A signal is to be transmitted through a wave of wavelength $\lambda ,$ using a linear antenna. The length $l$ of the
antenna and effective power radiated $P_{eff}$ will be given, respectively, as-
( $K$ is a constant of proportionality)
A physical quantity $P$ is described by the relation $P =a 2 b c d$ . If the relative errors in the measurement of
$a$ , $b$ , $c$ and $d$ respectively, are $2%$ , $1%$ , $3%$ and $5%$ . Then the relative error in $P$ will be:
a.
$12%$
b.
$8%$
c.
$25%$
d.
$32%$
Correct Answer
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Q3mcq
In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P = 4\,\Omega$ and
the neutral point $N$ is at $60\, cm$ from $A$ . Now an unknown resistance $R$ is connected in series to $P$ and the new
position of the neutral point is at $80\, cm$ from $A$ . The value of unknown resistance $R$ is -
a.
$\frac{33}{5\,}\,\Omega$
b.
$6\,\,\Omega$
c.
$\frac{20}{3}\,\Omega$
Correct Answer
d.
$7\,\Omega$
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Q4mcq
A steel rail of length $5\,m$ and area of cross section $40\, cm^{2}$ is prevented from expanding along its length while
the temperature rises by $10^{\circ}C$ . If coefficient of linear expansion and Young's modulus of steel are
$1.2 \times 10^{-5}\,\,K^{-1}$ and $2 \times 10^{11}\,N\,m^{-2}$ respectively, the force developed in the rail is approximately:
a.
$2 \times 10^{7}\,N$
b.
$2 \times 10^{9}\,N$
c.
$3 \times 10^{-5}\,N$
d.
$1 \times 10^{5}\,N$
Correct Answer
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Q5mcq
Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in figure. They collide
completely inelastic and move as a single particle $C$ . The angle $\theta$ that the path of $C$ makes with the $X$ -axis is
given by-
In an experiment to determine the period of a simple pendulum of length $1\,m$ , it is attached to different
spherical bobs of radii $r_{1}$ and $r_{2}$ . The two spherical bobs have uniform mass distribution. If the relative
difference in the periods, is found to be $5 \times 10^{-4}\,s$ , the difference in radii, $|r_{1}- r_{2}|$ is best-given by
a.
$0. 01\, cm$
b.
$0. 05\, cm$
Correct Answer
c.
$0. 5\, cm$
d.
$1\, cm$
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Q7mcq
The figure shows three circuits $I, \,II$ and $III$ which are connected to a $3\,V$ battery. If the powers dissipated by
the configurations $I, \,II$ and $III$ are $P_{1}, \,P_{2}$ and $P_{3}$ respectively, then -
a.
$P_{2} >P_{1} >P_{3}$
Correct Answer
b.
$P_{1}>P_{2} >P_{3}$
c.
$P_{3} >P_{2} >P_{1}$
d.
$P_{1} >P_{3} >P_{2}$
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Q8mcq
The mass density of a spherical body is given by $\rho (r) = \frac{k}{r}$ for $r\leq R$ and $\rho (r) = 0$ for $r>R,$ where $r$ is the
distance from the center. The correct graph that describes qualitatively the acceleration, $a$ of a test particle as a
function of $r$ is:
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Q9mcq
A uniform wire of length $l$ and radius $r$ has a resistance of $100\,\Omega$ . It is recast into a wire of radius $\frac{r}{2}$ . The
resistance of new wire will be-
a.
$1600\,\Omega$
Correct Answer
b.
$100\,\Omega$
c.
$200\,\Omega$
d.
$400\,\Omega$
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Q10mcq
A combination of parallel plate capacitors is maintained at a certain potential difference.
When a $3\, mm$ thick slab is introduced between all the plates, in order to maintain the same potential
difference, the distance between the plates is increased by $2. 4\, mm$ . Find the dielectric constant of the slab.
a.
$6$
b.
