The correct match between the entries in column I and column II are :
I II
Radiation Wavelength
a Microwave i $100\,m$
b Gamma rays ii $10^{-15}m$
c A.M. radio iii $10^{-10}m$
d X-rays iv $10^{-3}m$
Two Zener diodes ( $A$ and $B$ ) having breakdown voltages of $6\,V$ and $4\,V$ respectively, are connected as shown
in the circuit below. The output voltage $V_{0}$ variation with input voltage linearly increasing with time, is given
by ( $V_{input}\, = \,0V at t\, = \,0$ )
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Q3nat
A prism of angle $A= 1^{\circ}\mu = 1. 5$ . A good estimate for the minimum angle of deviation (in degrees) is close to
$\frac{N}{10} .$ Value of $N$ is $… … …$
✓ Accepted Answer:5
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Q4mcq
Two different wires having lengths $L_{1}$ and $L_{2}$ and respective temperature coefficient of linear expansion $\alpha _{1}$ and
$\alpha _{2},$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is :
A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_{1}$ and (ii)
back and forth in a direction perpendicular to its plane, with a period $T_{2}$ . The ratio $\frac{T_{1}}{T_{2}}$ will be :
a.
$\frac{2}{\sqrt{3}}$
Correct Answer
b.
$\frac{2}{3}$
c.
$\frac{3}{\sqrt{2}}$
d.
$\frac{\sqrt{2}}{3}$
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Q6mcq
Two coherent sources of sound, $S_{1}$ and $S_{2},$ produce sound waves of the same wavelength $\lambda = 1\,m$ are in
phase. $S_{1}$ and $S_{2}$ are placed $1. 5\,m$ apart (see fig). A listener, located at $L$ , directly in front of $S_{2}$ , finds that the
intensity is at a minimum when he is $2\,m$ away from $S_{2}$ . The listener moves away from $S_{1}$ , keeping the
distance from $S_{2}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$
from $S_{1}$ . Then $d$ is :
a.
$12m$
b.
$5m$
Correct Answer
c.
$2m$
d.
$3m$
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Q7mcq
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate
$\frac{dM(t)}{dt} =bv^{2}(t),$ where $v(t)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is:
a.
$-bv^{3}(t)$
b.
$\frac{-bv^{3}}{M(t)}$
Correct Answer
c.
$- \frac{2bv^{3}}{M(t)}$
d.
$- \frac{bv^{3}}{2M(t)}$
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Q8mcq
The acceleration due to gravity on the earth's surface at the poles is $g$ and angular velocity of the earth about the
axis passing through the pole is $\omega$ . An object is weighed at the equator and at a height $h$ above the poles by
using a spring balance. If the weights are found to be same, then $h$ is: ( $h\ll R$ , where $R$ is the radius of the
earth)
a.
$\frac{R^{2}\omega ^{2}}{2g}$
Correct Answer
b.
$\frac{R^{2}\omega ^{2}}{g}$
c.
$\frac{R^{2}\omega ^{2}}{4g}$
d.
$\frac{R^{2}\omega ^{2}}{8g}$
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Q9mcq
A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a
current of $6mA$ it produces a deflection of $2^{\circ}$ , its figure of merit is close to :
a.
$333^{\circ}\,A/div$
b.
$6 \times 10^{-3}A/ div$
c.
$\,666^{\circ}\,A/div.$
d.
$3 \times 10^{-3}A/ div$
Correct Answer
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Q10mcq
A parallel plate capacitor has plate of length $l$ , width $w$ and separation of plates is $d$ . It is connected to a battery
of emf $V$ . A dielectric slab of the same thickness $d$ and of dielectric constant $K = 4$ is being inserted between
the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be
two times the initial energy stored?
a.
$\frac{2l}{3}$
b.
$\frac{l}{3}$
Correct Answer
c.
$\frac{l}{4}$
d.
$\frac{l}{2}$
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Nitrogen gas is at $300\,^{\circ}C$ temperature. The temperature (in $K$ ) at which the rms speed of a $H_{2}$ molecule would
be equal to the rms speed of a nitrogen molecule, is $… … … .$ (Molar mass of $N_{2}$ gas $28\,g$ ).
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An iron rod of volume $10^{-3}\,m^{3}$ and relative permeability $1000$ is placed as core in a solenoid with
$10\, turns \, cm^{-1}$ . If a current of $0. 5\,A$ is passed through the solenoid, then the magnetic moment of the rod
will be :
a.
$50 \times 10^{2} Am^{2}$
b.
$5 \times 10^{2} Am^{2}$
c.
$500 \times 10^{2} Am^{2}$
d.
$0. 5 \times 10^{2} Am^{2}$
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A driver in a car, approaching a vertical wall notices that the frequency of his car horn has changed from
$440\, Hz$ to $480\, Hz$ , when it gets reflected from the wall. If the speed of sound in air is $345\,m\,s^{-1}$ , then the speed
of the car is:
a.
$54\,km/hr$
b.
$36\,km/hr$
c.
$18\,km/hr$
d.
