An $HCl$ molecule has rotational, translational and vibrational motions. If the rms velocity of $HCl$ molecules in
$-$
its gaseous phase is , m is its mass and ν $k_{B}$ is Boltzmann's constant, then its temperature will be:
a.
$-^{\,2}$
$\frac{mν}{5k_{B}}$
b.
$-^{\,2}$
$\frac{mν}{6k_{B}}$
c.
$-^{\,2}$
$\frac{mν}{3k_{B}}$
Correct Answer
d.
$-^{\,2}$
$\frac{mν}{7k_{B}}$
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Q2mcq
An $NPN$ transistor is used in common emitter configuration as an amplifier with $1\,k\Omega$ load resistance. Signal
voltage of $10\,mV$ is applied across the base-emitter. This produces a $3\,mA$ change in the collector current and
$15\,$ $\mu$ $A\,$ change in the base current of the amplifier. The input resistance and voltage gain are:
a.
$0.33\,k\Omega , \,1.5$
b.
$0.67\,k\Omega , \,300$
Correct Answer
c.
$0.67\,k\Omega , \,200$
d.
0.33 k $\Omega , \,300$
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Q3mcq
Taking the wavelength of first Balmer line in hydrogen spectrum $(n = 3\,$ to $n = 2)$ as $660\,nm$ , the
wavelength of the $2^{nd}$ Balmer line $(n\, = \,4\,$ to $\,n\, = \,2)$ will be :
a.
$889.2\,nm$
b.
$488.9\,nm$
Correct Answer
c.
$388.9\,nm$
d.
$642.7 nm$
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Q4mcq
A uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $( \frac{1}{n})^{th}$ part is hanging
below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:
a.
$\frac{MgL}{2n^{2}}$
Correct Answer
b.
$\frac{MgL}{n^{2}}$
c.
$nMgL$
d.
$\frac{2MgL}{n^{2}}$
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Q5mcq
A signal $Acos$ $\omega$ $t$ is transmitted using ν $_{0}sin$ $\omega$ $_{0}t$ as carrier wave. The correct amplitude modulated $\,(AM)$ signal
is:
The magnetic field of a plane electromagnetic wave is given by $\vec{B}= B_{0}ˆi[cos(kz -$ $\omega$ $t)] + B_{1}ˆjcos(kz +$ $\omega$ $t)$ ,
where $B_{0} = 3 \times 10^{-5}\,T$ and $B_{1} = 2 \times 10^{-6}\,T$ . The $RMS$ value of the force experienced by a stationary charge
$Q = 10^{-4}\,C$ at $z = 0$ is closest to
a.
$0.1\,N$
b.
$0.9\,N$
c.
$3 \times 10^{-2}\,N$
d.
$0.6\,N$
Correct Answer
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Q7mcq
A system of three charges are placed as shown in the figure:
If $D\, >> \,d,$ the potential energy of the system is best given by:
If $'M'$ is the mass of water that rises in a capillary tube of radius $'r'$ , then mass of water which will rise in a
capillary tube of radius $'2r'$ is:
a.
$4\,M$
b.
$2\,M$
Correct Answer
c.
$\frac{M}{2}$
d.
$M$
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Q9mcq
A capacitor with capacitance $5\,$ $\mu$ $F$ is charged to $5\,$ $\mu$ $C$ . If the plates are pulled apart to reduce the capacitance
to $2\,$ $\mu$ $F$ , how much work is done?
a.
$6.25 \times 10^{-6}\,J$
b.
$2.55 \times 10^{-6}\,J$
c.
$2.16 \times 10^{-6}\,J$
d.
$3.75 \times 10^{-6}\,J$
Correct Answer
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Q10mcq
A rectangular coil (Dimension $5\,cm\, \times \,2.5\,cm$ ) with $100$ turns, carrying a current of $\,3\,A$ in the clock-wise
direction, is kept centered at the origin and in the $X -Z$ plane. A magnetic field of $1\,T$ is applied along
$X -axis$ . If the coil is tilted through $45^{\circ}$ about $Z -axis$ , then the torque on the coil is:
a.
$0.42\,N\,m$
b.
$\,0.55\,N\,m$
c.