$4$
c.
$3$
d.
$5$
Correct Answer
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In an experiment a convex lens of focal length $15\, cm$ is placed coaxially on an optical bench in front of a
convex mirror at a distance of $5\, cm$ from it. It is found that an object and its image coincide, if the object is
placed at a distance of $20\, cm$ from the lens. The focal length of the convex mirror is-
a.
$20. 0\, cm$
b.
$30. 5\, cm$
c.
$25. 0\, cm$
d.
$27. 5\, cm$
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A laser light of wavelength $660 nm$ is used to weld Retina detachment. If a laser pulse of width $60 ms$ and
power $0. 5\, kW$ is used, the approximate number of photons in the pulse are (Take Planck's Constant,
$h= 6.62 \times 10^{-34} J\,s)$
a.
$10^{22}$
b.
$10^{19}$
c.
$10^{20}$
d.
$10^{18}$
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A block of mass $0. 1\, kg$ is connected to an elastic spring of spring constant $640\,N\,m^{-1}$ and oscillates in a
damping medium of damping constant $10^{-2}\, kg \,s^{-1}$ . The system dissipates its energy gradually. The time
taken for its mechanical energy of vibration to drop to half of its initial value, is closest to-
a.
$2\,s$
b.
$5\,s$
c.
$3\,s$
d.
$7\,s$
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A conical pendulum of length $l$ makes an angle $\theta = 45^{\circ}$ with respect to $Z-$ axis and moves in a circle in the $XY$
plane. The radius of the circle is $0.4\,m$ and its center is vertically below $O$ . The speed of the pendulum, in its
circular path, will be - $(Take\,g= 10\,m\,s^{-2})$
a.
$0.2\,m\,s^{-1}$
b.
$0.4\,m\,s^{-1}$
c.
$2\,m\,s^{-1}$
d.
$4\,m\,s^{-1}$
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A single slit of width $0. 1\, mm$ is illuminated by a parallel beam of light of wavelength $6000\,$ Åand diffraction
bands are observed on a screen $0. 5\,m$ from the slit. The distance of the third dark band from the central bright
band is:
a.
$9\, mm$
b.
$3\, mm$
c.
$4. 5\, mm$
d.
$1. 5\, mm$
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A negative test charge is moving near a long straight wire carrying a current. The force acting on the test
charge is parallel to the direction of the current. The motion of the charge is:
a.
Away from the wire
b.
Towards the wire
c.
Parallel to the wire along the current
d.
Parallel to the wire opposite to the current
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A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse
displacement is given by, $y(x, \,t) = 0.5 sin(\frac{5\pi}{4} x)cos(200\pi t)$ . What is the speed of the travelling wave moving
in the positive $x$ direction? ( $x$ and $t$ are in meter and second, respectively)
a.
$120\,m\,s^{-1}$
b.
$90\,m\,s^{-1}$
c.
$160\,m\,s^{-1}$
d.
$180\,m\,s^{-1}$
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A circular hole of radius $\frac{R}{4}$ is made in a thin uniform disc having mass and radius $R$ , as shown in figure. The
moment of inertia of the remaining portion of the disc about an axis passing through the point $O$ and
perpendicular to the plane of the disc is-
a.
$\frac{219MR^{2}}{256}$
b.
$\frac{237MR^{2}}{512}$
c.
$\frac{197MR^{2}}{256}$
d.
$\frac{19MR^{2}}{512}$
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Two tubes of radii $r_{1}$ and $r_{2}$ and lengths $l_{1}$ and $l_{2,}$ respectively, are connected in series and a liquid flows
through each of them in stream line conditions. $P_{1}$ and $P_{2}$ are pressure differences across the two tubes. If $P_{2}$ is
$4P_{1}$ and $l_{2}$ is $\frac{l_{1}}{4}$ then the radius $r_{2}$ will be equal to :
a.
$4r_{1}$
b.
