A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$ . It is surrounded by air. A light ray is incident
at the mid point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray
grazes along the wall of the rod is
a.
$sin^{-1} (\frac{1}{2})$
b.
$sin^{-1} (\frac{\sqrt{3}}{2})$
c.
$sin^{-1} (\frac{2}{\sqrt{3}})$
d.
$sin^{-1} (\frac{1}{\sqrt{3}})$
Correct Answer
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Q2mcq
The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output
waveform.
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Q3mcq
A mixture of light, consisting of wavelength $590\,nm$ and an unknown wavelength, illuminates Young's double
slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights
coincide. Further, it is observed that the third bright fringe of known light coincides with the $4^{th\,}$ bright fringe
of the unknown light. From this data, the wavelength of the unknown light is
a.
$393.4\,nm$
b.
$885.0\,nm$
c.
$442.5\,nm$
Correct Answer
d.
$776.8\,nm$
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Q4mcq
A motor cycle starts from rest and accelerates along a straight path at $2\,m/s^{2}$ . At the starting point of the motor
cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency
of the siren at $94%$ of its value when the motor cycle was at rest? (speed of sound $= 330\,ms^{-1})$
a.
$49\,m$
b.
$98\,m$
Correct Answer
c.
$147\,m$
d.
$196\,m$
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Q5mcq
The magnitude of the magnetic field $(B)$ due to loop $ABCD$ at the origin $(O)$ is
a.
zero
b.
$\frac{\mu _{0}(b-a)}{24ab}$
Correct Answer
c.
$\frac{\mu _{0}I}{4\pi}[ \frac{b-a}{ab}]$
d.
$\frac{\mu _{o}|}{4\pi} [2(b- a) + \frac{\pi}{3}(a+b)]$
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Q6mcq
Two points $P$ and $Q$ are maintained at the potentials of $10\,V$ and $-4\,V$ respectively. The work done in moving
100 electrons from $P$ to $Q$ is
a.
$-19 \times 10^{-17}\,J$
b.
$9.60 \times 10^{-17}\,J$
c.
$-2.24 \times 10^{-16}\,J$
d.
$2.24 \times 10^{-16}\,J$
Correct Answer
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Q7mcq
This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the
one that best describes the two statements. Statement-1: The temperature dependence of resistance is usually
given as $R=R_{0}(1 +\alpha \Delta t)$ . The resistance of a wire changes from $100\Omega$ to $150\Omega$ when its temperature is
increased from $27^{\circ }C$ to $227^{\circ }C$ . This implies that $\alpha = 2.5 \times 10^{-3}/^{\circ }C$ . Statement 2: $R=R_{i}(1 +\alpha \Delta T)$ is
valid only when the change in the temperature $\Delta T$ is small and $\Delta R= (R- R_{0}) \ll R_{0}$ .
a.
Statement-1 is true, Statement-2 is false
Correct Answer
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
c.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation of
Statement-1.
d.
Statement-1 is false, Statement-2 is true
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Q8mcq
A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two
corners. If the net electrical force on $Q$ is zero, then the $Q/q$ equals
a.
$-2\sqrt{2}$
Correct Answer
b.
$-1$
c.
1
d.
$-\frac{1}{\sqrt{2}}$
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Q9mcq
Three sound waves of equal amplitudes have frequencies $(v-1),v, (v+ 1)$ . They superpose to give beats. The
number of beats produced per second will be
a.
4
b.
3
c.
2
Correct Answer
d.
1
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Q10mcq
The transition from the state $n= 4$ to $n= 3$ in a hydrogen like atom results in ultraviolet radiation. Infrared
radiation will be obtained in the transition from
a.
$2 \rightarrow 1\rightarrow$
b.
$3 \rightarrow 2\rightarrow$
c.
$4 \rightarrow 2\rightarrow$
d.
$5 4$
Correct Answer
No explanation saved for this question yet.
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One kg of a diatomic gas is at a pressure of $8 \times 10^{4}\,N/m^{2}$ . The density of the gas is $4\,kg/m^{-3}$ . What is the
energy of the gas due to its thermal motion?
a.
$3 \times 10^{4}\,J$
b.
$5 \times 10^{4}\,J$
c.
$6 \times 10^{4}\,J$
d.
$7 \times 10^{4}\,J$
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Let $P(r) = \frac{Q}{\pi R^{4}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$ . for a
point ' $p$ ' inside the sphere at distance $r_{1}$ from the centre of the sphere, the magnitude of electric field is
a.
