Consider an electromagnetic wave propagating in vacuum. Choose the correct statement:
a.
For an electromagnetic wave propagating in $+y$
direction the electric field is $\vec{E} = \frac{1}{\sqrt{2}}E_{yz}(x,t)Λz$
and the magnetic field is $\vec{B}= \frac{1}{\sqrt{2}}B_{z}(x,t)Λy$
b.
For an electromagnetic wave propagating in + y
direction the electric field is $\vec{E} = \frac{1}{\sqrt{2}}E_{yz}(x,t)Λy$
and the magnetic field is $\vec{B}= \frac{1}{\sqrt{2}}B_{yz}(x,t)Λz$
c.
For an electromagnetic wave propagating in + x
direction the electric field is
$\vec{E} = \frac{1}{\sqrt{2}}E_{yz}(y, \,z, \,t)\,(yΛ+ Λz)$ and the magnetic
field is $\vec{B}= \frac{1}{\sqrt{2}}E_{yz}(y, \,z, \,t)\,(yΛ+ Λz)$
d.
For an electromagnetic wave propagating in + x
direction the electric field is
$\vec{E} = \frac{1}{\sqrt{2}} E_{yz}(x,t)\,(yΛ-Λz)$ and the magnetic field
is $\vec{B}= \frac{1}{\sqrt{2}} B_{yz}(x, \,t)(yΛ+ Λz)$
Correct Answer
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Q2mcq
A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m
and height 5 m is flying towards east over Delhi. Its speed is $240\,ms^{-1}.$ The earth's magnetic field over Delhi
is $5 \times 10^{-5}T$ with the declination angle $~0^{o}$ and dip of $\theta$ such that $sin\theta = \frac{2}{3}. \,$ If the voltage developed is $V_{B}$
between the lower and upper side of the plane and $V_{W}$ between the tips of the wings then $V_{B} and V_{W}$ are close
to :
a.
$V_{B} = 40\,mV;V_{W} = 135\,mV$ with left side of
pilot at higher voltage
b.
$V_{B} = 45\,mV;V_{W} = 120\,mV$ with right side of
pilot at higher voltage
c.
$V_{B} = 40\,mV;V_{W} = 135\,mV$ with right side of
pilot at high voltage
d.
$V_{B} = 45\,mV;V_{W} = 120\,mV$ with left side of
pilot at higher voltage
Correct Answer
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Q3mcq
A bottle has an opening of radius $a$ and length $b$ . A cork of length $b$ and radius $(a + \Delta a)$ where $(\Delta a \ll a)$ , is
compressed to fit into the opening completely (see figure). If the bulk modulus of cork is $B$ and the coefficient
of friction between the bottle and cork is , then the force needed to push the cork into the bottle is$\mu$
a.
$($ $\pi$$\mu$ $Bb)a$
b.
$(2$ $\pi$$\mu$ $Bb) \Delta a$
c.
$($ $\pi$$\mu$ $Bb) \Delta a$
d.
$(4$ $\pi$$\mu$ $Bb) \Delta a$
Correct Answer
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Q4mcq
To determine refractive index of glass slab using a travelling microscope, minimum number of readings
required are :
a.
Two
b.
Four
c.
Three
Correct Answer
d.
Five
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Q5mcq
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates
too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take
place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is
close to :
(Take the radius of the drum to be 1.25 m and its axle to be horizontal) :
a.
27.0
Correct Answer
b.
0.4
c.
1.3
d.
8.0
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Q6mcq
Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of
capacitance C if the equivalent capacitance between point A and B is to be $1\,\mu F$ is :
a.
$\frac{32}{23} \mu F$
Correct Answer
b.
$\frac{31}{23} \mu F$
c.
$\frac{33}{23}\mu F$
d.
$\frac{34}{23} \mu F$
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Q7mcq
A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics
measurement in a common emitter transistor configuration is :
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Q8mcq
$A, B, C$ , and $D$ are four different physical quantities having different dimensions. None of them is
dimensionless. But we know that the equation $AD=C ln(BD)$ holds true. Then which of the combination is
not a meaningful quantity?
a.
$\frac{C}{BD} - \frac{A^{2}D^{2}}{C}$
b.
$A^{2} - B^{2}C^{2}$
c.
$\frac{A}{B} - C$
d.
$\frac{A^{2}-AC}{D}$
Correct Answer
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Q9mcq
A Carnot freezer takes heat from water at $0^{o}C$ inside it and rejects it to the room at a temperature of $27^{o}C.$ The
latent heat of ice is $336 \times 10^{3} Jkg^{-1}.$ If 5kg of water at $0^{o}C$ is converted into ice at $0^{o}C$ by the freezer, then
the energy consumed by the freezer is close to :
a.
$1 .51 \times 10^{5}\,J$
b.
