An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two
positions of a thin lens separated by 10 $cm$ . The size of the images in two situations are in the ratio $3 : 3$ . What
is the distance between the screen and the object?
a.
$124.5\,cm$
b.
$144.5\,cm$
c.
$65.0\,cm$
d.
$99.0\,cm$
Correct Answer
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Q2mcq
A cone of base radius $R$ and height $h$ is located in a uniform electric field $\vec{E}$ parallel to its base. The electric
flux entering the cone is:
a.
$\frac{1}{2}EhR$
b.
EhR
Correct Answer
c.
$2EhR$
d.
$4EhR$
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Q3mcq
The bulk moduli of ethanol, mercury and water are given as $0.9, 25$ and $2.2$ respectively in units of $10^{9}Nm^{-2}$ .
For a given value of pressure, the fractional compression in volume is $\frac{\Delta V}{V}$ . Which of the following statements
about $\frac{\Delta V}{V}$ for these three liquids is correct ?
a.
Ethanol $>$ Water $>$ Mercury
Correct Answer
b.
Water $>$ Ethanol $>$ Mercury
c.
Mercury $>$ Ethanol $>$ Water
d.
Ethanol $>$ Mercury $>$ Water
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Q4mcq
A hot body, obeying Newton's law of cooling is cooling down from its peak value $80^{\circ }C$ to an ambient
temperature of $30^{\circ }C$ . It takes 5 minutes in cooling down from $80^{\circ }C$ to $40^{\circ }C$ . How much time will it take to
cool down from $62^{\circ }C$ to $32^{\circ }C$ ? (Given $In 2 = 0.693$ , In $5 = 1.609$ )
a.
$3.75$ minutes
b.
$8.6$ minutes
Correct Answer
c.
$9.6$ minutes
d.
$6.5$ minutes
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Q5mcq
The average mass of rain drops is $3.0 \times 10^{-5}\,kg$ and their avarage terminal velocity is $9\,m/s$ . Calculate the
energy transferred by rain to each square metre of the surface at a place which receives $100\,cm$ of rain in a year.
a.
$3.5 \times 10^{5}\,J$
b.
$4.05 \times 10^{4}\,J$
Correct Answer
c.
$3.0 \times 10^{5}\,J$
d.
$9.0 \times 10^{4}\,J$
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Q6mcq
Match the List-I (Phenomenon associated with electromagnetic radiation) with List-II (Part of electromagnetic
spectrum) and select the correct code from the choices given below this lists:
Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic
field, the field lines around them look as follows:
Make the correspondence of these bars with their material being diamagnetic ( $D)$ , ferromagnetic (F) and
paramagnetic $(P)$ :
a.
$A \leftrightarrow D, B \leftrightarrow P, C \leftrightarrow F$
b.
$A \leftrightarrow F, B \leftrightarrow D, C \leftrightarrow P$
Correct Answer
c.
$A \leftrightarrow P, B \leftrightarrow F, C \leftrightarrow D$
d.
$A \leftrightarrow F, B \leftrightarrow P, C \leftrightarrow D$
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Q8mcq
An electromagnetic wave of frequency $1 \times 10^{14}$ hertz is propagating along $z$ -axis. The amplitude of electric
field is $4\,V/m$ . If $\epsilon _{0} = 8.8 \times 10^{-12}C^{2}/N-m^{2}$ , then average energy density of electric field will be:
a.
$35.2 \times 10^{-10}\,J/m^{3}$
b.
$35.2 \times 10^{-11}\,J/m^{3}$
c.
$35.2 \times 10^{-12}\,J/m^{3}$
Correct Answer
d.
$35.2 \times 10^{-13}\,J/m^{3}$
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Q9mcq
From a sphere of mass $M$ and radius $R$ , a smaller sphere of radius $\frac{R}{2}$ is carved out such that the cavity made in
the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where
the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force
between the two sphere is:
a.
$\frac{41GM^{2}}{3600R^{2}}$
Correct Answer
b.
$\frac{41GM^{2}}{450R^{2}}$
c.