$0.38\,N\,m$
d.
$0.27\,N\,m$
Correct Answer
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A moving coil galvanometer has resistance $50\,\Omega$ and it indicates full deflection at $4\,mA$ current. A voltmeter is
made using this galvanometer and a $5\,k\Omega$ resistance. The maximum voltage, that can be measured using this
voltmeter, will be close to:
a.
$40\,V$
b.
$15\,V$
c.
$20\,V$
d.
$10\,V$
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A simple pendulum oscillating in air has period $T$ . The bob of the pendulum is completely immersed in a non-
viscous liquid. The density of the liquid is $\frac{1}{16}th$ of the material of the bob. If the bob is inside liquid all the
time, its period of oscillation in this liquid is:
a.
$2T\sqrt{\frac{1}{10}}$
b.
$2T\sqrt{\frac{1}{14}}$
c.
$4T\sqrt{\frac{1}{15}}$
d.
$4T\sqrt{\frac{1}{14}}$
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A body of mass $2\,kg$ makes an elastic collision with a second body at rest and continues to move in the original
direction but with one fourth of its original speed. What is the mass of the second body?
a.
$1.8\,kg$
b.
$1.2\,kg$
c.
$1.0\,kg$
d.
$1.5\,kg$
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A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and
mass $2M.$ The gravitational field at distance $3a$ from the centre will be:
a.
$\frac{GM}{9a^{2}}$
b.
$\frac{GM}{3a^{2}}$
c.
$\frac{2GM}{3a^{2}}$
d.
$\frac{2GM}{9a^{2}}$
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A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a
function of , where is the angle by which it has rotated, is given as $\theta$ $\theta$ $k$ $\theta$ $^{2}$ . If its moment of inertia is $I$ then the
angular acceleration of the disc is:
a.
$\frac{2k}{I}$ $\theta$
b.
$\frac{k}{2I}$ $\theta$
c.
$\frac{k}{4I}$ $\theta$
d.
$\frac{k}{I}$ $\theta$
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The total number of turns and cross-section area in a solenoid is fixed. However, its length $L$ is varied by
adjusting the separation between windings. The inductance of solenoid will be proportional to:
a.
$L$
b.
$\frac{1}{L^{2}}$
c.
$\frac{1}{L}$
d.
$L^{2}$
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In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,kg$ and
$(0.10 \pm 0.01)\,m,$ respectively. The error in the measurement of density is:
a.
$0.31$
b.
$0.10\,$
c.
$0.07\,$
d.
$0.01$
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$-$
The electric field of light wave is given as $\,\vec{E}\, = 10^{-3} cos( \frac{2$\pi$x}{5\times 10^{-7}} -2$ $\pi$ $\times 6 \times 10^{14}\,t)xˆ\frac{N}{C}$ . This light falls on a
metal plate of work function $2\,eV$ . The stopping potential of the photo-electrons is:
Given, $E$ (in $eV$ ) $= \frac{12375}{$\lambda$(in\,Å)}$
a.
$0.72\,V$
b.
$2.0\,V$
c.
$2.48\,V$
d.
$0.48\,V$
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A rigid square loop of side $‘a’$ and carrying current $I_{2}$ is lying on a horizontal surface near a long current $I_{1}$
carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:
a.
Attractive and equal to $\frac{$\mu$_{0}I_{1}I_{2}}{3$\pi$}$
b.
Repulsive and equal to $\frac{$\mu$_{0}I_{1}I_{2}}{4$\pi$}$
c.
Repulsive and equal to $\frac{$\mu$_{0}I_{1}I_{2}}{2$\pi$}$
d.
Zero
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The pressure wave, $P = 0.01 sin[1000t -3x]N\,m^{-2}$ , corresponds to the sound produced by a vibrating blade
on a day when atmospheric temperature is $0^{\circ}C$ . On some other day when temperature is $T$ , the speed of
sound produced by the same blade and at the same frequency is found to be $336\,m\,s^{-1}$ . Approximate value of
$T$ is:
a.
$12^{\circ}\,C$
b.
$15^{\circ}\,C$
c.
$4^{\circ}\,C$
d.
