A Zener diode with a breakdown voltage of $4\,V$ is connected in series with a resistance $R$ to a battery of emf
$10\,V$ . The maximum power dissipation rating for the Zener diode is $1\,W$ . The value of $R$ to ensure maximum
power dissipation across the diode is
a.
$12\,\Omega$
b.
$24\,\Omega$
Correct Answer
c.
$36\,\Omega$
d.
$6\,\Omega$
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Q2mcq
To find the focal length of a convex mirror, a student records the following data:
Object pin Convex Lens Convex Mirror Image Pin
22.2 cm 32.2 cm 45.8 cm 71.2 cm
The focal length of the convex lens is $f_{1}$ and that of mirror is $f_{2}$ . Then taking index correction to be negligibly
small, $f_{1}$ and $f_{2}$ are close to:
a.
$f_{1} = 7.8\,cm f_{2} = 12.7\,cm$
Correct Answer
b.
$f_{1} = 12.7\,cm f_{2} = 7.8\,cm$
c.
$f_{1} = 15.6\,cm f_{2} = 25.4\,cm$
d.
$f_{1} = 7.8\,cm f_{2} = 25.4\,cm$
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Q3mcq
The figure shows an elliptical path $ABCD$ of a planet around the sun $S$ such that the area of triangle $CSA$ is $\frac{1}{4}$
the area of the ellipse. (see figure) with $DB$ as the major axis, and $CA$ as the minor axis. If $t_{1}$ is the time taken
for the planet to go over path $ABC$ and $t_{2}$ for path taken over $CDA$ then:
a.
$t_{1} = 4t_{2}$
b.
$t_{1} = 2t_{2}$
c.
$t_{1} = 3t_{2}$
Correct Answer
d.
$t_{1} = t_{2}$
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Q4mcq
A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as
shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the
combination, is a real image, at a distance of:
a.
60 cm from the convex lens
Correct Answer
b.
60 cm form the concave lens
c.
70 cm from the convex lens
d.
70 cm from the concave lens
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Q5mcq
A simple pendulum made of a bob of mass m and a metallic wire of a negligible mass has a time period of $2\,s$ at
$T = 0^{\circ}C$ . If the temperature of the wire is increased, and the corresponding change in its time period is plotted
against its temperature, the resulting graph is a line of slope $S$ . If the coefficient of linear expansion of metal is
$\alpha$, then the value of $S$ is
a.
$\frac{$\alpha$}{2}$
b.
$2$ $\alpha$
c.
$\alpha$
Correct Answer
d.
$\frac{1}{$\alpha$}$
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Q6mcq
In the circuit shown, the resistance r is a variable resistance. If for $r = fR$ , the heat generation in r is
maximum then the value of $f$ is
a.
$\frac{1}{2}$
Correct Answer
b.
$1$
c.
$\frac{1}{4}$
d.
$\frac{3}{4}$
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Q7mcq
In Young's double-slit experiment, the distance between slits and the screen is $1\,m$ and monochromatic light of
wavelength $600\, nm$ is being used. A person standing near the slits is looking at the fringe pattern. When the
separation between the slits is varied, the interference pattern disappears for a particular distance $d_{0}$ between
the slits. If the angular resolution of the eye is $\frac{1}{60}^{\circ}$ , then the value of $d_{0}$ is close to
a.
$1\, mm$
b.
$3\, mm$
c.
$2\, mm$
Correct Answer
d.
$4\, mm$
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Q8mcq
Three capacitors each of $4\,$ $\mu$ $F$ are to be connected in such a way that the effective capacitance is $6\,$ $\mu$ $F$ . This
can be done by connecting them
a.
all in series
b.
all in parallel
c.
two in parallel and one in series
d.
two in series and one in parallel
Correct Answer
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Q9mcq
A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of $75^{o}$ .
One of the fields has a magnitude of $15\, mT$ . The dipole attains stable equilibrium at an angle of $30^{o}$ with this
field. The magnitude of the other field (in $mT$ ) is close to
a.
