One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room
temperature, $27^{o}C$ . The magnitude of work done on the gas will be:
a.
$300R$
b.
$300Rln 2$
Correct Answer
c.
$300 ln 6$
d.
$300Rln 7$
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Q2mcq
Light of wavelength $550\, nm$ falls normally on a slit of width $22.0 \times 10^{-5}\, cm$ . The angular position of the
second minima from the central maximum will be (in radians):
a.
$\frac{\pi}{4}$
b.
$\frac{\pi}{8}$
c.
$\frac{\pi}{12}$
d.
$\frac{\pi}{6}$
Correct Answer
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Q3mcq
A given object takes $n$ times more time to slide down a $45^{o}$ rough inclined plane as it takes to slide down a
perfectly smooth $45^{o}$ incline. The coefficient of kinetic friction between the object and the incline is:
a.
$\sqrt{1} - \frac{1}{n^{2}}$
b.
$1 - \frac{1}{n^{2}}$
Correct Answer
c.
$\frac{1}{2-n^{2}}$
d.
$\sqrt{\,} \frac{1}{1-n^{2}}$
No explanation saved for this question yet.
Q4mcq
A body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$ . At some instant, it splits
into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$ . And the other mass, in a circular
orbit of radius $\frac{3R}{2}.$ The difference between the final and the initial total energies is
a.
$+ \frac{Gm}{6R}$
b.
$- \frac{Gm}{2R}$
c.
$- \frac{Gm}{6R}$
Correct Answer
d.
$\frac{Gm}{2R}$
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Q5mcq
The relative error in the determination of the surface area of a sphere is $\alpha$ . The relative error in the
determination of its volume is
a.
$\frac{3}{2}$ $\alpha$
Correct Answer
b.
$\frac{2}{3}$ $\alpha$
c.
$\alpha$
d.
$\frac{5}{2}$ $\alpha$
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Q6mcq
Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de brogile
wavelengths are $\lambda _{1}$ and $\lambda _{2}$ , their de brogile wavelength in the frame of reference attached to their centre of
mass is:
A Carnot's engine works like a refrigerator between $250\,K$ and $300\,K$ . It receives $500\, cal$ heat from the
reservoir at a lower temperature. The amount of work done in each cycle to operate the refrigerator is,
a.
$772\,J$
b.
$420\,J$
Correct Answer
c.
$2100\,J$
d.
$2520\,J$
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Q8mcq
A charge $Q$ is placed at a distance $^{a}/_{2}$ above the centre of a square surface of side length $a$ . The electric flux
through the square surface due to the charge would be?
a.
$\frac{Q}{6\epsilon _{0}}$
Correct Answer
b.
$\frac{Q}{2\epsilon _{0}}$
c.
$\frac{Q}{3\epsilon _{0}}$
d.
$\frac{Q}{\epsilon _{0}}$
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Q9mcq
In a meter bridge as shown in the figure, it is given that resistance $Y = 12.5\,\Omega$ and that the balance is obtained
at a distance $39. 5\, cm$ from end $A$ (by jockey $J$ ). After interchanging the resistances $X$ and $Y$ a new balance
point is found at a distance $l_{2}$ from end $A$ . What are the values of $X$ (in $\Omega$ and $l_{2}$ ?
a.
$19. 15\,\Omega$ and $39. 5\, cm$
b.
$8. 16\,\Omega$ and $60. 5\, cm$
Correct Answer
c.
$8. 16\,\Omega$ and $39. 5\, cm$
d.
$19. 15\,\Omega$ and $60. 5\, cm$
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Q10mcq
Take the mean distance of the moon and the sun from the earth to be $0.4 \times 10^{6}\, km$ and $150 \times 10^{6}\, km$ ,
respectively. Their masses are $\,8 \times 10^{22} kg$ and $2 \times 10^{30} kg$ , respectively. The radius of the earth is $6400\, km$ .
Let $\Delta F_{1}$ be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and
$\Delta F_{2}$ be the difference in the forces exerted by the sun at the nearest and farthest points on the earth. Then, the
number closest to $\frac{\Delta F_{1}}{\Delta F_{2}}$ is,
a.
$6$
b.
$10^{-2}$
c.
$2$
Correct Answer
d.
$0. 6$
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A Helmholtz coil has a pair of loops, each with $N$ turns and radius $R$ . They are placed coaxially at distance $R$
and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at
$P,$ midway between the centres $A$ and $C,$ is given by [Refer to figure given below]:
a.
