Radiation of wavelength is incident on a photocell. The fastest emitted photoelectron has a speed $\lambda$ $v$ . If the
wavelength is changed to $\frac{3$\lambda$}{4}$ , the speed of the fastest emitted photoelectron will be
a.
$= v(\frac{4}{3} )\frac{1}{2}$
b.
$= v(\frac{3}{4})\frac{1}{2}$
c.
$> v(\frac{4}{3} )\frac{1}{2}$
Correct Answer
d.
$< v(\frac{4}{3})\frac{1}{2}$
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Q2mcq
Hysteresis loops for two magnetic materials $A$ and $B$ are given below:
These materials are used to make magnets for electric generators, transformer core and electromagnet core.
Then it is proper to use:
a.
$A$ for transformers and $B$
for electric generators.
b.
$B$ for electromagnets and transformers.
Correct Answer
c.
$A$ for electric generators and transformers.
d.
$A$ for electromagnets and $B$ for electric
generators.
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Q3mcq
A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that
half of it is in water. The fundamental frequency of the air column is now:
a.
$2f$
b.
$f$
Correct Answer
c.
$\frac{f}{2}$
d.
$\frac{3f}{4}$
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Q4mcq
A particle of mass m is moving along the side of a square of side 'a', with a uniform speed in the x-y plane asυ
shown in the figure:
Which of the following statements is false for the angular momentum $\vec{L}$ about the origin?
a.
$\vec{L}= m$ υ $[\frac{R}{\sqrt{2}} + a]ˆk$
when the particle is moving from B to C.
b.
$\vec{L}= \frac{mυ}{\sqrt{2}}Rˆk$
when the particle is moving from D to A.
Correct Answer
c.
$\vec{L}= -\frac{mυ}{\sqrt{2}} Rˆk$
when the particle is moving from A to B.
d.
$\vec{L}= m$ υ $[\frac{R}{\sqrt{2}} + a]ˆk$
when the particle is moving from C to D.
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Q5mcq
A screw gauge with a pitch of $0.5\, mm$ and a circular scale with $50$ divisions is used to measure the thickness
of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw
gauge are brought in contact, the $45^{th}$ division coincides with the main scale line and that the zero of the main
scale is barely visible. What is the thickness of the sheet if the main scale reading is $0 .5\, mm$ and the $25^{th}$
division coincides with the main scale line?
a.
$0.70\,mm$
b.
$0.50\,mm$
c.
$0.75\,mm$
d.
$0.80\,mm$
Correct Answer
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Q6mcq
A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point
charge Q (having a charge equal to the sum of the charges on the $4\,$ $\mu$ $F$ and $9\,$ $\mu$ $F$ capacitors), at a point distant
30 m from it, would equal:
a.
420 N/C
Correct Answer
b.
480 N/C
c.
240 N/C
d.
360 N/C
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Q7mcq
Choose the correct statement:
a.
In frequency modulation the amplitude of the
high frequency carrier wave is made to vary in
proportion to the amplitude of the audio signal.
b.
In frequency modulation the amplitude of the
high frequency carrier wave is made to vary in
proportion to the frequency of the audio signal.
c.
In amplitude modulation the amplitude of the
high frequency carrier wave is made to vary in
proportion to the amplitude of the audio signal.
Correct Answer
d.
In amplitude modulation the frequency of the
high frequency carrier wave is made to vary in
proportion to the amplitude of the audio signal.
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Q8mcq
An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC
supply, the series inductor needed for it to work is close to:
a.
0.044 H
b.
0.065 H
Correct Answer
c.
80 H
d.
0.08 H
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Q9mcq
In an experiment for determination of refractive index of glass of a prism by $i$ v/s plot, it was found that a ray$\delta$
incident at angle $35^{o}$ , suffers a deviation of $40^{o}$ and that it emerges at angle $79^{o}$ . In that case which of the
following is closest to the maximum possible value of the refractive index?
a.
1.7
b.
1.8
c.
1.5
Correct Answer
d.
1.6
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Q10mcq
A pendulum clock loses 12 s a day if the temperature is $40^{o}$ C and gains 4s a day if the temperature is $20^{o}$ C.
The temperature at which the clock will show correct time, and the co-efficient of linear expansion $($ $\alpha$ $)$ of the
metal of the pendulum shaft are respectively:
A galvanometer having a coil resistance of $100\,\Omega$ gives a full scale deflection, when a current of $1\, mA$ is
passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full
scale deflection for a current of $10\,A$ , is:
a.
$0.1\,\Omega$
b.
$3\,\Omega$
c.
$0.01\,\Omega$
d.
$2\,\Omega$
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A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1m 1000 times. Assume that
the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering
the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^{7}$ J of energy per kg which is converted
to mechanical energy with a 20% efficiency rate. Take $g = 9.8\,ms^{-2}$ :
a.