$1$
b.
$11$
Correct Answer
c.
$36$
d.
$1060$
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Q10mcq
In the following $I$ refers to current and other symbols have their usual meaning. Choose the option that
corresponds to the dimensions of electrical conductivity:
a.
$M^{-1}L^{-3}T^{3}I$
b.
$M^{-1}L^{-3}T^{3}I^{2}$
Correct Answer
c.
$M^{-1}L^{3}T^{3}I$
d.
$ML^{-3}T^{-3}I^{2}$
No explanation saved for this question yet.
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Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The
amplitude and time period for both particles are same and equal to $A$ and $T$ , respectively. At time $t = 0$ one
particle has displacement $A$ while the other one has displacement $-\frac{A}{2}$ and they are moving towards each
other. If they cross each other at time $t$ , then $t$ is:
a.
$\frac{5T}{6}$
b.
$\frac{T}{3}$
c.
$\frac{T}{4}$
d.
$\frac{T}{6}$
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$200\,g$ water is heated from $40^{\,o}C$ to $60^{\,o}C$ . Ignoring the slight expansion of water, the change in its internal
energy is close to (Given specific heat of water $= 4184 J\, kg^{-1} \,K^{-1}$ ):
a.
$167.4\,kJ$
b.
$8.4\,kJ$
c.
$4.2\,kJ$
d.
$16.7\,kJ$
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The potential (in volts) of a charge distribution is given by
$V(z) = 30 -5z^{2}$ for $|z| \leq 1\,m$
$V(z) = 35 -10\,|z|$ for $|z| \geq 1\,m$ .
$V(z)$ does not depend on x and y. If this potential is generated by a constant charge per unit volume $\rho$ $_{0}$ (in units
of $\epsilon$ $_{0}$ ) which is spread over a certain region, then choose the correct statement.
a.
$\rho$ $_{0} = 20\,$ $\epsilon$ $_{0}$ in the entire region
b.
$\rho$ $_{0} = 10\,$ $\epsilon$ $_{0}$ for $|z| \leq 1\,m$ and $\rho$ $_{0} = 0$ else where
c.
$\rho$ $_{0} = 20\,$ $\epsilon$ $_{0}$ for $|z| \leq 1\,m$ and $\rho$ $_{0} = 0$ else where
d.
$\rho$ $_{0} = 40\,$ $\epsilon$ $_{0}$ in the entire region
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A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended
length $L$ . The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R$ , respectively. The
upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium
extended length, of this wire, would equal:
a.
$L(1 + \frac{2}{9} \frac{Mg}{$\pi$YR^{2}})$
b.
$L(1 + \frac{1}{9} \frac{Mg}{$\pi$YR^{2}})$
c.
$L(1 + \frac{1}{3} \frac{Mg}{$\pi$YR^{2}})$
d.
$L(1 + \frac{2}{3} \frac{Mg}{$\pi$YR^{2}})$
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Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see
figure). Through a hole of radius r $(r << R)$ at its bottom, the water leaks out and the stream of water coming
down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of
water stream when it hits the ground is x. Then:
a.
$x = r(\frac{H}{H+h})\frac{1}{4}$
b.
$x = r(\frac{H}{H+h})$
c.
$x = r(\frac{H}{H+h})^{2}$
d.
$x = r(\frac{H}{H+h})\frac{1}{2}$
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Which of the following option correctly describes the variation of the speed and acceleration 'a' of a pointυ
mass falling vertically in a viscous medium that applies a force $F = -k$ υ, where 'k' is a constant, on the body?
(Graphs are schematic and not drown to scale)
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When photons of wavelength $\lambda$ $_{1}$ are incident on an isolated sphere, the corresponding stopping potential is
found to be $V$ . When photons of wavelength $\lambda$ $_{2}$ are used, the corresponding stopping potential was thrice that
of the above value. If light of wavelength $\lambda$ $_{3}$ is used then find the stopping potential for this case:
To know the resistance $G$ of a galvanometer by half deflection method, a battery of emf $V_{E}$ and resistance $R$ is
used to deflect the galvanometer by angle . If a shunt of resistance $\theta$ $S$ is needed to get half deflection the $G$ , $R$
and $S$ are related by the equation:
a.