$\frac{8N\mu _{0}I}{5^{1/2}R}$
b.
$\frac{4N\mu _{0}I}{5^{3/2}R}$
c.
$\frac{4N\mu _{0}I}{5^{1/2}R}$
d.
$\frac{8N\mu _{0}I}{5^{3/2}R}$
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An automobile, traveling at $40\, km \,h^{-1}$ , can be stopped at a distance of $40\,m$ by applying brakes. If the same
automobile is traveling at $80\, km \,h^{-1}$ , the minimum stopping distance in metres is (Assume no skidding):
a.
$150\,m$
b.
$100\,m$
c.
$75\,m$
d.
$160\,m$
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In a screw gauge, $5$ complete rotations of the screw cause it to move a linear distance of $0. 25\, cm$ . There are
$100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main
scale divisions and $30$ circular scale divisions. Assuming negligible error, the thickness of the wire is
a.
$0. 4300\, cm$
b.
$0. 3150\, cm$
c.
$0. 0430\, cm$
d.
$0. 2150\, cm$
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A plano-convex lens becomes an optical system of $28\, cm$ focal length when its plane surface is silvered and
illuminated from left to right as shown in fig $-A$ If the same lens is instead silvered on the curved surface and
illuminated from another side as in fig- $B$ , it acts as an optical system of focal length $10\, cm$ . The refractive
index of the material of the lens is:
a.
$1. 55$
b.
$1. 50$
c.
$1. 75$
d.
$1. 51$
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A uniform rod $AB$ is suspended from a point $X$ , at a variable distance $x$ from $A$ , as shown. To make the rod
horizontal, a mass $m$ is suspended from its end $A$ . A set of $(m, \,x)$ value is recorded. The appropriate variables
that give a straight line, when plotted, are:
a.
$m,x^{2}$
b.
$m, \frac{1}{x^{2}}$
c.
$m, \frac{1}{x}$
d.
$m,x$
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A tuning fork vibrates with frequency $256\, Hz$ and gives one beat per second with the third normal mode of
vibration of an open pipe. What is the length of the pipe? (speed of sound in air is $340\,m\,s^{-1}$ )
a.
$220\, cm$
b.
$200\, cm$
c.
$190\, cm$
d.
$180\, cm$
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A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible
liquids, Whose densities are $\rho _{1}$ and $\rho _{2}\,(\rho _{1} >\rho _{2}\,),$ fill half the circle. The angle $\theta$ between the radius vector
passing through the common interface and the vertical is:
In a common emitter configuration with suitable bias, it is given that $R_{L}$ is the load resistance and $R_{BE}$ is
small-signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given,
respectively, by: $\beta$ is current gain, $I_{B}$ , $I_{C}$ and $I_{E}$ are respectively base, collector, and emitter currents.
A particle is oscillating on the $x$ -axis with an amplitude $2\, cm$ about the point $x_{0} = 10\, cm$ with a frequency. A
concave mirror of focal length $5\, cm$ is placed at the origin (see figure).
Identify the correct statements?
(i) The image executes periodic motion.
(ii) The image executes non-periodic motion.
(iii) The turning points of the image are asymmetric with respect to the image of the point at $X = 10\, cm$ .
(iv) The distance between the turning points of the oscillation of the image is $\frac{100}{21}\, cm$ .
a.
(ii, iii)
b.
(i, iii, iv)
c.
(i, iv)
d.
(ii, iv)
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A monochromatic beam of light has a frequency $v= \frac{3}{2\pi} \times 10^{12} Hz$ and is propagating along the direction $\frac{ˆi+ˆj}{\sqrt{2}}$
. It is polarized along the $ˆk$ direction. The acceptance form the magnetic field is:
An ideal capacitor of capacitance $0 .2 \,$ $\mu$ $F$ is charged to a potential difference of $10\,V$ . The charging battery is
then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0. 5\, mH$ . The current
at a time when the potential difference across the capacitor is $5\,V$ is:
a.
$0. 15\,A$
b.
$0. 17\,A$
c.
$0. 34\,A$
d.
$0. 25\,A$
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A body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$ . It is oscillating along $x$ -direction
about its equilibrium position in the horizontal plane, taken to be at $x= 0$ , with an amplitude $A$ . An electric
field $E$ is applied along the $x$ -direction. Which of the following statements is correct?
a.
The total energy of the system is
$\frac{1}{2}m\omega ^{2}A^{2}+ \frac{1}{2} \frac{q^{2}E^{2}}{k}$
b.
