A planoconvex 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 other side as in Fig. B, it acts like an optical system of focal length $10\,cm$ . The refractive
index of the material of lens is
a.
1.50
b.
1.55
Correct Answer
c.
1.75
d.
1.51
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Q2mcq
The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with
1000 turns/cm.. The current that should be passed in the solenoid to demagnetize the ferromagnet completely
is:
a.
$2\,mA$
b.
$1\,mA$
Correct Answer
c.
$40\mu A$
d.
$20\mu A$
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Q3mcq
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:
a.
$20eV$
b.
$79eV$
Correct Answer
c.
$109eV$
d.
$34eV$
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Q4mcq
A particle is oscillating on the $X$ -axis with an amplitude $2\,cm$ about the point $x_{0} = 10\,cm$ with a frequency $\omega$ .
A concave mirror of focal length 5 $cm$ is placed at the origin (see figure) Identify the correct statements: (A)
The image executes periodic motion (B) The image executes non-periodic motion (C) The turning points of the
image are asymmetric w.r.t the image of the point at $x= 10\,cm$ (D) The distance between the turning points of
the oscillation of the image is $\frac{100}{21}$
a.
(B), (D)
b.
(B), (C)
c.
(A), (C), (D)
Correct Answer
d.
(A), (D)
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Q5mcq
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.
$\frac{\pi}{8}$
Correct Answer
b.
$\frac{\pi}{12}$
c.
$\frac{\pi}{4}$
d.
$\frac{\pi}{6}$
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Q6mcq
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 maximum moment of the force about point $A$ is given by:
a.
$tan\theta = \frac{1}{4}$
b.
$tan\theta = 2$
c.
$tan\theta = \frac{1}{2}$
Correct Answer
d.
$tan\theta = 4$
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Q7mcq
In a common emitter configuration with suitable bias, it is given than $R_{L}$ 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, $I_{B},I_{C},I_{E}$ are respectively base, collector and emitter currents]
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 initial total energies is:
a.
$- \frac{GMm}{2R}$
b.
$+ \frac{GMm}{6R}$
c.
$- \frac{GMm}{6R}$
Correct Answer
d.
$\frac{GMm}{2R}$
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Q9mcq
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 points on the earth and $\Delta F_{2}$
be the difference in the force 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.
$2$
Correct Answer
b.
$6$
c.
$10^{-2}$
d.
$0.6$
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Q10mcq
An automobile, travelling at $40\,km/h$ , can be stopped at a distance of $40\,m$ by applying brakes. If the same
automobile is travelling at $80\,km/h$ , the minimum stopping distance, in metres, is (assume no skidding)
a.
$75\,m$
b.
$160\,m$
Correct Answer
c.
$100\,m$
d.
$150\,m$
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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, 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
$2 2$
$\frac{1}{2}m\omega ^{2}A^{2}+ \frac{1}{2} \frac{qE}{k}$
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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A charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge a as shown in the figure.
The electric flux through the square surface is:
a.
$\frac{Q}{3\epsilon _{0}}$
b.
$\frac{Q}{6\epsilon _{0}}$
c.
$\frac{Q}{2\epsilon _{0}}$
d.
$\frac{Q}{\epsilon _{0}}$
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Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie
wavelengths are $\lambda _{1}$ and $\lambda _{2}$ , their de Broglie wavelength in the frame of reference attached to their centre of
mass is:
A given object takes $n$ times more time to slide down a $45^{\circ }$ rough inclined plane as it takes to slide down a
perfectly smooth $45^{\circ }$ incline. The coefficient of kinetic friction between the object and the incline is :
a.
$1 - \frac{1}{n^{2}}$
b.
$\sqrt{1} - \frac{1}{n^{2}}$
$\sqrt{\,}$
c.
$\frac{1}{2-n^{2}}$
d.
$\frac{1}{1-n^{2}}$
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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 zero error, the thickness of the wire is:
a.
$0.0430\,cm$
b.
$0.3150\,cm$
c.
$0.4300\,cm$
d.
$0.2150\,cm$
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One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at
room temperature, $27^{\circ }C$ . The work done on the gas will be:
a.
$300Rln 6$
b.
$300R$
c.
$300R ln 7$
d.
$300R ln 2$
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A uniform $rodAB$ is suspended from a point $X$ , at a variable distance from $x$ from $A$ , as shown. To make the
rod horizontal, a mass $m$ is suspended from its end $A$ . A set of $(m,x)$ values is recorded. The appropriate
variable that give a straight line, when plotted, are:
a.
$m, \frac{1}{x}$
b.
$m, \frac{1}{x^{2}}$
c.
$m,x$
d.
$m,x^{2}$
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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.
$337.5\,m$ and $25\,s$
b.
$225.5\,m$ and $10\,s$
c.
$112.5\,m$ and $22.5\,s$
d.
$112.5\,m$ and $15\,s$
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A Carnot's engine works as a refrigerator between $250\,K$ and $300\,K$ . It receives $500cal$ heat from the reservoir
at the lower temperature. The amount of work done in each cycle to operate the refrigerator is:
a.