$S(R + G) = RG$
b.
$2S(R + G) = RG$
c.
$2G = S$
d.
$2S = G$
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An electron in a hydrogen atom makes a transition from $n= 2$ to $n= 1$ and emits a photon. This photon
strikes a doubly ionized lithium atom which was already in an excited state and completely removes the
orbiting electron. The least quantum number for the excited state of the lithium-ion for the process is
a.
$2$
b.
$4$
c.
$5$
d.
$3$
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A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration.
On an inclined plane inside the rocket, making an angle with the horizontal, a point object of mass m is kept.$\theta$
The minimum coefficient of friction $\mu$ $_{min}$ between the mass and the inclined surface such that the mass does not
move is:
a.
$tan 2$ $\theta$
b.
$tan$ $\theta$
c.
$3 tan$ $\theta$
d.
$2 tan$ $\theta$
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A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant
frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10\,ms^{-1}$ , the car needs power P. If
it needs power $\frac{P}{2}$ while moving downhill at speed then value of is:υ υ
a.
$20\,ms^{-1}$
b.
$5\,ms^{-1}$
c.
$15\,ms^{-1}$
d.
$10\,ms^{-1}$
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A series $LR$ circuit is connected to a voltage source with $V(t) =V_{0}sin(\omega t)$ . After a very large time, current
$I(t)$ behaves as $(t_{0} \gg \frac{L}{R} )$ :
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A cubical block of side $30\, cm$ is moving with velocity $2\,m\,s^{-1}$ on a smooth horizontal surface. The surface has
a bump at a point $O$ as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits
the bump, is :
a.
13.3
b.
5.0
c.
9.4
d.
6.7
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An unknown transistor needs to be identified as a $npn$ or $pnp$ type. A multimeter, with +ve and -ve terminals,
is used to measure resistance between different terminals of transistor. If terminal 2 is the base of the transistor
then which of the following is correct for a $pnp$ transistor?
a.
+ve terminal 2, -ve terminal 3, resistance low
b.
+ve terminal 2, -ve terminal 1, resistance high
c.
+ve terminal 1, -ve terminal 2, resistance high
d.
+ve terminal 3, -ve terminal 2, resistance high
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Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. one of them is
blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they
pass each other. speed of sound is 330 m/sec:
a.
450 Hz
b.
540 Hz
c.
270 Hz
d.
648 Hz
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An audio signal consists of two distinct sounds: one a human speech signal in the frequency band of 200 Hz to
2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The
ratio of the AM signal band width required to send both the signals together to the AM signal band width
required to send just the human speech is:
a.
3
b.
5
c.
6
d.
2
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A $50\,\Omega$ resistance is connected to a battery of $5\,V$ . A galvanometer of resistance $100\,\Omega$ is to be used as an
ammeter to measure current through the resistance, for this a resistance $r_{S}$ is connected to the galvanometer.
Which of the following connections should be employed if the measured current is with in $1%$ of the current
without the ammeter in the circuit?
a.
$r_{S} = 0.5\Omega$ in series with galvanometer
b.
$r_{S} = 1\,\Omega$ in series with galvanometer
c.
$r_{S} = 1\,\Omega$ in parallel with galvanometer
d.
$r_{S} = 0.5\,\Omega$ in parallel with the galvanometer
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For the reaction,
$A(g) + B(g) \rightarrow C(g) + D(g), \, \Delta H\rightarrow^{o}$ and $\Delta S^{o}$ are, respectively, $-29.8\,kJ\,mol^{-1}$ and $-0.100\,kJ\,K^{-1}\,mol^{-1}$
at 298 K. The equilibrium constant for the reaction at 298 k is:
a.