$r_{1}$
c.
$2r_{1}$
d.
$\frac{r_{1}}{2}$
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The machine as shown has $2$ rods of length $1\,m$ connected by a pivot at the top. The end of one rod is connected
to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the
roller goes back and forth, a $2\, kg$ weight moves up and down. If the roller is moving towards right at a constant
speed, the weight moves up with a :
a.
Speed which is $\frac{3}{4}th$ of that of the roller when the
weight is $0. 4\,m$ above the ground
b.
Constant speed
c.
Decreasing speed
d.
Increasing speed
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A car is standing $200 m$ behind a bus, which is also at rest. The two start moving at the same instant but with
different forward accelerations. The bus has acceleration $2\,m\,s^{-2}$ and the car has acceleration $4 m\,s^{-2}$ . The car
will catch up with the bus after time :
a.
$\sqrt{120}\,s$
b.
$15\,s$
c.
$\sqrt{110}\,s$
d.
$10\,s\sqrt{2}$
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The electric field component of a monochromatic radiation is given by $\vec{E} = 2E_{0}coskzcos\omega tˆi$ , Its magnetic
field $\vec{B}$ is then given by:
a.
$\frac{2E_{0}}{c}sinkzsin\omega t\,ˆj$
b.
$\frac{2E_{0}}{c}coskzcos\omega t\,ˆj$
c.
$\frac{2E_{0}}{c}sinkzcos\omega t\,ˆj$
d.
$\frac{-2E_{0}}{c}sinkzsin\omega t ˆj$
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Imagine that a reactor converts all the given mass into energy and that it operates at a power level of $10^{9}\, Watt$
. The mass of the fuel consumed $per \, hour$ , in the reactor, will be:
(velocity of light, $c$ is $3 \times 10^{8\,}m\,s^{-1}$ )
a.
$6.6 \times 10^{-5}\,g$
b.
$0.96\,g$
c.
$4 \times 10^{-2\,}g$
d.
$0.8\,g$
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A uniform magnetic field $B$ of $0 .3 T$ is along the positive $Z$ -direction. A rectangular loop ( $abcd$ ) of sides
$10\,cm \times 5\, cm$ carries a current $I$ of $12\,A$ . Out of the following different orientations which one corresponds to
stable equilibrium?
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A sinusoidal voltage of peak value $283\,V$ and angular frequency $320\,s^{-1}$ is applied to a series $LCR$ circuit.
Given that $R= 5\,\Omega , \,L= 25\, mH$ and $C = 1000\,$ $\mu$ $F$ . The total impedance and phase difference between the
voltage across the source and the current will respectively be-
a.
$10\,\Omega \,and\,tan^{-1}( \frac{5}{3})$
b.
$7\,\Omega \,and\,45^{o}$
c.
$7\,\Omega \,and\,tan^{-1}(\frac{5}{3} )$
d.
$10\,\Omega \,and\,tan^{-1}(\frac{8}{3} )$
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Four closed surfaces and corresponding charge distributions are shown below.
Let the respective electric fluxes through the surfaces be $\phi _{1}, \,\phi _{2}, \,\phi _{3}$ and $\phi _{4}$ . Then:
$N$ moles of diatomic gas in a cylinder is at a temperature $T$ . Heat is supplied to the cylinder such that the
temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. The change
in the total kinetic energy of the gas is
a.
$0$
b.
$\frac{5}{2}nRT$
c.
$\frac{3}{2}nRT$
d.
$\frac{1}{2}nRT$
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Adsorption of gas on a surface follows Freundlich adsorption isotherm. The plot of $log \frac{x}{m}$ versus $log(P)$ gives
a straight line with slope equal to $0. 5$ , then:
( $\frac{x}{m}$ is the mass of the gas adsorbed per gram of adsorbent)
a.
adsorption is proportional to the square root of
pressure.
b.
adsorption is proportional to the square of
pressure.
c.
adsorption is proportional to the pressure.
d.
adsorption is independent of pressure.