$\frac{59GM^{2}}{450R^{2}}$
d.
$\frac{GM^{2}}{225R^{2}}$
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Q10mcq
A photon of wavelength $\lambda$ is scattered from an electron, which was at rest. The wavelength shift $\Delta \lambda$ is three
times of $\lambda$ and the angle of scattering $\theta$ is $60^{\circ }$ . The angle at which the electron recoiled is $\phi$ . The value of $tan\phi$
is : (electron speed is much smaller than the speed of light)
a.
$0.16$
b.
$0.22$
Correct Answer
c.
$0.25$
d.
$0.28$
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An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $8.0 \times 10^{-3}\,m^{2}$ .
Initially the gas is at $300\,K$ and occupies a volume of $2.4 \times 10^{-3}\,m^{3}$ and the spring is in its relaxed state as
shown in figure. The gas is heated by a small heater until the piston moves out slowly by $0.1\,m$ . The force
constant of the spring is $8000\,N/m$ and the atmospheric pressure is $1.0 \times 10^{5}\,N/m^{2}$ . The cylinder and the
piston are thermally insulated. The piston and the spring are massless and there is no friction between the
piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires
of the heater. The heat capacity of the heater coil is also negligible).
a.
$300\,K$
b.
$800\,K$
c.
$500\,K$
d.
$1000\,K$
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The initial speed of a bullet fired from a rifle is $630\,m/s$ . The rifle is fired at the centre of a target $700\,m$ away
at the same level as the target. How far above the centre of the target ?
a.
$1.0\,m$
b.
$4.2\,m$
c.
$6.1\,m$
d.
$9.8\,m$
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The angular frequency of the damped oscillator is given by, $\omega =\sqrt{\,} (\frac{k}{m} - \frac{r^{2}}{4\,m^{2}})$ where $k$ is the spring
constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{r^{2}}{mk}$ is $8%$ , the change in
time period compared to the undamped oscillator is approximately as follows:
a.
increases by $1%$
b.
increases by $8%$
c.
decreases by $1%$
d.
decreases by $8%$
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In the circuit diagrams (A, B, C and D) shown below, $R$ is a high resistance and $S$ is a resistance of the order
of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the
resistance and figure of merit of the galvanometer, is the circuit labelled as: (a)
(b)
(C)
(d)
a.
Circuit A with $G = \frac{RS}{(R-S)}$
b.
Circuit B with $G = S$
c.
Circuit $C$ with $G = S$
d.
Circuit $D$ with $G= \frac{RS}{(R-S})$
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Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright
and dark parts of the resultant pattern is:
a.
$\frac{16}{9}$
b.
$\frac{4}{3}$
c.
$\frac{7}{1}$
d.
$\frac{49}{1}$
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A coil of circular cross-section having 1000 turns and $4\,cm^{2}$ face area is placed with its axis parallel to a
magnetic field which decreases by $10^{-2}\,Wb m^{-2}$ in $0.01\,s$ . The e.m.f. induced in the coil is:
a.
$400mV$
b.
$200mV$
c.
$4mV$
d.
$0.4mV$
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A thin bar of length $L$ has a mass per unit length $\lambda$ , that increases linearly with distance from one end. If its total
mass is $M$ and its mass per unit length at the lighter end is $\lambda _{O}$ , then the distance of the centre of mass from the
lighter end is:
a.
$\frac{L}{2} - \frac{\lambda _{0}\,L^{2}}{4M}$
b.
$\frac{L}{3} + \frac{\lambda _{0}\,L^{2}}{8M}$
c.
$\frac{L}{3} + \frac{\lambda _{0}\,L^{2}}{4M}$
d.
$\frac{2\,L}{3} - \frac{\lambda _{0}\,L^{2}}{6M}$
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During an adiabatic compression, $830\,J$ of work is done on 2 moles of a diatomic ideal gas to reduce its
volume by $50%$ . The change in its temperature is nearly: $(R = 8.3JK^{-1}\,mol^{-1})$
a.
$40\,K$
b.