$1.0 \times 10^{-10}$
b.
$10$
c.
$1$
d.
$1.0 \times 10^{10}$
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A particular adsorption process has the following characteristics: (i) It arises due to van der Waals forces and
(ii) it is reversible. Identify the correct statement that describes the above adsorption process:
a.
Adsorption is monolayer
b.
Adsorption increases with increase in
temperature
c.
Enthalpy of adsorption is greater than
$100\,kJ\,mol^{-1}$
d.
Energy of activation is low
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Assertion: Rayon is a semisynthetic polymer whose properties are better than natural cotton.
Reason: Mechanical and aesthetic properties of cellulose can be improved by acetylation.
a.
Both assertion and reason are correct, but the
reason is not the correct explanation for the
assertion.
b.
Both assertion and reason are correct, and the
reason is the correct explanation for the assertion.
c.
Assertion in incorrect statement, but the reason is
correct.
d.
Both assertion and reason are incorrect.
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The most appropriate method of making egg-albumin sol is:
a.
Break an egg carefully and transfer the
transparent part of the content to $100\, mL$ of $5%$
w/V saline solution and stir well
b.
Keep the egg in boiling water for $10$ minutes.
After removing the shell, transfer the yellow part
of the content to $100\, mL$ of $5%$ w/V saline
solution and homogenize with a mechanical
shaker
c.
Keep the egg in boiling water for $10$ minutes.
After removing the shell, transfer the white part
of the content to $100\, mL$ of $5%$ w/V saline
solution and homogenize with a mechanical
shaker
d.
Break an egg carefully and transfer only the
yellow part of the content to $100\, mL$ of $5%$ w/V
saline solution and stir well
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The plot shows the variation of $-ln K_{P}$ Versus temperature for the two reactions.
$M(s) + \frac{1}{2}O_{2}(g) \rightarrow MO\rightarrow (s)$ and
$C(s) + \frac{1}{2} O_{2}(g) \rightarrow CO\rightarrow (s)$
Identify the correct statement:
a.
At $T < 1200\,K$ , oxidation of carbon is
unfavourable
b.
Oxidation of carbon is favourable at all
temperatures
c.
At $T < 1200\,K$ , the reaction
$MO(s) + C(s) \rightarrow M(s) + CO(g)\rightarrow$ is spontaneous
d.
At $T > 1200\,K$ , carbon will reduce
$MO_{(s)}\, to \,M_{(s)}$ .
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The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process
shown below:
$O_{3}(g) + Cl^{\cdot } \rightarrow O\rightarrow_{2}(g) + ClO^{\cdot }(g)$ ...(i)
$k_{i} = 5.2 \times 10^{9}\,L\,mol^{-1}\,s^{-1}$
$ClO^{\cdot }(g) + O^{\cdot }(g) O_{2}(g) + Cl^{\cdot }(g)$ ...(ii)
$k_{ii} = 2.6 \times 10^{10}\,L\,\vec{m}ol^{-1}\,s^{-1}$
The closest rate constant for the overall reaction
$O_{3}(g) + O^{\cdot }(g) 2O_{2}(g)$ is:
a.
$1.4 \times 10^{20}\,L\,mol^{-1}\,s^{-1}$
b.
$3.1 \times 10^{10}\,L\,mol^{-1}\,s^{-1}$
c.
$5.2 \times 10^{9}\,L\,\vec{m}ol^{-1}\,s^{-1}$
d.
$2.6 \times 10^{10}\,L\,mol^{-1}\,s^{-1}$
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The amount of arsenic pentasulphide that can be obtained when $35. 5\,g$ arsenic acid is treated with excess $H_{2}S$
in the presence of conc. $HCl$ (assuming $100%$ conversion) is
a.
$0. 25\, mol$
b.
$0. 50\, mol$
c.
$0. 333\, mol$
d.