$11^{\circ}\,C$
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For given gas at $1\,atm$ pressure, $rms\,$ speed of the molecules is $200\,m/s$ at $127^{\circ}C.$ At $2\,atm$ pressure and at
$227^{\circ}\,C,$ the $rms$ speed of the molecules will be:
a.
$100\,m/s$
b.
$80\,m/s$
c.
$80\,m/s\sqrt{5}$
d.
$100\,m/s\sqrt{5}$
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A concave mirror for face viewing has a focal length of $0.4\,m$ . The distance at which you hold the mirror from
your face in order to see your image upright with a magnification of $5$ is
a.
$1.60\,m$
b.
$0.16\,m$
c.
$0.32\,m$
d.
$0.24\,m$
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A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance
between $E$ and $C$ is:
( $E$ is mid-point of arm $CD$ )
a.
$R$
b.
$\frac{7}{64} R$
c.
$\frac{1}{16}R$
d.
$\frac{3}{4}R$
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The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i)
a ring of radius $R,$ (ii) a solid cylinder of radius $\frac{R}{2}$ and (iii) a solid sphere of radius $\frac{R}{4}.$ If, in each case, the
speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:
a.
$2 : 3 : 4$
b.
$20 : 15 : 14$
c.
$4 : 3 : 2$
d.
$14 : 15 : 20$
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The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of
thickness t and refractive index is put in front of one of the slits, the central maximum gets shifted by a$\mu$
distance equal to n fringe width. If the wavelength of light used is then $\lambda$ $t$ will be:
a.
$\frac{D$\lambda$}{a($\mu$-1)}$
b.
$\frac{n$\lambda$}{($\mu$-1)}$
c.
$\frac{2n$\lambda$}{($\mu$-1)}$
d.
$\frac{2D$\lambda$}{a($\mu$-1)}$
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Following figure shows two processes $A$ and $B\,$ for a gas. If $\Delta Q_{A}$ and $\Delta Q_{B}$ are the amount of heat absorbed
by the system in two cases, and $\Delta U_{A}$ and $\Delta U_{B}$ are changes in internal energies, respectively, then:
A string is clamped at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave
is $y= 0.3 sin(0.157x)\,cos(200$ $\pi$ $t)$ . The length of the string is
(All quantities are in $SI$ units.)
a.
$20\,m$
b.
$60\,m$
c.
$40\,m$
d.
$80\,m$
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The stream of a river is flowing with a speed of $2\,km\,h^{-1}$ . A swimmer can swim at a speed of $4\, km \,h^{-1}$ . The
direction of the swimmer with respect to the flow of the river, to cross the river straight, is
a.
$150^{\circ}$
b.
$90^{\circ}$
c.
$120^{\circ}$
d.
$60^{\circ}$
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The osmotic pressure of a dilute solution of an ionic compound $XY$ in water is four times that of a solution
$0.01\,M\,BaCl_{2}$ in water. Assuming complete dissociation of the given ionic compounds in water, the
concentration of $XY$ ( $in\,mol\,L^{-1}$ ) in solution is
a.
$4 \times 10^{-2}$
b.
$16 \times 10^{-4}$
c.
$4 \times 10^{-4}$
d.
$6 \times 10^{-2}$
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Match the catalysts (Column $I$ ) with products (Column $II$ )
Column I Column II
Catalyst Product
A. $V_{2}O_{5}$ P. Polyethylene
B. $TiCl_{4}/Al(Me)_{3}$ Q. Ethanal
C. $PdCl_{2}$ R. $H_{2}SO_{4}$
D. Iron Oxide S. $NH_{3}$
a.
$(A) -(S); \,(B) -(R); \,(C) -(Q); \,(D) -(P)$
b.
$(A) -(R); \,(B) -(S); \,(C) -(P); \,(D) -(Q)$
c.
$(A) -(Q); \,(B) -(R); \,(C) -(P); \,(D) -(S)$
d.
$(A) -(R); \,(B) -(P); \,(C) -(Q); \,(D) -(S)$
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$- = - -$
For any given series of spectral lines of atomic hydrogen, let $\Delta v v_{max}- v_{min}$ be the difference in
maximum and minimum wave number in $cm^{-1}$ .