0
b.
$\frac{Q}{4\pi \epsilon _{0}r^{2}_{1}}$
c.
$\frac{Qr^{2}}{4\pi \epsilon _{0}R^{4}}^{1}$
d.
$\frac{Q^{2}}{3\pi \epsilon _{0}R^{4}}^{1}$
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A thin uniform rod of length $\ell$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its
maximum angular speed is $\omega$ . Its centre of mass rises to a maximum height of
a.
$\frac{1}{3} \frac{\ell ^{2}\omega ^{2}}{g}$
b.
$\frac{1}{6} \frac{\ell \omega}{g}$
c.
$\frac{1}{2} \frac{\ell ^{2}\omega ^{2}}{g}$
d.
$\frac{1}{6} \frac{\ell ^{2}\omega ^{2}}{\,g}$
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The above is a plot of binding energy per nucleon $E_{b}$ , against the nuclear mass $M;A,B,C,D,E,F$
correspond to different nuclei. Consider four reactions: (i) $\vec{A}+B\rightarrow \rightarrow C+\epsilon$ (ii) $C \rightarrow A + B +\rightarrow \epsilon$ (iii)
$D + E \rightarrow F +\rightarrow \epsilon$ and (iv) $F \rightarrow \rightarrow D+E+\epsilon$ where $\epsilon$ is the energy released? In which reactions is $\epsilon$ positive?
a.
(i) and (iv)
b.
(i) and (iii)
c.
(ii) and (iv)
d.
(ii) and (iii)
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Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $A$
and wire-2 has cross-sectional area $3A$ . If the length of wire 1 increases by $\Delta x$ on applying force $F$ , how much
force is needed to stretch wire 2 by the same amount?
a.
$F$
b.
$4\,F$
c.
$6\,F$
d.
$9\,F$
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The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g =$ the acceleration due to gravity on
the surface of the earth) in terms of $R$ , the radius of the earth is
a.
$2R$
b.
$\frac{R}{\sqrt{2}}$
c.
$\frac{R}{2}$
d.
$\sqrt{2}R$
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In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale
exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-
degree $(= 0.5^{\circ })$ , then the least count of the instrument is
a.
one minute
b.
half minute
c.
one degree
d.
half degree
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If $x,v$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic
motion of time period $T$ , then, which of the following does not change with time?
a.
$a^{2}T^{2} + 4\pi ^{2}v^{2}$
b.
$\frac{aT}{x}$
c.
$aT + 2\pi v$
d.
$\frac{aT}{v}$
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Consider a rubber ball freely falling from a height $h= 4.9\,m$ onto a horizontal elastic plate. Assume that the
duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a
function of time the height as function of time will be
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This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the
one that best describes the two statements. Statement - 1: For a charged particle moving from point $P$ to point
$Q$ , the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to
point $Q$ . Statement-2: The net work done by a conservative force on an object moving along a closed loop is
zero
a.
Statement-1 is true, Statement-2 is false
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
c.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation of
Statement-1.
d.
Statement-1 is false, Statement-2 is true
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A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of
temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figure.
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In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and
for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance
$u$ and the image distance $v$ , from the lens, is plotted using the same scale for the two axes. A straight line
passing through the origin and making an angle of $45^{\circ }$ with the x-axis meets the experimental curve at $P$ . The
coordinates of $P$ will be
a.
$(2f, 2f)$
b.
$(\frac{f}{2}, \frac{f}{2})$
c.
$(f,f)$
d.
$(4f, 4f)$
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The surface of a metal is illuminated with the light of $400\,nm$ . The kinetic energy of the ejected photoelectrons
was found to be $1.68eV$ . The work function of the metal is $(hc = 1240eVnm)$
a.
$3.09eV$
b.
$1.41eV$
c.
$151eV$
d.
$1.68eV$
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An inductor of inductance $L = 400mH$ and resistors of resistances $R_{1} = 2\Omega$ and $R_{2} = 2\Omega$ are connected to a
battery of emf $12\,V$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is
closed at $t= 0$ . The potential drop across $L$ as a function of time is
a.
$6e^{-5t}V$
b.
$\frac{12}{t}e^{-3t}V$
c.
$6(1 - e^{-t/0.2})V$
d.
$12e^{-5t}V$
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Given : $E^{\circ }_{Fe^{3+}/Fe} = -0.036\,V, E^{\circ }_{Fe^{2+}/Fe} = -0.439\,V$ . The value of standard electrode potential for the
change, $Fe^{3+}_{(aq\,)} + e^{-} \rightarrow Fe\rightarrow^{2+}(aq)$ will be :
a.