$9.89 \times 10^{-3}\,kg$
b.
$12.89 \times 10^{-3}\,kg$
c.
$2.45 \times 10^{-3}\,kg$
d.
$6.45 \times 10^{-3}\,kg$
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An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If
during this process the relation of pressure P and volume V is given by $PV^{n} =$ constant, then n is given by
(Here $C_{P}$ and $C_{V}$ are molar specific heat at constant pressure and constant volume, respectively) :
a.
$n = \frac{C_{P}-C}{C-C_{V}}$
b.
$n = \frac{C-C_{V}}{C-C_{P}}$
c.
$n = \frac{C_{P}}{C_{V}}$
d.
$n = \frac{C-C_{P}}{C-C_{V}}$
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A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient
of friction, between the particle and the rough track equals . The particle is released, from rest, from the point$\mu$
P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are
equal to each other, and no energy is lost when particle changes direction from PQ to QR.
The values of the coefficient of friction and the distance $\mu$ $x = (QR)$ , are respectively close to:
a.
0.29 and 3.5 m
b.
0.29 and 6.5 m
c.
0.2 and 6.5 m
d.
0.2 and 3.5 m
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A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a
distance $\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is:
a.
$A\sqrt{3}$
b.
$\frac{7A}{3}$
c.
$\frac{A}{3}\sqrt{41}$
d.
$3A$
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A uniform string of length $20\,m$ is suspended from a rigid support. A short wave pulse is introduced at its
lowest end. It starts moving up the string. The time taken to reach the support is
(Take, $g = 10\,m\,s^{-2}$ )
a.
$2\sqrt{2}\,s$
b.
$\sqrt{2}\,s$
c.
$2$ $\pi$ $\sqrt{2}\,s$
d.
$2\,s$
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The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge
density $\rho$ $= \frac{A}{r}$ , where A is a constant and r is the distance from the centre. At the centre of the spheres is a
point charge Q. The value of A such that the electric field in the region between the spheres will be constant,
is:
a.
$\frac{2Q}{$\pi$(a^{2}-b^{2})}$
b.
$\frac{2Q}{$\pi$a^{2}}$
c.
$\frac{Q}{2$\pi$a^{2}}$
d.
$\frac{Q}{2$\pi$(b^{2}-a^{2})}$
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Half-lives of two radioactive elements $A$ and $B$ are $20\, minutes$ and $40\, minutes$ , respectively. Initially, the
samples have an equal number of nuclei. After $80\, minutes$ , the ratio of decayed numbers of $A$ and $B$ nuclei
will be:
a.
$1\, : \,4$
b.
$5\, : \,4$
c.
$1\, : \,16$
d.
$4\, : \,1$
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A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91
s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:
a.
$92 \pm 1.8\,s$
b.
$92 \pm 3\,s$
c.
$92 \pm 2\,s$
d.
$92 \pm 5.0\,s$
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Two identical wires $A$ and $B$ , each of length $l$ , carry the same current $I$ . Wire $A$ is bent into a circle of radius
$R$ and wire $B$ is bent to form a square of side $a$ . If $B_{A}$ and $B_{B}$ are the values of magnetic field at the centres of
the circle and square respectively, then the ratio $\frac{B_{A}}{B_{B}}$ is
a.
$\frac{$\pi$^{2}}{16}$
b.
$\frac{$\pi$^{2}}{8\sqrt{2}}$
c.
$\frac{$\pi$^{2}}{8}$
d.
$\frac{$\pi$^{2}}{16\sqrt{2}}$
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$n$ moles of an ideal gas undergoes a process $A \rightarrow B\rightarrow$ as shown in the figure. The maximum temperature of the
gas during the process will be:
a.
$\frac{9\,P_{0}V_{0}}{2nR}$
b.
$\frac{9\,P_{0}V_{0}}{nR}$
c.
$\frac{9\,P_{0}V_{0}}{4nR}$
d.
$\frac{3\,P_{0}V_{0}}{2nR}$
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Arrange the following electromagnetic radiations per quantum in the order of increasing energy:
$A : \,$ Blue light
$B : \,$ Yellow light
$C : \,$ X-ray
$D : \,$ Radiowave
a.
C, A, B, D
b.
B, A, D, C
c.
D, B, A, C
d.
A, B, D, C
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The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is
illuminated by a parallel beam of light of wavelength the spread of the spot (obtained on the opposite wall of$\lambda$
the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its
minimum size (say $b_{min}$ ) when:
a.
$a =\sqrt{L}$ $\lambda$ and $b_{min} =\sqrt{4L}$ $\lambda$
b.
$a = \frac{$\lambda$^{2}}{L}$ and $b_{min} = \sqrt{4L}$ $\lambda$ $\,$
c.
$a = \frac{$\lambda$^{2}}{L}$ and $b_{min} =(\frac{2$\lambda$^{2}}{L} )$
d.