$24\,km/hr$
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Ten charges are placed on the circumference of a circle of radius R with constant angular separation between
successive charges. Alternate charges $1, 3, 5, 7, 9$ have charge $(+q)$ each, while $2, 4, 6, 8, 10$ have charge $(-q)$
each. The potential V and the electric field E at the centre of the circle are respectively : (Take $V = 0$ at
infinity)
In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then
potential at point $B$ with respect to the point $A$ is:
a.
$+2V$
b.
$-2V$
c.
$-1V$
d.
$+1V$
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An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor $C$ with a
sliding connector are located in the same plane, as shown in the figure. The connector has length l. and
resistance $R$ . It slides to the right with a velocity $v$ . The resistance of the conductor and the self inductance of
the loop are negligible. The induced current in the loop, as a function of separation r, between the connector
and the straight wire is
a.
$\frac{\mu _{0}}{4\pi} \frac{Iv \ell}{Rr}$
b.
$\frac{\mu _{0}}{\pi} \frac{Iv \ell}{Rr}$
c.
$\frac{2\mu _{0}}{\pi} \frac{Iv \ell}{Rr}$
d.
$\frac{\mu _{0}}{2\pi} \frac{Iv \ell}{Rr}$
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A thin rod of mass $0. 9\, kg$ and length $1\,m$ is suspended, at rest, from one end so that it can freely oscillate in
the vertical plane. A particle of move $0. 1\, kg$ moving in a straight line with velocity $80\,m\,s^{-1}$ hits the rod at its
bottom most point and sticks to it (see figure). The angular speed (in $rad \,s^{-1}$ ) of the rod immediately after the
collision will be …………
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The velocity $(v)$ and time $(t)$ graph of a body in a straight line motion is shown in the figure. The point $S$ is at
$4. 333$ seconds. The total distance covered by the body in $6\,s$ is :
a.
$\frac{37}{3}m$
b.
$12m$
c.
$11m$
d.
$\frac{49}{4}m$
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In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through
a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its
velocity just before entering the water surface, then the value of $h$ is proportional to: (ignore viscosity of air)
a.
$r^{4}$
b.
$r$
c.
$r^{3}$
d.
$r^{2}$
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The surface of a metal is illuminated alternately with photons of energies $E_{1}= 4\, eV$ and $E_{2}= 2. 5\, eV$
respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is $2.$ The work
function of the metal in $(eV)$ is..........
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The quantities $x=_{\sqrt{\mu _{0}\in _{0}}} ,y=_{B}$ and $z=_{CR}$ are defined where C-capacitance, R-Resistance, $\ell -$ length, E-
Electric field, B-magnetic field and $\in 0, \,\mu 0, -$ free space permittivity and permeability respectively. Then:
a.
x, y and z have the same dimension.
b.
Only x and z have the same dimension
c.
Only x and y have the same dimension
d.
Only y and z have the same dimension.
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A radioactive nucleus decays by two different processes. The half-life for the first process is $10\,s$ and that for
the second is $100\,s$ . The effective half-life of the nucleus is close to:
a.
$9\,s$
b.
$6\,s$
c.
$55\,s$
d.
$12\,s$
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A body of mass $2\, kg$ is driven by an engine delivering a constant power of $1\,J\,s^{-1}$ . the body starts from rest
and moves in a straight line. After $9\,s$ , the body has moved a distance (in $m$ )….
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In an adiabatic process, the density of a diatomic gas becomes $32n$ times its initial value. The final pressure of
the gas is found to be $n$ times the initial pressure. The value of $n$ is:
a.
$32$
b.
$326$
c.
$128$
d.
$\frac{1}{32}$
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The volume, in $mL$ , of $0. 02 MK_{2}Cr_{2}O_{7}$ , solution required to react with $0. 288g$ of ferrous oxalate in
acidic medium is $… … … …$ (Molar mass of $Fe = 56 gmol^{-1}$ )
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For a reaction $X+Y = 2Z, 1. 0 mol$ of $X, 1. 5 mol$ of $Y$ and $0. 5 mol$ of $Z$ were taken in a $1L$ vessel
and allowed to react. At equilibrium, the concentration of $Z$ was $1. 0 molL^{-1}$ . the equilibrium constant of
the reaction is $… … … … \frac{x}{15}.$ The value of x is $… … .$
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Adsorption of a gas follows Freudlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on mass $m$ of
the adsorbent, the correct plot of $\frac{x}{m}$ versus p is:
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The rate constant $(k)$ of a reaction is measured at different temperature $(T)$ , and the data are plotted in the
given figure. the activation energy of the reaction in $kJmol^{-1}$ is : $(R$ is gas constant)
a.
$2/R$
b.
$1/R$
c.
$R$
d.
$2R$
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For a dimerization reaction,
$2A(g) \rightarrow A\rightarrow_{2}(g)$
at $298K,\Delta U^{-} = -20 kJmol^{-1},\Delta S^{-} = -30 JK^{-1} mol^{-1}$ ,then the $\Delta G^{-}$ will be …..J.
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An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the
centres of two nearest octahedral voids in the crystal lattice is:
a.
$\frac{a}{\sqrt{2}}$
b.
$a$
c.