$-0.072\,V$
b.
$0.385\,V$
c.
$0.770\,V$
d.
$-0.270$
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In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is
$CH_{3}OH(\ell ) + \frac{3}{2}O_{2}(\,g) \rightarrow CO\rightarrow_{2}(\,g) + 2H_{2}O(\ell )$ At $298\,K$ standard Gibb's energies of formation for
$CH_{3}OH(\ell ), H_{2}O(\ell )$ and $CO_{2}(\,g)$ are $-166.2, -237.2$ and $-394.4\,kJ\,mol^{-1}$ respectively. If standard enthalpy
of combustion of methanol is $-726\,kJ\,mol^{-1}$ , efficiency of the fuel cell will be
a.
$80%$
b.
$87%$
c.
$90%$
d.
$97%$
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Solid Ba $(NO_{3})_{2}$ is gradually dissolved in a $1.0 \times 10^{-4}MNa_{2}CO_{3}$ solution. At what concentration of $Ba^{2+}$
will a precipitate begin to form ? $(K_{sp}$ for $BaCO_{3} = 5.1 \times 10^{-9})$ .
a.
$4.1 \times 10^{-5}M$
b.
$5.1 \times 10^{-5}M$
c.
$8.1 \times 10^{-8}M$
d.
$8.1 \times 10^{-7}M$
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In an atom, an electron is moving with a speed of $600\,m/s$ with an accuracy of $0.005%$ . Certainity with which
the position of the electron can be located is $(h= 6.6 \times 10^{-34}\,kg\,m^{2}\,s^{-1}$ , mass of electron,
$e_{m} = 9.1 \times 10^{-31}\,kg$ )
a.
$1.52 \times 10^{-4}\,m$
b.
$5.10 \times 10^{-3}\,m$
c.
$1.92 \times 10^{-3}\,m$
d.
$3.84 \times 10^{-3}\,m$
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Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^{3}\,ms^{-1}$ (Mass of proton
$= 1.67 \times 10^{-27}\,kg$ and $h = 6.63 \times 10^{-34}Js$ ):
a.
$0.032\,nm$
b.
$0.40\,nm$
c.
$2.5\,nm$
d.
$14.0\,nm$
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The bond dissociation energy of $B -F$ in $BF_{3}$ is $646\,kJ$ mol $^{-1}$ whereas that of $C -F$ in $CF_{4}$ is $515\,kJ$ mol
$^{-1}$ . The correct reason for higher B-F bond dissociation energy as compared to that of $C$ - $F$ is :
a.
smaller size of B-atom as compared to that of C-
atom
b.
stronger $\sigma$ bond between $B$ and $F$ in $BF_{3}$ as
compared to that between $C$ and $F$ in $CF_{4}$
c.
significant $p\pi -p\pi$ interaction between $B$ and $F$
in $BF_{3}$ whereas there is no possibility of such
interaction between $C$ and $F$ in $CF_{4}$ .
d.
lower degree of $p\pi -p\pi$ interaction between $B$
and $F$ in $BF_{3}$ than that between $C$ and $F$ in $CF_{4}$ .
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The half life period of a first order chemical reaction is $6.93$ minutes. The time required for the completion of
$99%$ of the chemical reaction will be $(log 2 = 0.301)$ :
a.
$230.3$ minutes
b.
$23.03$ minutes
c.
$46.06$ minutes
d.
$460.6$ minutes
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A binary liquid solution is prepared by mixing $n$ -heptane and ethanol. Which one of the following statements
is correct regarding the behaviour of the solution?
a.
The solution formed is an ideal solution
b.
The solution is non-ideal, showing +ve deviation
from Raoult's law.
c.
The solution is non-ideal, showing -ve deviation
from Raoult's law.
d.
n-heptane shows +ve deviation while ethanol
shows -ve deviation from Raoult's law.
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On the basis of the following thermochemical data: $(\Delta fG^{\circ }H^{+}_{(aq)\,} = 0)$
$H_{2}O(\ell ) \rightarrow H\rightarrow^{+}(aq) + OH^{-}(aq); \Delta H = 57.32\,kJ$
$H_{2}(\,g) + \frac{1}{2}O_{2}(\,g) \rightarrow H\rightarrow_{2}O(\ell ); \Delta H = -286.20\,kJ$
The value of enthalpy of formation of $OH^{-}$ ion at $25^{\circ }C$ is:
a.