The new equilibrium position is at a distance $\frac{2qE}{k}$
from $x= \,0$
c.
The new equilibrium position is at a distance $\frac{qE}{2k}$
from $x= \,0$
d.
The total energy of the system is
$\frac{1}{2}m\omega ^{2}A^{2}- \frac{1}{2} \frac{q^{2}E^{2}}{k}$ .
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The $B- H$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid
with $1000\, turns \, cm^{-1}$ . The current that should be passed in the solenoid to demagnetize the ferromagnet
completely is,
a.
$2\, mA$
b.
$20\,$ $\mu$ $A$
c.
$1\, mA$
d.
$40\,$ $\mu$ $A$
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The energy required to remove the electron from a singly ionized Helium atom is $2. 2$ times the energy
required to remove an electron from helium atom. The total energy required to ionize the Helium atom
completely is close to
a.
$34\, eV$
b.
$20\, eV$
c.
$79\, eV$
d.
$109\, eV$
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The velocity time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance
travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are,
respectively.
a.
$112. 5\,m$ and $22. 5\,s$
b.
$337. 5\,m$ and $25\,s$
c.
$225. 5\,m$ and $10\,s$
d.
$112. 5\,m$ and $15\,s$
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A solution containing active cobalt $^{60}_{27}Co$ having an activity of $0 .8 \,$ $\mu$ $Ci$ and decay constant $\lambda$ is injected in an
animal's body. When $1\,cm^{3}$ blood is drawn from the animal's body after $10\,h$ of injection, the activity was
found to be $300\, dpm$ (decays per minute), then the total volume of blood in the animal's body is close to
$[1\,Ci = 3 .7 \times 10^{10}\, dps$ (decays per second) and at $t= 10\,h$ the value of $e^{-\lambda t} = 0.84]$
a.
$4\,L$
b.
$6\,L$
c.
$5\,L$
d.
$7\,L$
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A force of $40\,N$ acts on a point $B$ at the end of an L-shaped object as shown in the figure. The angle $\theta$ that will
produce the maximum moment of the force about point $A$ is given by:
a.
$tan\theta = 4$
b.
$tan\theta = \frac{1}{4}$
c.
$tan\theta = \frac{1}{2}$
d.
$tan\theta = 2$
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The number of amplitude-modulated broadcast stations that can be accommodated in a $300\, kHz$ bandwidth for
the highest modulating frequency $15\, kHz$ will be:
a.
$15$
b.
$20$
c.
$8$
d.
$10$
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When an electric current is passed through acidified water, 112 mL of hydrogen gas at N.T.P was collected at
the cathode in 965 seconds. The current passed, in ampere, is:
a.
2.0
b.
0.1
c.
0.5
d.
1.0
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The correct match between items of List-I and List-II is
List - I List - II
(A) Coloured impurity (P) Steam distillation
(B) Mixture of o - nitrophenol and p -nitrophenol (Q) Fractional distillation
(C) Crude Naphtha (R) Charcoal treatment
(D) Mixture of glycerol and sugars (S) Distillation under reduced pressure
a.
$(A) -(R), (B) -(S), (C) -(P), (D) -(Q)$
b.
$(A) -(P), (B) -(S), (C) -(R), (D) -(Q)$
c.
$(A) -(R), (B) -(P), (C) -(Q), (D) -(S)$
d.
$(A) -(R), (B) -(P), (C) -(S), (D) -(Q)$
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An ideal gas undergoes a cyclic process as shown in the figure
$\Delta U_{BC} = -5 KJmol^{-1}, q_{AB} = 2 KJmol^{-1}$
$W_{AB} = -5 KJmol^{-1}, W_{CA} = 3 KJmol^{-1}$
Heat absorbed by the system during process $CA \,$ is
a.
$-5 KJmol^{-1}$
b.
$+5 KJmol^{-1}$
c.
$-18 KJmol^{-1}$
d.
$18 KJmol^{-1}$
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A sample of $NaClO_{3}$ is converted by heat to $NaCl$ with a loss of $0. 16\,g$ of oxygen. The residue is dissolved in
water and precipitated as $AgCl$ . The mass of $AgCl$ (in $g$ ) obtained will be: (Given: Molar mass of
$AgCl = 143 .5 \,g\, mol^{-1}$ )
a.
$0. 35$
b.
$0. 54$
c.
$0. 41$
d.