$33\,K$
c.
$20\,K$
d.
$14\,K$
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Two factories are sounding their sirens at 800 $Hz$ . A man goes from one factory to other at a speed of $2\,m/s$ .
The velocity of sound is $320\,m/s$ . The number of beats heard by the person in one second will be:
a.
2
b.
4
c.
8
d.
10
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A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$ ). The
height of water is $3\,m$ and that of kerosene $2\,m$ . When the hole is opened the velocity of fluid coming out from
it is nearly: (take $g = 10\,ms^{-2}$ and density of water $= 10^{3}\,kg\,m^{-3})$
a.
$10.7\,ms^{-1}$
b.
$9.6\,ms^{-1}$
c.
$8.5\,ms^{-1}$
d.
$7.6\,ms^{-1}$
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A parallel plate capacitor is made of two plates of length 1 , width $w$ and separated by distance $d$ . A dielectric
slab (dielectric constant $K$ ) that fits exactly between the plates is held near the edge of the plates. It is pulled
into the capacitor by a force $F = -\frac{∂U}{∂x}$ where $U$ is the energy of the capacitor when dielectric is inside the
capacitor up to distance $x$ (See figure). If the charge on the capacitor is Q then the force on the dielectric when
it is near the edge is:
a.
$\frac{Q^{2}\,d}{2wl^{2}\epsilon _{o}}K$
b.
$\frac{Q^{2}\,W}{2dl^{2}\epsilon _{0}}(\,K -1)$
c.
$\frac{Q^{2}\,d}{2wl^{2}\epsilon _{o}}(K -1)$
d.
$\frac{Q^{2}w}{2dl^{2}\epsilon _{o}}K$
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A small ball of mass $m$ starts at a point $A$ with speed $v_{o}$ and moves along a frictionless track $AB$ as shown. The
track $BC$ has coefficient of friction $\mu$ . The ball comes to stop at $C$ after travelling a distance $L$ which is:
a.
$\frac{2\,h}{\mu} + \frac{v^{2}_{o}}{2\mu g}$
b.
$\frac{h}{\mu} + \frac{v^{2}_{0}}{2\mu g}$
c.
$\frac{h}{2\mu} + \frac{v2o}{\mu g}$
d.
$\frac{h}{2\mu} + \frac{v^{2}_{o}}{2\mu g}$
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A body of mass $5\,kg$ under the action of constant force $\vec{F} =F_{x}\hat{i}+F_{y}\hat{j}$ has velocity at $t = 0\,s$ as
$\vec{v}= (6\hat{i}-2\hat{j}m/s)$ and at $t = 10\,s$ as $\vec{v}= +6\hat{j}m/s$ . The force $\vec{F}$ is:
a.
$(-3\hat{i}+ 4\hat{j})N$
b.
$(-\frac{3}{5}\hat{i}+ \frac{4}{5}\hat{j})N$
c.
$(3\hat{i}-4\hat{j})N$
d.
$(\frac{3}{5}\hat{i}- \frac{4}{5}\hat{j})N$
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A radioactive nuclei with decay constant $0.5/s$ is being produced at a constant rate of 100 nuclei/s. If at $t= 0$
there were no nuclei, the time when there are 50 nuclei is:
a.
$1\,s$
b.
$2 ln( \frac{4}{3})s$
c.
$ln 2\,s$
d.
$ln(\frac{4}{3})s$
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An air bubble of radius $0.1\,cm$ is in a liquid having surface tension $0.06\,N/m$ and density $10^{3}\,kg/m^{3}$ . The
pressure inside the bubble is $1100Nm^{-2}$ greater than the atmospheric pressure. At what depth is the bubble
below the surface of the liquid? $(g = 9.8\,ms^{-2})$
a.
$0.1\,m$
b.
$0.15\,m$
c.
$0.20\,m$
d.
$0.25\,m$
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In a compound microscope the focal length of objective lens is $1.2\,cm$ and focal length of eye piece is $3.0\,cm$ .