$1 .68 \times 10^{6}\,J$
c.
$1 .71 \times 10^{7}\,J$
d.
$1 .67 \times 10^{5}\,J$
Correct Answer
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Q10mcq
A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at
time t is given by $n^{2}Rt^{2}$ , where $n$ is a constant. The power delivered to the particle by the force acting on it, is :
a.
$\frac{1}{2} Mn^{2}R^{2}t^{2}$
b.
$Mn^{2}R^{2}t$
Correct Answer
c.
$MnR^{2}t^{2}$
d.
$MnR^{2}t$
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In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top
of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the
washer no longer stays in contact with the piston, is close to :
a.
0.7 Hz
b.
1.9 Hz
c.
1.2 Hz
d.
0.1 Hz
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A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small
air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble
made by the mirror is seen :
a.
14cm below flat surface
b.
20cm below flat surface
c.
16cm below flat surface
d.
30cm below flat surface
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The ratio (R) of output resistance $r_{0},$ and the input resistance $r_{i}$ in measurements of input and output
characteristics of a transistor is typically in the range :
a.
$R~10^{2} -10^{3}$
b.
$R~1 -10$
c.
$R~0.1 -1.0$
d.
$R~0.1 -0.01$
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A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state.
The minimum kinetic energy of the neutron for which perfactly inelastic collision will take place is :
a.
20.4 eV
b.
10.2 eV
c.
12.1 eV
d.
16.8 eV
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A thin $1\,m$ long rod has a radius of $5\, mm$ . A force of $50$ $\pi$ $\times 10 \,N$ is applied at one end to determine its Young's
modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is
$0. 01\, mm$ , which of the following statements is false?
a.
The maximum value of $Y$ that can be determined
is $2 \times 10^{14}\,N\,m^{-2}$
b.
$\frac{\Delta Y}{Y}$ gets minimum contribution from the
uncertainty in the length.
c.
$\frac{\Delta Y}{Y}$ gets its maximum contribution from the
uncertainty in strain.
d.
The figure of merit is the largest for the length of
the rod.
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The velocity-time graph of a particle of mass $10\, kg$ is shown in the figure. The net work done on the particle in
the first two seconds of the motion is
a.
$-9300\,J$
b.
$12000\,J$
c.
$-4500\,J$
d.
$-12000\,J$
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A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of
40 divisions when $R.B. = 2400\,\Omega .\,$ Deflection becomes 20 divisions when resistance taken from resistance
box is 4900 β¦. Then we can conclude :
Note: This question is awarded as the bonus. Now the question is corrected.
a.
Current sensitivity of galvanometer is
$20\,$ $\mu$ $A/division$
b.
Resistance of galvanometer is $200\,\Omega .$
c.
Resistance required on R.B. for a deflection of 10
divisions is $9800\,\Omega .$
d.
Full scale deflection current is 2 mA.
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A conducting metal circular-wire-loop of radius $r$ is placed perpendicular to a magnetic field which varies with
time as $B=B_{0}e^{-}\frac{t}{Ο},$ where $B_{0}\, and \,Ο$ are constants at time $t= 0$ . If the resistance of the loop is $R$ , then the
heat generated in the loop after a long time $(t\rightarrow \infty )\rightarrow$ is
a.
$\frac{\pi ^{2}r^{4}B^{4}_{0}}{2ΟR}$
b.
$\frac{\pi ^{2}r^{4}B^{2}_{0}}{2ΟR}$
c.
$\frac{\pi ^{2}r^{4}B^{2}_{0}R}{Ο}$
d.
$\frac{\pi ^{2}r^{4}B^{2}_{0}}{ΟR}$
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Within a spherical charge distribution of charge density $\rho (r), \,$ N equipotential surfaces of potential
$V_{0}, \,V_{0}+ \Delta V, \,V_{0}+ 2 \Delta V, β¦V_{0}+N \Delta V\,(\Delta V > 0),$ are drawn and have increasing radii
$r_{0}, \,r_{1}, \,r_{2}, β¦r_{N},$ respectively. If the difference in the radii of the surfaces is constant for all values of
$V_{0} and\, \Delta V$ then :
a.
$\rho (r)\,=$ constant
b.
$\rho (r)\, \propto \frac{1}{r^{2}}$
c.
$\rho (r)\, \propto \,\frac{1}{r}$
d.
$\rho (r)\, \propto \,r$
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A toy-car, blowing its horn, is moving with a steady speed of $5\,m\,s^{-1}$ , away from a wall. An observer, towards
whom the toy car is moving, is able to hear $5\,$ beats per second. If the velocity of sound in air is $340\,m\,s^{-1}$ the
frequency of the horn of the toy car is close to
a.
$680\, Hz$
b.
$510\, Hz$
c.
$340\, Hz$
d.