$420\,J$
b.
$2100\,J$
c.
$772\,J$
d.
$2520\,J$
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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 $X$ and $l_{2}$ ?
a.
$19.15\Omega$ and $39.5\,cm$
b.
$8.16\Omega$ and $60.5\,cm$
c.
$19.15\Omega$ and $60.5\,cm$
d.
$8.16\Omega$ and $39.5\,cm$
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A Helmholtz coil has 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 magnetic field at $P$ ,
midway between the centres $A$ and $C$ , is given by (Refer to figure):
a.
$\frac{4N\mu _{0}I}{5^{3/2}R}$
b.
$\frac{8N\mu _{0}I}{5^{3/2}R}$
c.
$\frac{4N\mu _{0}I}{5^{1/2}R}$
d.
$\frac{8N\mu _{0}I}{5^{1/2}R}$
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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 $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$ .
It is polarized along the $\hat{k}$ direction. The acceptable form for 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 $0.5mH$ . The current
at a time when the potential difference across the capacitor is $5\,V$ , is:
a.
$0.17\,A$
b.
$0.15\,A$
c.
$0.34\,A$
d.
$0.25\,A$
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A thin uniform tube is bent into a circle of radius $r$ in the virtical 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
The number of amplitude modulated broadcast stations that can be accommodated in a $300kHz$ band width for
the highest modulating frequency $15kHz$ will be:
a.
20
b.
10
c.
8
d.
15
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A tuning fork vibrates with frequency $256\,Hz$ and gives one best per second with the third normal mode of
vibration of an open pipe. What is the length of the pipe? (Speed of sound of air is $340\,ms^{-1}$ )
a.
(a) $190\,cm$
b.
$180\,cm$
c.
$220\,cm$
d.
$200\,cm$
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A solution containing active cobalt $^{60}_{27}Co$ having activity of $0.8\mu Ci$ and decay constant $\lambda$ is injected in an
animal's body. If $1\,cm^{3}$ of blood is drawn from the animal's body after $10hrs$ of injection, the activity found
was 300 decays per minute. What is the volume of blood that is flowing in the body? $(1Ci = 3.7 \times 10^{10}$ decay
per second and at $t = 10hrs^{-\lambda t} = 0.84)$
a.
6 litres
b.
7 litres
c.
4 litres
d.
5 litres
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When an electric current is passes 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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Xenon hexafluoride on partial hydrolysis produces compounds ' $X$ ' and ' $Y$ '. Compounds ' $X$ ' and ' $Y$ ' and the
oxidation state of $Xe$ are respectively :
a.
$XeOF_{4}(+6)$ and $XeO_{3}(+6)$
b.
$XeO_{2}(+4)$ and $XeO_{3}(+6)$
c.
$XeOF_{4}(+6)$ and $XeO_{2}F_{2}(+6)$
d.
$XeO_{2}F_{2}(+6)$ and $XeO_{2}(+4)$
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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.
$17.95\,L$
d.
$0.18\,L$
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$N_{2}O_{5}$ decomposes to $NO_{2}$ and $O_{2}$ and follows 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.
$136.25\,mm\,Hg$
b.
$106.25\,mm\,Hg$
c.
$175.0\,mm\,Hg$
d.
$116.25\,mm\,Hg$
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An ideal gas undergoes a cyclic process as shown in Figure.
$\Delta U_{BC} = -5\,kJ\,mol^{-1}, q_{AB} = 2\,kJ\,mol^{-1}$
Heat absorbed by the system during process CA is:
$\,W_{AB} = -5\,kJ\,mol^{-1}, \,W_{CA} = 3\,kJ\,mol^{-1}$
a.
$-5\,kJ\,mol^{-1}$
b.
$+5\,kJ\,mol^{-1}$
c.
$18\,kJ\,mol^{-1}$
d.
$-18\,kJ\,mol^{-1}$
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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 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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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 aforementioned solution, a white precipitate is obtained which does not dissolve in dil.
nitric acid. The anion is :
a.
$CO^{2-}_{3}$
b.
$SO^{2-}_{4}$
c.
$S^{2-}$
d.
$Cl^{-}$
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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 $x_{3} =h_{2} = 8$ and $x_{8} =h_{7} = 20$ , then $x_{5}.h_{10}$
equals.
a.
2560
b.
2650
c.
3200
d.
1600
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Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx} + 2y=f(x)$ , where
$1, x\in [0, 1]$
$f(x) ={$
$0, \,otherwise\,$
If $y(0) = 0$ , then $y(\frac{3}{2})$ is
a.
$\frac{e^{2}-1}{2e^{3}}$
b.
$\frac{e^{2}-1}{e^{3}}$
c.
$\frac{1}{2\vec{e}}$
d.