When object is kept at $1.25\,cm$ in front of objective, final image is formed at infinity. Magnifying power of the
compound microscope should be:
a.
200
b.
100
c.
400
d.
150
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The molar heat capacity $(C_{p})$ of $CD_{2}O$ is 10 cals at $1000\,K$ . The change in entropy associated with cooling of
$32\,g$ of $CD_{2}O$ vapour from $1000\,K$ to $100\,K$ at constant pressure will be: $(D =$ deuterium, atomic mass $= 2u)$
a.
$23.03caldeg^{-1}$
b.
$-23.03caldeg^{-1}$
c.
$2.303caldeg^{-1}$
d.
$-2.303caldeg^{-1}$
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If $\lambda _{0}$ and $\lambda$ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected
from the metal surface is:
In the reaction of formation of sulphur trioxide by contact process $2SO_{2}+ O_{2} \rightleftharpoons 2SO_{3}$ the rate of reaction
was measured as $\frac{d[O_{2}]}{dt} = -2.5 \times 10^{-4}\,mol\,L^{-1}\,s^{-1}$ . The rate of reaction is terms of $[SO_{2}]$ in $molL^{-1}\,s^{-1}$ will
be:
a.
$-1.25 \times 10^{-4}$
b.
$-2.50 \times 10^{-4}$
c.
$-3.75 \times 10^{-4}$
d.
$-5.00 \times 10^{-4}$
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For the reaction, $2\,N_{2}O_{5} 4NO_{2}+ O_{2}$ , the rate equation can be expressed in two ways
$- \frac{d[N_{2}O_{5}]}{dt} = k [N_{2}O_{5} ]n\vec{n}d +\frac{d[NO_{2}]}{dt} = k' [N_{2}O_{5}] k$ and $k'$ are related as:
a.
$k = k'$
b.
$2k = k'$
c.
$k = 2k'$
d.
$k = 4k'$
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Given
$Fe^{3+}(aq) + e^{-} \rightarrow Fe\rightarrow^{2+}(aq); E^{0} = +0.77\,V$
$Al^{3+}(aq) + 3e^{-} \rightarrow Al(s); E\rightarrow^{0} = -1.66\,V$
$Br_{2}(aq) + 2e^{-} \rightarrow 2Br\rightarrow^{-}; E^{0} = +1.09\,V$
Considering the electrode potentials, which of the following represents the correct order of reducing power?
a.
$Fe^{2+} < Al< Br^{-}$
b.
$Br^{-} < Fe^{2+} < Al$
c.
$Al < Br^{-} < Fe^{2+}$
d.
$Al < Fe^{2+} < Br^{-}$
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Based on the equation:
$\Delta E = -2.0 \times 10^{-18}\,J(\frac{1}{n^{2}} - \frac{1}{n^{2}})$
$2 1$
the wavelength of the light that must be absorbed to excite hydrogen electron from level $n= 1$ to level $n = 2$
will be: $(h = 6.625 \times 10^{-34}Js, C = 3 \times 10^{8}\,ms^{-1})$
a.
$1.325 \times 10^{-7}\,m$
b.
$1.325 \times 10^{-10}\,m$
c.
$2.650 \times 10^{-7}\,m$
d.
$5.300 \times 10^{-10}\,m$
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The initial volume of a gas cylinder is $750.0\,mL$ . If the pressure of gas inside the cylinder changes from
$840.0\,mmHg$ to $360.0\,mmHg$ , the final volume the gas will be:
a.
$1.750\,L$
b.
$3.60\,L$
c.
$4.032\,L$
d.
$7.50\,L$
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Consider the following equilibrium
$AgCl ↓+2NH_{3} \rightleftharpoons [Ag(NH_{3}2_{2}]^{+} + Cl^{-}$
White precipitate of $AgCl$ appears on adding which of the following?
a.
$NH_{3}$
b.
aqueous $NaCl$
c.
aqueous $HNO_{3}$
d.
aqueous $NH_{4}Cl$
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A gaseous compound of nitrogen and hydrogen contains $12.5%$ (by mass) of hydrogen. The density of the
compound relative to hydrogen is 16. The molecular formula of the compound is:
a.