$0. 48$
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The minimum volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution ( $K_{sp}$ of
$PbCl_{2} = 3.2 \times 10^{-8}$ ;atomic mass of $Pb= 207\,u$ ) is:
a.
1.798 L
b.
0.36 L
c.
17.98 L
d.
0.18 L
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$N_{2}O_{5}$ decomposes to $NO_{2}$ and $O_{2}$ follows the first order kinetics. After $50$ minutes, the pressure inside the
vessel increases from $50\, mm \, Hg$ to $87. 5\, mm \, Hg$ . The pressure of the gaseous mixture after $100$ minutes at
constant temperature will be:
a.
$136. 5\, mm \, Hg$
b.
$106. 25\, mm \, Hg$
c.
$175. 0\, mm \, Hg$
d.
$116. 25\, mm \, Hg$
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Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying
$0. 5\,V$ , when the radiation of $250\, nm$ is used. The work function of the metal is
a.
$4\, eV$
b.
$5. 5\, eV$
c.
$4. 5\, eV$
d.
$5\, eV$
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A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate
solution is added to the before mentioned solution, a white precipitate is obtained which does not dissolve in
dilute nitric acid. The anion is:
a.
$CO^{2-}_{3}$
b.
$SO^{2-}_{4}$
c.
$S^{2-}$
d.
$Cl^{-}$
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An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3}\, km$ above it is observed at an
elevation of $60^{^{\circ}}$ from a point on the ground. If after five seconds, its elevation from the same point is $30^{^{\circ}}$ , then
the speed (in $km / hr$ ) of the aeroplane is
a.
$720$
b.
$1500$
c.
$750$
d.
$1440$
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$||$
A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black balls. If
two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be
white while the other ball turns out to be red, then the probability that both balls are drawn from box $B$ is :
a.
$\frac{7}{8\,}$
b.
$\frac{9}{16\,}$
c.
$\frac{7}{16\,}$
d.
$\frac{9}{32\,}$
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A variable plane passes through a fixed point $(3, \,2, \,1)$ and meets $x, \,y$ and $z$ -axes at $A, \,B\,&\,C$ respectively. A
plane is drawn parallel to the $yz-$ plane through $A$ , a second plane is drawn parallel to the $zx-$ plane through
$B$ and a third plane is drawn parallel to the $xy$ - plane through $C$ . Then the locus of the point of intersection of
these three planes, is
If $tanA$ and $tanB$ are the roots of the quadratic equation $3x^{2} -10x-25 = 0$ , then the value of
$3 sin^{2}(A+B) -10 sin(A+B) cos(A+B) -25 cos^{2}(A+B)$ is :
a.
$-25$
b.
$10$
c.
$-10$
d.
$25$
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$\rightarrow \rightarrow$
If $\vec{a}, \,\vec{b}, \,\vec{c}$ are unit vectors such that $\vec{a}+ 2\vec{b}+ 2\vec{c}= 0$ , then $\vec{a}\times \vec{c}$ is equal to :
a.
$\frac{1}{4}$
b.
$\frac{15}{16}$
c.
$\frac{\sqrt{15}}{4}$
d.
$\frac{\sqrt{15}}{16}$
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Let $S$ be the set of all real values of $k$ for which the system of linear equations
$x+y+z= 2$
$2x+y- z= 3$
$3x+ 2y+kz= 4$
has a unique solution. Then, $S$ is :
a.
equal to $R\,-{0}$
b.
an empty set
c.
equal to $R$
d.
equal to ${0}$
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If the tangent drawn to the hyperbola $4y^{2} =x^{2} + 1$ intersect the co-ordinates axes at the distinct points $A$ and
$B$ , then the locus of the midpoint of $AB$ is :
a.
$x^{2} -4y^{2} + 16x^{2}y^{2} = 0$
b.
$4x^{2} - y^{2} + 16x^{2}y^{2} = 0$
c.
$x^{2} -4y^{2} -16x^{2}y^{2} = 0$
d.
$4x^{2} - y^{2} -16x^{2}y^{2} = 0$
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If $n$ is the degree of the polynomial, $[\frac{2}{\sqrt{5x^{3}+1}-\sqrt{5x^{3}-1}} ]^{8} + \,[\frac{2}{\sqrt{5x^{3}+1}+\sqrt{5x^{3}-1}} ]^{8}$ and $m$ is the coefficient of $x^{n}$
in it, then the ordered pair $(n, \,m)$ is equal to
a.
$(8, \,5(10)^{4})$
b.