$\frac{e^{2}+1}{2e^{4}}$
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A variable plane passes through a fixed point ( 3 , $2, 1)$ and meets $x,y$ and $z$ axes at $A,B$ and $C$ respectively. A
plane is drawn parallel to $yz$ - plane through $A$ , a second plane is drawn parallel $zx$ plane through $B$ and a
third plane is drawn parallel to $xy$ - plane through $C$ . Then the locus of the point of intersection of these three
planes, is
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 $Rez\neq 1$ , is
a.
${0}$
b.
an empty set
c.
${0, \frac{1}{4}, -\frac{1}{4}}$
d.
equal to $R$
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If the tangents drawn to the hyperbola $4y^{2} =x^{2}+$ 1 intersect the co-ordinate axes at the distinct points $A$ and
$B$ , then the locus of the mid point of $AB$ is
a.
$x^{2} -4y^{2} + 16x^{2}y^{2} = 0$
b.
$4x^{2} - y^{2} + 16x^{2}y^{2} = 0$
c.
$4x^{2} - y^{2} -16x^{2}y^{2} = 0$
d.
$x^{2} -4y^{2} -16x^{2}y^{2} = 0$
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A box ' $A$ ' contanis 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.
$\frac{7}{16}$
b.
$\frac{9}{32}$
c.
$\frac{7}{8}$
d.
$\frac{9}{16}$
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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.
1500
b.
750
c.
720
d.
1440
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Consider the following two binary relations on the set $A= {a,b,c} :R_{1} = {(c,a)(b,b), (a,c), (c$ ,
$c), (b,c), (a,a)}$ and $R_{2} = {(a, b), (b, a), (c, c)$ , (c, a), (a, a), (b, b), (a, c). Then
a.
$R_{2}$ is symmetric but it is not transitive
b.
Both $R_{1}$ and $R_{2}$ are transitive
c.
Both $R_{1}$ and $R_{2}$ are not symmetric
d.
$R_{1}$ is not symmetric but it is transitive
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If a right circularcone 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.
$8\sqrt{3}\pi$
b.
$6\sqrt{2}\pi$
c.
$6\sqrt{3}\pi$
d.
$8\sqrt{2}\pi$
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Let $S ={(\lambda ,\mu ) \in R\times R:f(t) =(|\lambda |e^{t} - \mu )\cdot sin(2|t|)$ , $t\in R$ , is a differentiable function $}$ . Then $S$ is a
subest of?
a.
$R\times [0, \infty )$
b.
$(-\infty , 0) \times R$
c.
$[0, \infty ) \times R$
d.
$R\times (-\infty , 0)$
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Two parabolas with a common vertex and with axes along $x$ -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.
$4(x+y) + 3 = 0$
d.
$x+ 2y+ 3 = 0$
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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
$(-3 sin\theta , cos\sqrt{3} \theta ); \in (0, \frac{\pi}{2});$ then $\frac{2 cot\beta}{sin 2\theta}$ is equal to
a.
$\sqrt{2}$
b.
$\frac{2}{\sqrt{3}}$
c.
$\frac{1}{\sqrt{3}}$
d.
$\frac{\sqrt{3}}{4}$
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In a triangle $ABC$ , coordianates of $A$ are $(1, 2)$ and the equations of the medians through $B$ and $C$ are
$x+y= 5$ and $x= 4$ respectively. Then area of $\triangle ABC$ (in sq. units) is
a.
5
b.
9
c.
12
d.
4
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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.
an empty set
b.
equal to $R -{0}$
c.
equal to ${0}$
d.
equal to $R$
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If $n$ is the degree of the polynomial,
$1^{8} 1^{8}$
$[ ] +[ ]$
$\sqrt{5x^{3}+ 1}- \sqrt{5x^{3}-1} \sqrt{5x^{3}+ 1}+ \sqrt{5x^{3}-1}$
and $m$ is the coefficient of $x^{n}$ in it, then the ordered pair $(n, m)$ is equal to
a.
$(12, (20)^{4})$
b.
$(8, 5(10)^{4})$
c.
$(24, (10)^{8})$
d.
$(12, 8(10)^{4})$
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If $tanA$ and $tanB$ are the roots of the quadratic equation, $3x^{2} -10x-25 = 0$ then the value of
$3 sin^{2}(A+B) -10 sin(A+B) \cdot cos(A+B) -25 cos^{2} (A+B)$ is
a.
25
b.
$-25$
c.
$-10$
d.
10
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$\rightarrow \rightarrow$
If $\vec{a}, b$ , and $\vec{c}$ 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.
$\frac{\sqrt{15}}{4}$
c.
$\frac{15}{16}$
d.
$\frac{\sqrt{15}}{16}$
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The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number $\lambda$ and
then each of them is decreased by 25 , their mean remains the same. The $\lambda$ is equal to equal to ${0}$
a.
$\frac{10}{3}$
b.
$\frac{4}{3}$
c.
$\frac{1}{3}$
d.
$\frac{2}{3}$
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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.
20
b.
$2\sqrt{5}$
c.
$2\sqrt{7}$
d.
$4\sqrt{2}$
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