$
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The line parallel to the $x$ -axis and passing through the intersection of the lines ax $+ 2by+ 3b= 0$ and
$bx-2ay-3a= 0$ , where $(a,b) \neq (0, 0)$ is
a.
below the $x$ -axis at a distance of $\frac{3}{2}$ from it
b.
below the $x$ -axis at a distance of $\frac{2}{3}$ from it
c.
above the $x$ -axis at a distance of $\frac{3}{-}$ from it
d.
above the $x$ -axis at a distance of $\frac{2}{3}$ from it
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If the pair of lines $ax^{2} + 2(a+b)xy+by^{2} = 0$ lie along diameters of a circle and divide the circle into four
sectors such that the area of one of the sectors is thrice the area of another sector then
a.
$3a^{2} -10ab+ 3b^{2} = 0$
b.
$3a^{2} -2ab+ 3b^{2} = 0$
c.
$3a^{2} + 10ab+ 3b^{2} = 0$
d.
$3a^{2} + 2ab+ 3b^{2} = 0$
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If the coefficient of $x^{7}$ in $[ax^{2} +(\frac{1}{bx})]^{11}$ equals the coefficient of $x^{-7}$ in $[ax^{2} - (\frac{1}{bx} )]^{11}$ , then $a$ and $b$
satisfy the relation
a.
$a- b= 1$
b.
$a+b= 1$
c.
$\frac{a}{b} = 1$
d.
$ab= 1$
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The resultant $R$ of two forces acting on a particle is at right angles to one of them and its magnitude is one
third of the other force. The ratio of larger force to smaller one is
a.
$2 : 1$
b.
$3 : \sqrt{2}$
c.
$3 : 2$
d.
$3 : 2\sqrt{2}$
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$| |$
$| |$
A function is matched below against an interval where it is supposed to be increasing. Which of the following
pairs is incorrectly matched? $Interval\rightarrow \rightarrow Function$
ABC is a triangle. Forces $\vec{P}, \vec{Q}, \vec{R}$ acting along $IA,IB$ and $IC$ respectively are in equilibrium, where $I$ is the
incentre of $\triangle ABC$ . Then $P :Q:R$ is
a.
$sinA: sinB: sinC$
b.
$sin \frac{A}{2} : sin \frac{B}{2} : sin \frac{C}{2}$
c.
$cos \frac{A}{2} : cos \frac{B}{2} : cos \frac{C}{2}$
d.
$cosA: cosB: cosC$
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$-$
Let $A$ and $B$ be two events such that $P(A\cup B) = \frac{1}{6},P(A\cap B) = \frac{1}{4}$ and $P( A-) = \frac{1}{4}$ , where $A-$ stands for
complement of event $A$ . Then events $A$ and $B$ are
a.
equally likely and mutually exclusive
b.
equally likely but not independent
c.
independent but not equally likely
d.
mutually exclusive and independent
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Let $a,b$ and $c$ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}, \hat{i}+ \hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a
plane, then $c$ is
a.
the Geometric Mean of $a$ and $b$
b.
the Arithmetic Mean of $a$ and $b$
c.
equal to zero
d.
the Harmonic Mean of $a$ and $b$
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If the circles $x^{2} +y^{2} + 2ax+cy+a= 0$ and $x^{2} +y^{2} -3ax+dy-1 = 0$ intersect in two distinct points $P$
and $Q$ then the line $5x+$ by $-a= 0$ passes through $P$ and $Q$ for
a.
exactly one value of a
b.
no value of a
c.
infinitely many values of a
d.
exactly two values of a
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A lizard, at an initial distance of $21\,cm$ behind an insect, moves from rest with an acceleration of $2\,cm/s^{2}$ and
pursues the insect which is crawling uniformly along a straight line at a speed of $20\,cm/s$ . Then the lizard
will catch the insect after
a.
$20\,s$
b.
$1\,s$
c.
$21\,s$
d.
$24\,s$
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The parabolas $y^{2} = 4x$ and $x^{2} = 4y$ divide the square region bounded by the lines $x = 4,y= 4$ and the
coordinate axes. If $S_{1},S_{2},S_{3}$ are respectively the areas of these parts numbered from top to bottom; then
$S_{1} : S_{2} : S_{3}$ is
a.
$1 : 2 : 1$
b.
$1 : 2 : 3$
c.
$2 : 1 : 2$
d.
$1 : 1 : 1$
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If non-zero numbers $a,b,c$ are in H.P., then the straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed
point. That point is
a.
$(-1, 2)$
b.
$(-1, -2)$
c.
$(1, -2)$
d.
$(1, - \frac{1}{2})$
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If the angle $\theta$ between the line $\frac{x+1}{1} = \frac{y-1}{2} = \frac{z-2}{2}$ and the plane $2x- y+ \sqrt{\lambda}z+ 4 =$ 0 is such that
$sin\theta = \frac{1}{3}$ the value of $\lambda$ is
a.
$\frac{5}{3}$
b.
$\frac{-3}{5}$
c.
$\frac{3}{4}$
d.
$\frac{-4}{3}$
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Let $f :R\rightarrow \rightarrow R$ be a differentiable function having $f(2) = 6,f'(2) =( \frac{1}{48})$ . Then $lim_{x\rightarrow 2\rightarrow } \int _{6}^{f(x)} \frac{4t^{3}}{x-2}dt$ equals
a.
24
b.
36
c.
12
d.
18
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If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then $[\lambda (\vec{a}+ \vec{b})\lambda ^{2}\vec{b}\lambda \vec{c}]= [\vec{a}\vec{b}+ \vec{c}\vec{b}]$ for
a.
exactly one value of $\lambda$
b.
no value of $\lambda$
c.
exactly three values of $\lambda$
d.
exactly two values of $\lambda$
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