$(12, \,8(10)^{4})$
c.
$(12, \,(20)^{4})$
d.
$(24, \,(10)^{8})$
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If a right circular cone, having maximum volume, is inscribed in a sphere of radius $3\,cm$ , then the curved
surface area (in $cm^{2}$ ) of this cone is :
a.
$8\sqrt{2}\pi$
b.
$6\sqrt{2}\pi$
c.
$8\sqrt{3}\pi$
d.
$6\sqrt{3}\pi$
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Two parabolas with a common vertex and with axes along the $x$ -axis and $y$ -axis respectively, intersect each
other in the first quadrant. If the length of the latus rectum of each parabola is $3$ , then the equation of the
common tangent to the two parabolas is :
a.
$\,3(x+y) + 4 = 0$
b.
$8(2x+y) + 3 = 0$
c.
$x+ 2y+ 3 = 0$
d.
$4(x+y) + 3 = 0$
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$n$ -digit numbers are formed using only three digits $2, \,5$ and $7$ . The smallest value of $n$ for which $900$ such
distinct numbers can be formed is :
a.
$9$
b.
$7$
c.
$8$
d.
$6$
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If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda )x+ (10 - \lambda ) = 0$ is
minimum, then the magnitude of the difference of the roots of this equation is :
a.
$4\sqrt{2}$
b.
$20$
c.
$2\sqrt{5}$
d.
$2\sqrt{7}$
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In a triangle $ABC$ , coordinates of $A$ are $(1, \,2)$ and the equations of the medians through $B$ and $C$ are
respectively, $x+y= 5$ and $x= 4$ . Then area of $\Delta ABC$ (in sq. units) is :
a.
$12$
b.
$4$
c.
$9$
d.
$5$
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If $x_{1}, \,x_{2}, \, … . . , \,x_{n}$ and $\frac{1}{h_{1}}, \,\frac{1}{h_{2}} , \, … . . , \,\frac{1}{h_{n}}$ are two A.P.s such that $x_{3} =h_{2} = 8\,&\,x_{8} =h_{7} = 20$ , then
$x_{5}\cdot h_{10}$ is equal to
a.
$3200$
b.
$1600$
c.
$2650$
d.
$2560$
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The mean of a set of $30$ observation is $75$ . If each observations is multiplied by non-zero number $\lambda$ and then
each of them is decreased by $25$ , their mean remains the same. Then, $\lambda$ is equal to :
a.
$\frac{4}{3}$
b.
$\frac{1}{3}$
c.
$\frac{10}{3}$
d.
$\frac{2}{3}$
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Let $S ={(\lambda , \,\mu ) \in R\times R\, : \,f(t) =(|\lambda \,|e^{|t|} - \mu )sin(2|t|), \,t\in R$ is a differential function}. Then, $S$ is a
subset of :
a.
$(-\infty ,\, 0) \times R$
b.
$R\times [0 ,\, \infty )$
c.
$[0 ,\, \infty ) \times R$
d.
$R \times (-\infty ,\, 0)$
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If $\beta$ is one of the angles between the normals to the ellipse $x^{2} + 3y^{2} = 9$ at the points $(3 cos\theta , sin\sqrt{3} \theta )$ and
$(-3 sin\theta , \sqrt{3}cos\theta ); \,\theta \in (0, \frac{\pi}{2})$ ; then $\frac{2 cot\beta}{sin 2\theta}$ is equal to :
a.
$\frac{1}{\sqrt{3}}$
b.
$\frac{\sqrt{3}}{4}$
c.
$\frac{2}{\sqrt{3}}$
d.
$\sqrt{2}$
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The set of all $\alpha \in R$ , for which $w= \frac{1+(1-8\alpha )z}{1-z}$ is a purely imaginary number, for all $z\in C$ satisfying $|z| = 1$
and $Re(z) \neq 1$ , is :
a.
${0}$
b.
${0, \frac{1}{4}, -\frac{1}{4}}$
c.
equal to $R$
d.
an empty set
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$| |$
$1, x\in [0, \,1]$
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx} + 2y=f(x)$ , where $f(x) = \,{$ . If
$0, otherwise$
$y(0) = 0$ , then $y (\frac{3}{2})$ is
a.
$\frac{e^{2}-1}{e^{3}}$
b.
$\frac{1}{2e}$
c.
$\frac{e^{2}+1}{2e^{4}}$
d.
$\frac{e^{2}-1}{2e^{3}}$
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