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The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal:
$Fe_{2}O_{3}(s) + 3CO(g)\,\, \rightleftharpoons 2Fe\,(l) + 3CO_{2}(g)$
Using the Le Chatelier's principle, predict which one of the following will not disturb the equilibrium?
a.
Addition of $CO_{2}$
b.
Removal of $CO_{2}$
c.
Addition of $Fe_{2}O_{3}$
d.
Removal of CO
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The rate of a reaction quadruples when the temperature changes from $300$ to $310 K$ . The activation energy of
this reaction is:
(Assume Activation energy and pre-exponential factor are independent of temperature;
$ln(2)= 0. 693; \,R = 8. 314\,J\, mol^{-1} K^{-1}$ )
a.
$53. 6\, kJ mol^{-1}$
b.
$214. 4\, kJ mol^{-1}$
c.
$107. 2\, kJ mol^{-1}$
d.
$53. 7\, kJ mol^{-1}$
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The incorrect statement among the following is
(1) $\alpha$ $-D-$ glucose and $\beta$ $-D-$ glucose are (2) the penta acetate of glucose does not react with
enantiomers. hydroxyl amine.
(3) $\alpha$ $-D-$ glucose and $\beta$ $-D-$ glucose are anomers.(4) cellulose is a straight chain polysaccharide made
up of only $\beta$ $-D-$ glucose units.
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A compound of molecular formula $C_{8}H_{8}O_{2}$ reacts with acetophenone to form a single cross-aldol product in
the presence of base. The same compound on reaction with concentrated $NaOH$ forms benzyl alcohol as one of
the products. The structure of the compound is:
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A solution is prepared by mixing $8. 5$ g of $CH_{2}Cl_{2}$ and $11.95\,g$ of $CHCl_{3}$ . If vapour pressure of $CH_{2}Cl_{2}$ and
$CHCl_{3}$ at $298$ K are $415$ and $200$ mm Hg respectively, the mole fraction of $CHCl_{3}$ in vapour form is:
$(Molar\,mass\,of\,Cl = 35.5\,g\,mol^{-1})$
a.
$0. 162$
b.
$0. 675$
c.
$0. 325$
d.
$0. 486$
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$50\, mL$ of $0 .2 M$ ammonia solution is treated with $25\, mL \, of \,0. 2\,M\, HCl$ . If $pK_{b}$ of ammonia solution is
$4. 75$ , the $pH$ of the mixture will be:
a.
$8. 25$
b.
$9. 25$
c.
$3. 75$
d.
$4. 75$
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$XeF_{6}$ on partial hydrolysis with water, produces a compound $X.$ The same compound $X$ is formed when $XeF_{6}$
reacts with silica. The compound $X$ is:
a.
$XeF_{4}$
b.
$XeF_{2}$
c.
$XeO_{3}$
d.
$XeOF_{4}$
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A gas undergoes change from state $A$ to state $B$ . In this process, the heat absorbed and work done by the gas is
$5\,J\,and\,8\,J$ , respectively. Now gas is brought back to $A$ by another process during which $3\,J$ of heat is
evolved. In this reverse process of $B\, to \,A$ .
a.
$6\,J\,$ of the work will be done by the gas
b.
$6\,J$ of the work will be done by the surroundings
on gas
c.
$10\,J$ of the work will be done by the surroundings
on gas
d.
$10\,J$ of the work will be done by the gas
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To find the standard potential of $M^{3+}/M$ electrode, the following cell is constituted:
$Pt /M/M^{3+} (0 .001 \, mol \,L^{-1})/ Ag^{+} (0 .01 \, mol \,L^{-1})/ Ag$
The emf of the cell is found to be $0. 421\, volt$ at $298\,K$ . The standard potential of half-reaction
$M^{3+} + 3e^{-} M$ at $298\,K$ will be:
(Given: $E^{⊝}_{^{Ag}^{+}/_{\vec{A}}_{g}}$ at $298\,K = 0. 80\, volt$ )
a.