$\sqrt{2}a$
d.
$\frac{a}{2}$
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Let $A= {a,b,c}$ and $B= {1, 2, 3, 4}.$ Then the number of elements in the set $C = {f :A\rightarrow \rightarrow B|2 \in f(A)$
and $f$ is not one-one $}$ is $…$
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$|| |$
$||$
In a bombing attack, there is $50%$ chance that a bomb will hit the target. At least two independent hits are
required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure
that there is at least $99%$ chance of completely destroying the target, is $. . . . .$
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If the sum of the second, third and fourth terms of a positive term G.P. is $3$ and the sum of its sixth, seventh
and eighth terms is $243$ , then the sum of the first $50$ terms of this G.P. is :
a.
$\frac{1}{26}(3^{49}-1)$
b.
$\frac{1}{26} (3^{50}-1)$
c.
$\frac{2}{13}(3^{50}-1)$
d.
$\frac{1}{13} (3^{50}-1)$
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The area (in sq. units) of the region $A={(x,y):(x-1)[x]\leq y\leq 2\sqrt{x}, 0 \leq x\leq 2},$ where $[t]$ denotes the
greatest integer function, is :
a.
$\frac{8}{3}\sqrt{2}- \frac{1}{2}$
b.
$\frac{4}{3}\sqrt{2}+ 1$
c.
$\frac{8}{3}\sqrt{2}-1$
d.
$\frac{4}{3}\sqrt{2}- \frac{1}{2}$
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If $\alpha$ and $\beta$ are the roots of the equation, $7x^{2} -3x-2 = 0,$ then the value of $\frac{\alpha}{1-\alpha ^{2}} + \frac{\beta}{1-\beta ^{2}}$ is equal to:
a.
$\frac{27}{32}$
b.
$\frac{1}{24}$
c.
$\frac{3}{8}$
d.
$\frac{27}{16}$
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Let the vectors $\vec{a}, \vec{b}, \vec{c}$ be such that $\vec{a} = 2, \vec{b} = 4$ and $\vec{c} = 4.$ If the projection of $\vec{b}$ on $\vec{a}$ is equal to the
projection of $\vec{c}$ on $\vec{a}$ and $\vec{b}$ is perpendicular to $\vec{c},$ then the value of $\vec{a}+ \vec{b}- \vec{c}$ is $…$
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If for some, $\alpha \in R,$ the lines $L_{1}: \frac{x+1}{2} = \frac{y-2}{-1} = \frac{z-1}{1}$ and $L_{2}: \frac{x+2}{\alpha} = \frac{y+1}{5-\alpha} = \frac{z+1}{1}$ are coplanar, then the line $L_{2}$
passes through the point :
a.
$(10, \,2, \,2)$
b.
$(2, \,-10, \,-2)\,$
c.
$\,(10, \,-2, \,-2)$
d.
$\,(-2, \,10, \,2)$
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If the lines $x+y=a$ and $x- y=b$ touch the curve $y=x^{2} -3x+ 2$ at the points where the curve
intersects the $x-$ axis, then $\frac{a}{b}$ is equal to $…$
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If the system of linear equations
$x+y+ 3z= 0$
$x+ 3y+k^{2}z= 0$
$3x+y+ 3z= 0$
has a non-zero solution $(x, \,y, \,z)$ for some $k \in R,$ then $x +(\frac{y}{z} )$ is equal to :
a.
$-3$
b.
$9$
c.
$3$
d.
$-9$
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Let $y=y(x)$ be the solution of the differential equation $cosx\frac{dy}{dx} + 2ysinx= sin 2x,x\in (0, \frac{\pi}{2})$
If $y(\pi /3) = 0,$ then $y(\pi /4)$ is equal to :
a.
$2 - \sqrt{2}$
b.
$2 + \sqrt{2}$
c.
$\sqrt{2}-2$
d.
$\frac{1}{\sqrt{2}} -1$
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There are $3$ sections in a question paper and each section contains $5$ questions. A candidate has to answer a
total of $5$ questions, choosing at least one question from each section. Then the number of ways, in which the
candidate can choose the questions, is:
a.
$3000$
b.
$1500$
c.
$2255$
d.
$2250$
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If the line $y=m x+c$ is a common tangent to the hyperbola $\frac{x^{2}}{100} - \frac{y^{2}}{64} = 1$ and the circle $x^{2} +y^{2} = 36,$ then
which one of the following is true?
a.
$c^{2} = 369$
b.
$5m= 4$
c.
$4c^{2} = 369$
d.
$8m+ 5 = 0$
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If $\int \frac{cos\theta}{5+7 sin\theta -2 cos^{2}\theta}d\theta =Alog_{e} B(\theta ) +C,$ where $C$ is a constant of integration, then $\frac{B(\theta )}{A}$ can be:
a.
$\frac{2 sin\theta +1}{sin\theta +3}$
b.
$\frac{2 sin\theta +1}{5(sin\theta +3)}$
c.
$\frac{5(sin\theta +3)}{2 sin\theta +1}$
d.
$\frac{5(2 sin\theta +1)}{sin\theta +3}$
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