$NH_{2}$
b.
$N_{3}H$
c.
$NH_{3}$
d.
$N_{2}H_{4}$
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Which of the following statements about the depletion of ozone layer is correct?
a.
The problem of ozone depletion is less serious at The problem of ozone depletion is more serious
poles because $NO_{2}$ solidifies and is not available at poles because ice crystals in the clouds over
for consuming $CIO^{\circ }$ radicals. poles act as catalyst for photochemical reactions
involving the decomposition of ozone of $Cl^{\cdot }$ and
$CIO^{\cdot }$ radicals.
c.
Freons, chlorofluorocarbons, are inert. Oxides of nitrogen also do not react with ozone
Chemically, they do not react with ozone in in stratosphere.
stratosphere.
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In some solutions, the concentration of $H_{3}O^{+}$ remains constant even when small amounts of strong acid or
strong base are added to them. These solutions are known as:
a.
Ideal solutions
b.
Colloidal solutions
c.
True solutions
d.
Buffer solutions
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Let $f$ be an odd function defined on the set of real numbers such that for $x \geq 0$ , $f(x) = 3 sinx+ 4 cosx$ . Then
$f(x)$ at $x = -\frac{11\pi}{6}$ is equal to:
a.
$\frac{3}{2} + 2\sqrt{3}$
b.
$- \frac{3}{2} + 2\sqrt{3}$
c.
$\frac{3}{2} -2\sqrt{3}$
d.
$- \frac{3}{2} -2\sqrt{3}$
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Two ships A and B are sailing straight away from a fixed point $O$ along routes such that $\angle AOB$ is always $120^{\circ }$
. At a certain instance, $OA = 8\,km, OB = 6\,km$ and the ship $A$ is sailing at the rate of $20\,km/hr$ while the
ship B sailing at the rate of $30\,km/hr$ . Then the distance between $A$ and $B$ is changing at the rate (in $km/hr$ ):
a.
$\frac{260}{\sqrt{37}}$
b.
$\frac{260}{37}$
c.
$\frac{80}{\sqrt{37}}$
d.
$\frac{80}{37}$
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The set of all real values of $\lambda$ for which exactly two common tangents can be drawn to the circles
$x^{2} +y^{2} -4x-4y+ 6 = 0$ and $x^{2} + y^{2} -10x -10y +\lambda = 0$ is the interval:
a.
$(12, 32)$
b.
$(18, 42)$
c.
$(12, 24)$
d.
$(18, 48)$
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If the general solution of the differential equation $y' = \frac{y}{x} + Φ(\frac{x}{y})$ , for some function $Φ$ , is given by
$yln |cx| =x$ , where $c$ is an arbitrary constant, then $Φ(2)$ is equal to:
a.
4
b.
$\frac{1}{4}$
c.
$-4$
d.
$- \frac{1}{4}$
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The plane containing the line $\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$ and parallel to the line $\frac{x}{1} = \frac{y}{1} = \frac{z}{4}$ passes through the point:
a.
$(1, -2, 5)$
b.
$(1, 0, 5)$
c.
$(0, 3, -5)$
d.
$(-1, -3, 0)$
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The angle of elevation of the top of a vertical tower from a point $P$ on the horizontal ground was observed to
be $\alpha$ . After moving a distance 2 metres from $P$ towards the foot of the tower, the angle of elevation changes to
$\beta$ . Then the height (in metres) of the tower is:
Let $L_{1}$ be the length of the common chord of the curves $x^{2} +y^{2} = 9$ and $y^{2} = 8x$ , and $L_{2}$ be the length of the
latus rectum of $y^{2} = 8x$ , then:
a.
$L_{1} > L_{2}$
b.
$L_{1} = L_{2}$
c.
$L_{1} < L_{2}$
d.