$0. 38\, volt$
b.
$1. 28\, volt$
c.
$0. 32\, volt$
d.
$0. 66\, volt$
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What quantity (in $mL$ ) of a $45%$ acid solution of a mono-protic strong acid must be mixed with a $20%$ solution
of the same acid to produce $800\, mL$ of a $29. 875%$ acid solution?
a.
$316$
b.
$320$
c.
$325$
d.
$330$
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At $300\,K$ , the density of a certain gaseous molecule at $2$ bar is double to that of dinitrogen $(N_{2})$ at $4$ bar. The
molar mass of the gaseous molecule is
a.
$224\,g\, mol^{-1}$
b.
$112\,g\, mol^{-1}$
c.
$56\,g\, mol^{-1}$
d.
$28\,g\, mol^{-1}$
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The increasing order of the boiling points for the following compounds is:
$(I)C_{2}H_{5}OH (II)C_{2}H_{5}Cl (III)C_{2}H_{5}CH_{3} (IV) C_{2}H_{5}OCH_{3}$
a.
$(IV) < (III) < (I) < (II)$
b.
$(III) < (II) < (I) < (IV)$
c.
$(III) < (IV) < (II) < (I)$
d.
$(II) < (III) < (IV) < (I)$
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The function $f\, :N \rightarrow \rightarrow I$ defined by $f(x) =x-5[\frac{x}{5}]$ , where $N$ is the set of natural numbers and $[x]$ denotes
the greatest integer less than or equal to $x$ , is:
a.
one-one but not onto
b.
one-one and onto
c.
neither one-one nor onto
d.
onto but not one-one
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The lengths of two adjacent sides of a cyclic quadrilateral are $2$ units and $5$ units and the angle between them is
$60^{o}$ . If the area of the quadrilateral is $4\sqrt{3}$ sq. units, then the perimeter of the quadrilateral is
a.
$12.5$ units
b.
$13$ units
c.
$13.2$ units
d.
$12$ units
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Let $S_{n} = \frac{1}{1^{3}} + \frac{1+2}{1^{3}+2^{3}} + \frac{1+2+3}{1^{3}+2^{3}+3^{3}} + … + \frac{1+2+…,+n}{1^{3}+2^{3}+…n^{3}}$ . If $100\,S_{n} =n,$ then $n$ is equal to:
a.
$200$
b.
$199$
c.
$99$
d.
$19$
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If a variable plane, at a distance of $3$ units from the origin, intersects the coordinate axes at $A, \,B\,&\,C$ , then the
locus of the centroid of $\Delta ABC$ is
The sum of $100$ observations and the sum of their squares are $400\,&\,2475$ , respectively. Later on, three
observations $3, \,4\,&\,5$ were found to be incorrect. If the incorrect observations are omitted, then the variance of
the remaining observations is
a.
$8. 25$
b.
$8. 50$
c.
$9. 00$
d.
$8. 00$
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If $_{n}lim_{\rightarrow \infty \rightarrow } (_{(n+1)^{a}^{-1}[(na}^{1}_{+1)+(}^{^{a}+2^{a}+…+}_{na+2)+…+(}^{n^{a}}_{na+n)]} )= \frac{1}{60}$ for some positive real number $a$ , then $a$ is equal to
a.
$\frac{17}{2}$
b.
$\frac{15}{2}$
c.
$7$
d.
$8$
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If $x=a, \,y=b, \,z=c$ is a solution of the system of linear equations
$x+ 8y+ 7z= 0$
$9x+ 2y+ 3z= 0$
$x+y+z= 0$
Such that the point $(a,b,c)$ lies on the plane $x+ 2y+z= 6$ , then $2a+b+c$ equals:
a.