$- -$
The ratio $\Delta v_{Lyman}/\Delta v_{Balmar}$ is
a.
$5 : 4$
b.
$27 : 5$
c.
$4 : 1$
d.
$9 : 4$
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For a reaction,
$N_{2}(g) + 3H_{2}(g)\longrightarrow 2NH_{3}(g)$ , identify di-hydrogen $(H_{2})$ as a limiting reagent in the following reaction
mixtures.
a.
$28\,g\,of\,N_{2}+ 6\,g\,of\,H_{2}$
b.
$35\,g\,of\,N_{2}+ 8\,g\,of\,H_{2}$
c.
$56\,g\,of\,N_{2}+ 10\,g\,of\,H_{2}$
d.
$14\,g\,of\,N_{2}+ 4\,g\,of\,H_{2}$
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The organic compound that gives following qualitative analysis is:
Test Inference
$(a) Dil. HCl$ Insoluble
$(b) NaOH\,solution$ Soluble
$(c) Br_{2}/water$ Decolourization
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The standard Gibbs energy for the given cell reaction in $kJ\,mol^{-1}$ at $298\,K$ is:
$Zn(s) + Cu^{2+}(aq)\longrightarrow Zn^{2+}(aq) + Cu(s)$ ,
$E^{0} = 2\,V\,at\,298\,K$
$(Faraday's\,constant\,, F = 96000\,C\,mol^{-1})$
a.
$-192$
b.
$192$
c.
$384$
d.
$-384$
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Liquid $M$ and liquid $N$ form an ideal solution. The vapour pressures of pure liquids $M$ and $N$ are $450$ and
$700\,mmHg,$ respectively, at the same temperature. Then correct statements is:
( $x_{M} = Mole\,fraction\,of\,'M'\,in\,solution;$
$x_{N} = Mole\,fraction\,of\,'N'in\,solution;$
$y_{M} = Mole\,fraction\,of\,'M'\,in\,vapour\,phase;$
$y_{N} = Mole\,fraction\,of\,'N'\,in\,vapour\,phase;$ )
a.
$\frac{x_{M}}{x_{N}} > \frac{y_{M}}{y_{N}}$
b.
$\frac{x_{M}}{x_{N}} = \frac{y_{M}}{y_{N}}$
c.
$\frac{x_{M}}{x_{N}} < \frac{y_{M}}{y_{N}}$
d.
$(x_{M}-y_{M}) < (x_{N}-y_{N})$
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Consider the van der Waal's constants, $a$ and $b,$ for the following gases.
Gas $Ar Ne Kr Xe$
$a/(atm\,dm^{6}\,mol^{-2}) 1.3 0.2 5.1 4.1$
$b/(10^{-2}\,dm^{3}\,mol^{-1}) 3.2 1.7 1.0 5.0$
Which gas is expected to have the highest critical temperature?
a.
$Kr$
b.
$Ar$
c.
$Xe$
d.
$Ne$
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The given plots represent the variation of the concentration of a reactant $R$ with time for two different
reactions $(i)\, and \,(ii)$ . The respective orders of the reaction are
(i)
(ii)
a.
$1,1$
b.
$0,1$
c.
$1,0$
d.
$0,2$
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Aniline dissolved in dilute $HCl$ is reacted with sodium nitrite at $0^{\circ}C$ . This solution was added dropwise to a
solution containing an equimolar mixture of aniline and phenol in dilute $HCl$ . The structure of the major
product is
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Let $\sum ^{10}_{k=1} f(a+k) = 16(2^{10}-1),$ where the function $f$ satisfies $f(x+y) =f(x)f(y)$ for all natural numbers
$x, \,y$ and $f(1) = 2.$ Then the natural number $'a'$ is:
a.
$3$
b.
$16$
c.
$4$
d.
$2$
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$y+ 1 \alpha \beta$
Let $\alpha$ and $\beta$ be the roots of the equation $x^{2} +x+ 1 = 0.$ Then for $y\neq 0$ in $R, \, \alpha y+\beta 1$ is equal
$\beta 1 y+\alpha$
to
a.
$y^{3}$
b.
$y(y^{2}-1)$
c.
$y^{3}-1$
d.