$a = \sqrt{L}$ $\lambda$ and $b_{min} =(\frac{2$\lambda$^{2}}{L})$
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A satellite is revolving in a circular orbit at a height $h$ from the earth's surface (radius of earth $R$ ; $h<<R$ ). The
minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational
field, is close to (Neglect the effect of atmosphere.)
a.
$\sqrt{\frac{gR}{2}}$
b.
$\sqrt{gR}\,(\sqrt{2}-1)$
c.
$\sqrt{2\,gR}$
d.
$\sqrt{\,gR}$
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A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are
placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line
joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel
to CD in the direction shown. As it moves, the roller will tend to:
a.
go straight.
b.
turn left and right alternately.
c.
turn left.
d.
turn right.
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At $300\,K$ and $1\, atm$ , $15\, mL$ of a gaseous hydrocarbon requires $375\, mL$ air containing $20%\,O_{2}$ by volume,
for complete combustion. After combustion, the gases occupy $345\, mL$ . Assuming that the water formed is in
liquid form and the volumes were measured at the same temperature and pressure, the formula of the
hydrocarbon is:
(Assume complete combustion of reactant)
a.
$C_{4}H_{8}$
b.
$C_{4}H_{10}$
c.
$C_{3}H_{6}$
d.
$C_{3}H_{8}$
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Decomposition of $H_{2}O_{2}$ follows a first order reaction. In fifty minutes the concentration of $H_{2}O_{2}$ decreases
from $0.5$ to $0.125\,M$ in one such decomposition. When the concentration of $H_{2}O_{2}$ reaches $0.05\,M$ , the rate of
formation of $O_{2}$ will be:
a.
$2.66\,Lmin^{-1}\,at\,STP$
b.
$1.34 \times 10^{-2}\,mol\,min^{-1}$
c.
$6.93 \times 10^{-2}\,mol\,min^{-1}$
d.
$6.93 \times 10^{-4}\,mol\,min^{-1}$
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The heats of combustion of carbon and carbon monoxide are $-393.5\,and -283.5\,kJ\,mol^{-1},$ respectively. The
heat of formation $(in \, kJ)$ of carbon monoxide per mole is:
a.
$-\,676.5$
b.
$-110$
c.
$110.5$
d.
$676.5$
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Two closed bulbs of equal volume $(V)$ containing an ideal gas initially at pressure $p_{i}$ and temperature $T_{1}$ are
connected through a narrow tube of negligible volume, as shown in the figure below. The temperature of one
of the bulbs is then raised to $T_{2}.$ The final pressure $P_{f}$ is:
a.
$2p_{i}( \frac{T_{2}}{T_{1}+T_{2}})$
b.
$2p_{i} (\frac{T_{1}T_{2}}{T_{1}+T_{2}})$
c.
$p_{i} (\frac{T_{1}T_{2}}{T_{1}+T_{2}} )$
d.
$2p_{i}(\frac{T_{1}}{T_{1}+T_{2}})$
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For a linear plot of $log \,(\frac{x}{m})$ versus $log \,p$ in a Freundlich adsorption isotherm, which of the following
statements is correct? ( $k$ and $n$ are constants)
a.
Only $\frac{1}{n}$ appears as the slope.
b.
$log(\frac{1}{n})$ appears as the intercept.
c.
Both $k\,and\, \frac{1}{n}$ appear in the slope term.
d.
$\frac{1}{n}$ appears as the intercept.
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The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to
be $1000\, ppb, \,40\, ppb, \,100\, ppm \, and \,0. 2\, ppm$ , respectively. This water is unsuitable for drinking due to
high concentration of:
a.
Nitrate
b.
Iron
c.
Fluoride
d.
Lead
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A stream of electrons from a heat filament was passed between two charge plates kept at a potential difference
$V\, esu$ . If $e$ and $m$ are charge and mass of an electron, respectively, then the value of $\frac{h}{$\lambda$}$ (where is$\lambda$
wavelength associated with the electron wave) is given by:
a.
$\sqrt{meV}$
b.
$\sqrt{2\,meV}$
c.
$me\,V$
d.
$2\,me\,V$
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The equilibrium constant at $298\,K$ for a reaction $A + B \rightleftharpoons C + D$ is $100$ . If the initial concentration of all the
four species were $1\,M$ each, then the equilibrium concentration of $D$ (in mol $L^{-1}$ ) will be:
a.
$1. 818$
b.
$1. 182$
c.
$0. 182$
d.
$0. 818$
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If a curve $y=f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation,
$y\,(1 +xy)dx=x dy,$ then $f(-\frac{1}{2} )$ is equal to
a.
$\frac{2}{5}$
b.
$\frac{4}{5}$
c.
$-\frac{2}{5}$
d.