$2$
b.
$-1$
c.
$1$
d.
$0$
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If the vector $\vec{b}= 3ˆj+ 4ˆk$ is written as the sum of a vector $\vec{b}_{1}$ , parallel to $\vec{a}= \,ˆi+ \,ˆj$ and a vector $\vec{b}_{2},$
perpendicular to $\vec{a},$ then $\vec{b}_{1}\times \vec{b}_{2}$ is equal to :
a.
$6ˆi-6ˆj+ \frac{9}{2}ˆk$
b.
$-3ˆi+ 3ˆj-9ˆk$
c.
$-6ˆi+ 6ˆj- \frac{9}{2}ˆk$
d.
$3ˆi-3ˆj+ 9ˆk$
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For two $3 \times 3$ matrices $A$ and $B$ , let $A+B= 2B'$ and $3A+ 2B=I_{3},$ where $B'$ is the transpose of $B$ and $I_{3}$ is
$3 \times 3$ identity matrix. Then :
a.
$10A+ 5B= 3I_{3}$
b.
$3A+ 6B= 2I_{3}$
c.
$5A+ 10B=2I_{3}$
d.
$B+ 2A=I_{3}$
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$\frac{tan 4x}{tan 5x,}$
$(\frac{4}{5} ) 0 <x< \frac{\pi}{2}$
The value of $k$ which the function $f(x) = \,{$ is continuous at $x= \frac{\pi}{2},$ is
$k+ \frac{2}{5}, x= \frac{\pi}{2}$
a.
$\frac{2}{5}$
b.
$-\frac{2}{5}$
c.
$\frac{17}{20}$
d.
$\frac{3}{5}$
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The number of ways in which $\,5$ boys and $3$ girls can be seated on a round table if a particular boy $B_{1}$ and a
particular girl $G_{1}$ never sit adjacent to each other, is:
a.
$7!$
b.
$5 \times 6!$
c.
$6 \times 6!$
d.
$5 \times 7!$
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If the line, $\frac{x-3}{1} = \frac{y+2}{-1} = \frac{z+\lambda}{-2}$ lies in the plane, $2x-4y+ 3z= 2$ , then the shortest distance between this line
and the line, $\frac{x-1}{12} = \frac{y}{9} = \frac{z}{4}$ is
a.
$1$
b.
$2$
c.
$3$
d.
$0$
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A tangent to the curve, $y=f(x)$ at $P(x, \,y)$ meets $x$ -axis at $A$ and $y$ -axis at $B$ . If $AP :BP = 1 : 3$ and
$f(1) = 1,$ then the curve also passes through the point
a.
$(\frac{1}{3}, \,24)$
b.
$( \frac{1}{2}, \,4)$
c.
$(2, \frac{1}{8})$
d.
$(3, \frac{1}{28})$
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Let $E\,&\,F$ be two independent events. The probability that $E\,&\,F$ happen is $\frac{1}{12}$ and the probability that
neither $E$ nor $F$ happens is $\frac{1}{2}$ , then a value of $\frac{P(E)}{P(F)}$ is:
a.
$\frac{4}{3}$
b.
$\frac{1}{3}$
c.
$\frac{3}{2}$
d.
$\frac{5}{12}$
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From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain
at least one women. Then the probability for these committees to have more women than men, is :
a.
$\frac{3}{11}$
b.
$\frac{2}{23}$
c.
$\frac{1}{11}$
d.
$\frac{21}{220}$
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A square, of each side $2$ , lies above the $x$ -axis and has one vertex at the origin. If one of the sides passing
through the origin makes an angle $30^{\circ}$ with the positive direction of the $x$ -axis , then the sum of the $x$ -
coordinates of the vertices of the square is $:$
a.
$2 -2\sqrt{3}$
b.
$\sqrt{3}-2$
c.
$2 -1\sqrt{3}$
d.
$\sqrt{3}-1$
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