$\frac{L_{1}}{\,L_{2}} = \sqrt{2}$
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If $\alpha$ and $\beta$ are roots of the equation, $x^{2} -4\sqrt{2}kx+ 2e^{4 lnk} -1 = 0$ for some $k$ , and $\alpha ^{2} +\beta ^{2} = 66$ , then
$\alpha ^{3} +\beta ^{3}$ is equal to:
a.
$248\sqrt{2}$
b.
$280\sqrt{2}$
c.
$-32\sqrt{2}$
d.
$-280\sqrt{2}$
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Let $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5,\mu )$ be the vertices of a $\triangle ABC$ . If the median through $A$ is equally
inclined to the coordinate axes, then:
a.
$5\lambda -8\mu = 0$
b.
$8\lambda -5\mu = 0$
c.
$10\lambda -7\mu = 0$
d.
$7\lambda -10\mu = 0$
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An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The
number of ways in which this can be done is:
a.
$72(7!)$
b.
$18(7!)$
c.
$40(7!)$
d.
$36(7!)$
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A stair-case of length $l$ rests against a vertical wall and a floor of a room. Let $P$ be a point on the stair-case,
nearer to its end on the wall, that divides its length in the ratio $1 : 2$ . If the staircase begins to slide on the floor,
then the locus of $P$ is:
a.
an ellipse of eccentricity $\frac{1}{2}$
b.
an ellipse of eccentricity $\frac{\sqrt{3}}{2}$
c.
a circle of radius $\frac{1}{2}$
d.
a circle of radius $\frac{\sqrt{3}}{2}l$
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In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49 , and the
sum of the first and the third term is 35. Then the first term of this geometric progression is:
a.
7
b.
21
c.
28
d.
42
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For the curve $y = 3 sin\theta cos\theta , x = e^{\theta } sin\theta$ , $0 \leq \theta \leq \pi$ , the tangent is parallel to $x$ -axis when $\theta$ is:
a.
$\frac{3\pi}{4}$
b.
$\frac{\pi}{2}$
c.
$\frac{\pi}{4}$
d.
$\frac{\pi}{6}$
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Let for $i = 1, 2, 3, p_{i}(x)$ be a polynomial of degree 2 in $x,p'_{i}(x)$ and $p''_{i}(x)$ be the first and second order
derivatives of $p_{i}(x)$ respectively. Let,
$p (x) p' (x) p''x($
$[^{1}^{1}^{1} ])$
$A(x) = p_{2}(x) p'_{2}(x) p''_{2}($
$[''' ])$
$p_{3}(x) p_{3}(x) p_{3}(x$
and $B(x) = [A(x)]^{T}A(x)$ . Then determinant of $B(x)$ :
a.
is a polynomial of degree 6 in $x$ .
b.
is a polynomial of degree 3 in $x$ .
c.
is a polynomial of degree 2 in $x$ .
d.
does not depend on $x$ .
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The base of an equilateral triangle is along the line given by $3x+ 4y= 9$ . If a vertex of the triangle is $(1, 2)$ ,
then the length of a side of the triangle is:
a.
$\frac{2\sqrt{3}}{15}$
b.
$\frac{4\sqrt{3}}{15}$
c.
$\frac{4\sqrt{3}}{5}$
d.
$\frac{2\sqrt{3}}{5}$
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$\rightarrow \rightarrow$
If $|\vec{c}|^{2} = 60$ and $\vec{c}\times (\hat{i}+ 2\hat{j}+ 5\hat{k}) = 0$ , then a value of $\vec{c}\cdot (-7\hat{i}+ 2\hat{j}+ 3\hat{k})$ is:
a.
$4\sqrt{2}$
b.
12
c.
24
d.
$12\sqrt{2}$
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Let $P(3 sec\theta , 2 tan\theta )$ and $Q(3 sec\phi , 2 tan\phi )$ where $\theta +\phi = \frac{\pi}{2}$ , be two distinct points on the hyperbola
$\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ . Then the ordinate of the point of intersection of the normals at $P$ and $Q$ is:
a.
$\frac{11}{3}$
b.
$- \frac{11}{3}$
c.
$\frac{13}{2}$
d.
$- \frac{13}{2}$
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