$y(y^{2}-3)$
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If the line, $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{4}$ meets the plane, $x+ 2y+ 3z= 15$ at a point $P,$ then the distance of $P$ from the
origin is,
a.
$2\sqrt{5}$
b.
$\frac{9}{2}$
c.
$\frac{\sqrt{5}}{2}$
d.
$\frac{7}{2}$
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Let $S$ be the set of all values of $x$ for which the tangent to the curve $y=f(x) =x^{3} - x^{2} -2x$ at $(x, \,y)$ is
parallel to the line segment joining the points $(1, \,f(1))$ and $(-1, \,f(-1)),$ then $S$ is equal to
a.
${-\frac{1}{3} , -1}$
b.
${-\frac{1}{3} , 1}$
c.
${\frac{1}{3}, 1}$
d.
${ \frac{1}{3}, -1}$
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Four persons can hit a target correctly with probabilities $\frac{1}{2} , \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target
independently, then the probability that the target would be hit, is
a.
$\frac{25}{192}$
b.
$\frac{7}{32}$
c.
$\frac{1}{192}$
d.
$\frac{25}{32}$
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If $f(x)$ is a non-zero polynomial of degree four, having local extreme points at $x= \,-1, \,0, \,1;$ then the set
$S = {x\in R\, :f(x) =f(0)}$ contains exactly
a.
Two irrational and two rational numbers
b.
Four rational numbers
c.
Two irrational and one rational number
d.
Four irrational numbers
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If a tangent to the circle $x^{2} +y^{2} = 1$ intersects the coordinate axes at distinct points $P$ and $Q,$ then the locus of
the mid-point of $PQ$ is:
a.
$x^{2} +y^{2}-16x^{2}y^{2} = 0$
b.
$x^{2} +y^{2}-4x^{2}y^{2} = 0$
c.
$x^{2} +y^{2}-2xy= 0$
d.
$x^{2} +y^{2}-2x^{2}y^{2} = 0$
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A plane passing though the points $(0, \, -1,\,0)$ and $(0, \,0,\,1)$ and making an angle $\frac{\pi}{4}$ with the plane
$y-z+ 5 = 0,$ also passes through the point
a.
$(\sqrt{2}, \, -1,\,4)$
b.
$(\sqrt{2}, \,1,\,4)$
c.
$(-, \, -1, \, -4\sqrt{2} )$
d.
$(-, \,1, \, -4\sqrt{2} )$
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A committee of $11$ member is to be formed from $8$ males and $5$ females. If $m$ is the number of ways the
committee is formed with at least $6$ males and $n$ is the number of ways the committee is formed with at least $3$
females, then:
a.
$m=n= 68$
b.
$n= \,m\,-8$
c.
$m=n= 78$
d.
$m+n= 68$
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$\frac{\sqrt{2}cosx-1}{cotx-1}, \,x\neq \frac{\pi}{4}$
If the function $f$ defined on $(\frac{\pi}{6}, \frac{\pi}{3})$ by $f(x) ={$ is continuous, then $k$ is equal to
$k, \,\,\,\,\,\,\,\,\,\,\,\,\,x= \frac{\pi}{4}$
a.
$\frac{1}{2}$
b.
$1$
c.
$2$
d.
$\frac{1}{\sqrt{2}}$
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$| |$
If the tangent to the curve, $y=x^{3} +ax-b$ at the point $(1, \,-5)$ is perpendicular to the line, $-x+y+ 4 = 0,$
then which one of the following points lies on the curve?
a.
$(2, \,-2)$
b.
$(2, \,-1)$
c.
$(-2,\,1)$
d.
$(-2,\,2)$
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Let the sum of the first $n$ terms of a non-constant $A.P. , \,a_{1}, \,a_{2}, \,a_{3}, \,. . . . , \,a_{n}$ be $50n+ \frac{n(n-7)}{2} A,$ where $A$ is
a constant. If $d$ is the common difference of this $A.P.$ , then the ordered pair $(d, \,a_{50})$ is equal to
a.
$(50, \,50 + 46A)$
b.
$(A, \,50 + 45A)$
c.
$(50,\,50 + 45A)$
d.
$(A, \,50 + 46A)$
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