$0. 125\, mol$
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Match the items in Column $I$ with its main use listed in Column $\, II$ :
Column $\,I$ Column $\, II$
$A$ Silica gel $i.$ Transistor
$B$ Silicon $ii.$ Ion-exchanger
$C$ Silicone $iii.$ Drying agent
$D$ Silicate $iv.$ Sealant
a.
$A\, -\, iii, \,B\, -\,i, \,C\, -\, iv, \,D\, -ii$
b.
$A\, -\, iv, \,B\, -\,i, \,C\, -\, ii, \,D\, -\, iii$
c.
$A\, -\, ii, \,B\, -\,i, \,C\, -\, iv, \,D\, -\, iii$
d.
$A\, -\, ii, \,B\, -\, iv, \,C\, -\,i, \,D\, -\, iii$
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The solubility of $N_{2}$ in water at $300 K$ and $500 torr$ partial pressure is $0 .01\, g\,L^{-1}.$ The solubility (in $g\,L^{-1}$ )
at $750 torr$ partial pressure is:
a.
$0.0075$
b.
$0.005$
c.
$0. 02$
d.
$0.015$
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A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature.
Identify the correct statement about the reaction among the following:
a.
$\Delta H$ is negative while $\Delta S$ is positive
b.
Both $\Delta H$ and $\Delta S$ are negative
c.
$\Delta H$ is positive while $\Delta S$ is negative
d.
Both $\Delta H$ and $\Delta S$ are positive
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$5\,L$ of an alkane requires $25\,L$ of oxygen for its complete combustion. If all volumes are measured at constant
temperature and pressure, the alkane is
a.
Isobutane
b.
Ethane
c.
Butane
d.
Propane
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For $x\, \in R, \,x\neq 0, \,x\neq 1,$ let $f_{0}(x) = \frac{1}{1-x}$ and $f_{n+1}(x) =f_{0}(f_{n}(x)), \,n= 0, \,1, \,2, … . .$ Then the value of
$f_{100}(3) +f_{1}( \frac{2}{3})+f_{2}( \frac{3}{2})$ is equal to :
a.
$\frac{8}{3}$
b.
$\frac{4}{3}$
c.
$\frac{5}{3}$
d.
$\frac{1}{3}$
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The shortest distance between the lines $\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$ and $\frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4},$ lies in the interval:
a.
$(3, 4]$
b.
$(2, 3]$
c.
$[1, 2)$
d.
$[0, 1)$
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$| |$
If $f(x)$ is a differentiable function in the interval $(0, \,\infty )$ such that $f(1) = 1$ and $lim_{t\rightarrow \rightarrow x}\frac{t^{2}f(x)-x^{2}f(t)}{t-x} = 1,$ for each
$x> 0,$ then $f(\frac{3}{2})$ is equal to
a.
$\frac{23}{18}$
b.
$\frac{13}{6}$
c.
$\frac{25}{9}$
d.
$\frac{31}{18}$
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Consider the following two statements:
$P$ : If $7$ is an odd number, then $7$ is divisible by $2$ .
$Q$ : If $7$ is a prime number, then $7$ is an odd number.
If $V_{1}$ is the truth value of the contrapositive of $P$ and $V_{2}$ is the truth value of contrapositive of $Q$ , then the
ordered pair $(V_{1},V_{2})$ equals
a.
$(F,T)$
b.
$(F,F)$
c.
$(T,F)$
d.
$(T,T)$
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The distance of the point $(1, \, -2, \,4)$ from the plane passing through the point $(1, \,2, \,2)$ and perpendicular to
the planes $x- y+ 2z= 3$ and $2x-2y+z+ 12 = 0,$ is :
a.
$2$
b.
$\sqrt{2}$
c.
$2\sqrt{2}$
d.
$\frac{1}{\sqrt{2}}$
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If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1$ , meets the coordinate
axes at $A$ and $B$ , $(A\, \neq B),$ then the locus of the midpoint of $AB$ is:
a.
$7xy= 6(x+y)$
b.
$4(x+y)^{2} -28(x+y) + 49 = 0$
c.
$6xy= 7(x+y)$
d.