$-22.88\,kJ$
b.
$-228.88\,kJ$
c.
$+228.88\,kJ$
d.
$-343.52\,kJ$
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Two liquids $X$ and $Y$ form an ideal solution. At $300\,K$ , vapour pressure of the solution containing 1 mol of $X$
and $3\,mol$ of $Y$ is $550\,mmHg$ . At the same temperature, if $1\,mol$ of $Y$ is further added to this solution, vapour
pressure of the solution increases by $10\,mmHg$ . Vapour pressure (in $mmHg$ ) of $X$ and $Y$ in their pure states
will be, respectively :
a.
200 and 300
b.
300 and 400
c.
400 and 600
d.
500 and 600
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Let $f(x) =x|x|$ and $g(x) = sinx$ . Statement-1 : gof is differentiable at $x= 0$ and its derivative is continuous
at that point. Statement-2 : gof is twice differentiable at $x= 0$ .
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is a correct explanation for
Statement-1
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not a correct explanation for
Statement-1
c.
Statement-1 is true, Statement-2 is false
d.
Statement-1 is false, Statement-2 is true
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$| | |$
$a a+ 1 a-1 a+ 1 b+ 1 c-1$
Let $a,b,c$ be such that $b(a+c) \neq 0$ . If $-b b+ 1 b-1 + a-1 b-1 c+ 1 = 0$ , then the
$c c-1 c+ 1 (-1)^{n+2}a (-1)^{n+1}b (-1)^{n}c$
value of ' $n$ ' is
a.
zero
b.
any even integer
c.
any odd integer
d.
any integer
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$||$
Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the
distance of any one of them from the point $(1, 0)$ to the distance from the point $(-1, 0)$ is equal to $\frac{1}{3}$ . Then the
circumcentre of the triangle $ABC$ is at the point
a.
$(0, 0)$
b.
$(\frac{5}{4}, 0)$
c.
$(\frac{5}{2}, 0)$
d.
$(\frac{5}{3}, 0)$
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Statement-1 : The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$ Statement-2 : The sum of first $n$ natural
numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is a correct explanation for
Statement-1
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not a correct explanation for
Statement-1
c.
Statement-1 is true, Statement-2 is false
d.
Statement-1 is false, Statement-2 is true
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If $P$ and $Q$ are the points of intersection of the circles $x^{2} +y^{2} + 3x+ 7y+ 2p-5 = 0$ and
$x^{2} +y^{2} + 2x+ 2y- p^{2} = 0$ , then there is a circle passing through $P,Q$ and $(1, 1)$ for
a.
all values of $p$
b.
all except one value of $p$
c.
all except two values of $p$
d.
exactly one value of $p$
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The ellipse $x^{2} + 4y^{2} = 4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in
inscribed in another ellipse that passes through the point $(4, 0)$ . Then the equation of the ellipse is
a.
$x^{2} + 16y^{2} = 16$
b.
$x^{2} + 12y^{2} = 16$
c.
$4x^{2} + 48y^{2} = 48$
d.
$4x^{2} + 64y^{2} = 48$
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If $\vec{u}, v, \vec{w}$ are non-coplanar vectors and $p,\vec{q}$ are real numbers, then the equality
$[3\vec{u} \bar{p}v p\vec{w}] -[p\vec{v} \vec{w} q\vec{u}] -[2\vec{w} qv q\vec{u}] = 0$ holds for
a.
exactly one value of $(p,q)$
b.
exactly two values of $(p,q)$
c.
more than two but not all values of $(p,q)$
d.
all values of $(p,q)$
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From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged
in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is
a.
less than 500
b.
at least 500 but less than 750
c.
at least 750 but less than 1000
d.
at least 1000
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One ticket is selected at random from 50 tickets numbered $00, 01, 02, … , 49$ . Then the probability that the sum
of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals
a.
$\frac{1}{14}$
b.
$\frac{1}{7}$
c.
$\frac{5}{14}$
d.
$\frac{1}{50}$
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In a binomial distribution $B(n,p= \frac{1}{4})$ , if the probability of at least one success is greater than or equal to $\frac{9}{10}$ ,
then $n$ is greater than
a.
$\frac{1}{log_{10}^{4}-log_{10}^{3}}$
b.
$\frac{1}{log_{10}4+log_{10}3}$
c.
$\frac{9}{log_{10}^{4}-log_{10}3}$
d.
$\frac{4}{log_{10}^{4}-log_{10}3}$
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