$-\frac{4}{5}$
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A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $=x$ units and
a circle of radius $=r$ units. If the sum of the areas of the square and the circle so formed is minimum, then
a.
$x= 2r$
b.
$2x=r$
c.
$2x= (\pi + 4)r$
d.
$(4 - \pi )x=\pi r$
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Two sides of a rhombus are along the lines, $x- y+ 1 = 0$ and $7x- y-5 = 0$ . If its diagonals intersect at
$(-1, \, -2)$ , then which one of the following is a vertex of this rhombus ?
a.
$( \frac{1}{3}, \, - \frac{8}{3})$
b.
$(-\frac{10}{3} , \, - \frac{7}{3})$
c.
$(-3, \, -9)$
d.
$(-3, \, -8)$
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If all the words (with or without meaning) having five letters, formed using the letters of the word $SMALL$
and arranged as in a dictionary; then the position of the word $SMALL$ is
a.
$52^{nd}$
b.
$58^{th}$
c.
$46^{th}$
d.
$59^{th}$
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Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_{1}$ is the event that die $A$ shows up four, $E_{2}$
is the event that die $B$ shows up two and $E_{3}$ is the event that the sum of numbers on both dice is odd, then
which of the following statements is not true?
a.
$E_{1}$ and $E_{3}$ are independent
b.
$E_{1}, \,E_{2}$ and $E_{3}$ are independent
c.
$E_{1}$ and $E_{2}$ are independent
d.
$E_{2}$ and $E_{3}$ are independent
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If the $2^{nd}, \,5^{th}$ and $9^{th}$ terms of a non-constant arithmetic progression are in geometric progression, then the
common ratio of this geometric progression is
a.
$1$
b.
$\frac{7}{4}$
c.
$\frac{8}{5}$
d.
$\frac{4}{3}$
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Let $\vec{a}, \,\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a}\, \times (\vec{b}\, \times \,\vec{c})= \frac{\sqrt{3}}{2}(\vec{b}\, + \,\vec{c}).$ If $\vec{b}$ is not parallel to $\vec{c}$ , then the
angle between $\vec{a}$ and $\vec{b}$ is
a.
$\frac{2\pi}{3}$
b.
$\frac{5\pi}{6}$
c.
$\frac{3\pi}{4}$
d.
$\frac{\pi}{2}$
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Let $P$ be the point on the parabola, $y^{2} = 8x$ which is at a minimum distance from the center $C$ of the circle
$x^{2} + (y+ 6)^{2} = 1$ . Then the equation of the circle, passing through $C$ and having its center at $P$ is
a.
$x^{2} +y^{2} - \frac{x}{4} + 2y-24 = 0$
b.
$x^{2} +y^{2} -4x+ 9y+ 18 = 0$
c.
$x^{2} +y^{2} -4x+ 8y+ 12 = 0$
d.
$x^{2} +y^{2} - x+ 4y-12 = 0$
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If the number of terms in the expansion of $(1 - \frac{2}{x} + \frac{4}{y^{2}})^{n}, \,x, \,y\neq 0,$ is $28$ , then the sum of the coefficients
of all the terms in this expansion is
a.
$243$
b.
$729$
c.
$64$
d.
$2187$
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If the sum of the first ten terms of the series $1 \frac{3}{5}^{2}+ 2\frac{2}{5}^{2}+ 3\frac{1}{5}^{2}+ 42+ 4\frac{4}{5}^{2}+ … . ,$ is $\frac{16}{5}m$ , then $m$
$( ) ( ) ( ) ( )$
is equal to
a.
$100$
b.
$99$
c.
$102$
d.
$101$
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Consider $f(x) = tan^{-1}(\sqrt{\frac{1+sinx}{1-sinx}}), \,x\, \in (0, \frac{\pi}{2}).$ A normal to $y=f(x)$ at $x= \frac{\pi}{6}$ also passes through the
point
a.
$( \frac{\pi}{6}, \,0)$
b.
$(\frac{\pi}{4} , \,0)$
c.
$(0, \,0)$
d.
$(0, \frac{2\pi}{3})$
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If one of the diameters of the circle, given by the equation, $x^{2} +y^{2} -4x+ 6y-12 = 0,$ is a chord of a circle
$S$ , whose centre is at $(-3, \,2)$ , then the radius of $S$ is
a.
$5$
b.
$10$
c.
$5\sqrt{2}$
d.
$5\sqrt{3}$
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A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point $A$ on the
path, he observes that the angle of elevation of the top of the pillar is $30^{^{\circ}}$ . After walking for $10$ minutes from
$A$ in the same direction, at a point $B$ , he observes that the angle of elevation of the top of the pillar is $60^{^{\circ}}$ .
Then the time taken (in minutes) by him, from $B$ to reach the pillar, is
a.
$20$
b.
$5$
c.
$6$
d.
$10$
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