$14(x+y)^{2} -97(x+y) + 168 = 0$
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The point $(2, 1)$ is translated parallel to the line $L:x- y= 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third
quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is
a.
$x+y= 2 - \sqrt{6}$
b.
$2x+ 2y= 1 - \sqrt{6}$
c.
$x+y= 3 -3\sqrt{6}$
d.
$x+y= 3 -2\sqrt{6}$
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Let $a$ and $b$ respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose
eccentricity satisfies the equation $9e^{2} -18e+ 5 = 0$ . If $S(5, \,0)$ is a focus and $5x= 9$ is the corresponding
directrix of this hyperbola, then $a^{2} - b^{2}$ is equal to
a.
$-7$
b.
$-5$
c.
$5$
d.
$7$
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A circle passes through $(-2, 4)$ and touches the $y-$ axis at $(0, 2)$ . Which one of the following equations can
represent a diameter of this circle ?
a.
$2x-3y+ 10 = 0$
b.
$3x+ 4y-3 = 0$
c.
$4x+ 5y-6 = 0$
d.
$5x+ 2y+ 4 = 0$
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If the tangent at a point $P$ , with parameter $t$ , on the curve $x= 4t^{2} + 3, \,y= 8t^{3} -1, \,t\, \in R,$ meets the curve
again at a point $Q$ , then the coordinates of $Q$ are :
a.
$(16t^{2} + 3, \, -64t^{3} -1)$
b.
$(4t^{2} + 3, \, -8t^{3} -1)$
c.
$(t^{2} + 3, \,t^{3} -1)$
d.
$(t^{2} + 3, \, - t^{3} -1)$
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In a triangle $ABC$ , right angle at vertex $A$ , if the position vectors of $A,B$ and $C$ are respectively
$3ˆi+ \,ˆj-\,ˆk, \, - ˆi+ 3ˆj+pˆk$ and $5ˆi+qˆj-4ˆk$ , then the point $(p,q)$ lies on a line:
a.
Making an obtuse angle with the positive
direction of $x- axis$
b.
Parallel to $x- axis$
c.
Parallel to $y- axis$
d.
Making an acute angle with the positive direction
of $x- axis$
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If the four letter words (need not be meaningful) are to be formed using the letters from the word
"MEDITERRANEAN" such that the first letter is $R$ and the fourth letter is $E$ , then the total number of all such
words is :
a.
$110$
b.
$59$
c.
$\frac{11!}{(2!)^{3}}$
d.
$56$
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If the tangent at a point on the ellipse $\frac{x^{2}}{27} + \frac{y^{2}}{3} = 1$ meets the coordinate axes at $A$ and $B$ , and $O$ is the origin,
then the minimum area (in sq. units) of the triangle $OAB$ is
a.
$3\sqrt{3}$
b.
$\frac{9}{2}$
c.
$9$
d.
$9\sqrt{3}$
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$cosx sinx sinx$
The number of distinct real roots of the equation, $sinx cosx sinx = 0$ in the interval $[- \frac{\pi}{4}, \frac{\pi}{4}]$ is :
$sinx sinx cosx$
a.
$1$
b.
$4$
c.
$2$
d.
$3$
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$|$
If $A$ and $B$ are any two events such that $P(A) = \frac{2}{5}$ and $P(A\cap B) = \frac{3}{20},$ then the conditional probability,
$P(A|(A' \cup B')),$ where $A'$ denotes the complement of $A$ , is equal to :
a.
$\frac{11}{20}$
b.
$\frac{5}{17}$
c.
$\frac{8}{17}$
d.
$\frac{1}{4}$
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The point represented by $2 +i$ in the Argand plane moves $1$ unit eastwards, then $2$ units northwards and finally
from there $2\sqrt{2}$ units in the south-west wards direction. Then its new position in the Argand plane is at the
point represented by :
a.
$1 +i$
b.
$2 + 2i$
c.
$-2 -2i$
d.
$-1 - i$
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