$170\, Hz$
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A particle of mass $m$ is acted upon by a force $F$ given by the empirical law $F = \frac{R}{t^{2}} v(t).$ If this law is to be
tested experimentally by observing the motion starting from rest, the best way is to plot
a.
$logv(t)\, against \frac{1}{t}$
b.
$v(t)\, against \,t^{2}$
c.
$logv(t)\, against \frac{1}{t^{2}}$
d.
$logv(t)\, against \,t$
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A modulated signal $C_{m}(t)$ has the form $C_{m}(t) = 30 sin 300\pi t+ 10(cos 200\pi t-cos 400\pi t)$ . The carrier
frequency $f'_{c}$ the modulating frequency(message frequency) $f_{\omega }$ and the modulation index $\mu$ are respectively
given by :
An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The
radius of the earth is $R$ , while its mass is $M$ . The gravitational pull $F_{G}$ on the astronaut is
Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30
cm. The wavelength of light is 600nm. To see the stars just resolved by the telescope, the minimum distance
between them should be $(1\,light year= 9.46 \times 10^{15}m)$ of the order of :
a.
$10^{8}km$
b.
$10^{10}km$
c.
$10^{11}km$
d.
$10^{6}km$
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A photoelectric surface is illuminated successively by monochromatic light of wavelengths $\lambda and\,\frac{\lambda}{2}.$ If the
maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the
work function of the surface is :
a.
$\frac{hc}{2\lambda}$
b.
$\frac{hc}{\lambda}$
c.
$\frac{hc}{3\lambda}$
d.
$\frac{3hc}{\lambda}$
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The resistance of an electrical toaster has a temperature dependence given by $R(T) =R_{0}[1 +\alpha (T - T_{0})]$ in
its range of operation. At $T_{0} = 300\,K, \,R= 100\,\Omega \,and\,at T = 500\,K, \,R= 120\,\Omega$ . The toaster is connected
to a voltage source at $200\,V$ and its temperature is raised at a constant rate from $300\,to\,500\,K$ in $30\,s$ . The
total work done in raising the temperature is :
Note: This question was awarded as the bonus since all options were incorrect in the exam.
a.
$60000\, ln(\frac{6}{5})\,\,J$
b.
$200\, ln \frac{2}{3}\,J$
c.
$300\,J$
d.
$400\, ln( \frac{1.5}{1.3})\,J$
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Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform
magnetic field $B$ going into the plane of the paper (see figure). If charge densities $\sigma$ $_{1}$ and $\sigma$ $_{2}$ are induced on the
left and right surfaces respectively of the sheet, then (ignore fringe effects)
An aqueous solution of a salt $MX_{2}$ at certain temperature has a Van't Hoff factor of $2$ . What is the degree of
dissociation for this solution of the salt?
a.
$0. 50$
b.
$0. 33$
c.
$0. 67$
d.
$0. 80$
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Assertion:Among the carbon allotropes, diamond is an insulator, whereas, graphite is a good conductor of
electricity.
Reason:Hybridization of carbon in diamond and graphite are $sp^{3}$ and $sp^{2}$ respectively.
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, but the
reason is the correct explanation for the assertion.
c.
Both assertion and reason are incorrect.
d.
Assertion is incorrect statement, but the reason is
correct.
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Gold numbers of some colloids are Gelatin: $0. 005 -0. 01$ , Gum Arabic: $0. 15 -0. 25$ , Oleate: $0. 04 -1. 0$
, Starch: $15 -25$ . Which among the following is a better protective colloid?
a.
Gelatin
b.
Starch
c.
Oleate
d.
Gum Arabic
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Oxidation of succinate ion produces ethylene and carbon dioxide gases. On passing $0. 2$ Faraday electricity
through an aqueous solution of potassium succinate, what is the total volume of gases (at both cathode and
anode) at STP ( $1\, atm$ and $273\,K$ )?
a.
$8. 96\,L$
b.
$4. 48\,L$
c.
$6. 72\,L$
d.
$2. 24\,L$
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Fluorination of an aromatic ring is easily accomplished by treating a diazonium salt with $HBF_{4}$ . Which of the
following conditions is correct about this reaction?
a.
$NaF/Cu$
b.
$Cu_{2}O/H_{2}O$
c.
Only Heat
d.
$NaNO_{2}/Cu$
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A solid $XY \,$ kept in an evacuated sealed container undergoes decomposition to form a mixture of gases
$X\, and \,Y$ at temperature $T$ .
The equilibrium pressure is $10\, bar$ in this vessel. $K_{p}$ for this reaction is?
a.
$25$
b.
$100$
c.
$10$
d.
$5$
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Initially, the root-mean-square (RMS) velocity of $N_{2}$ molecules at certain temperature is $u$ . If this temperature
is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new RMS velocity will be:
a.
$2\,u$
b.
$14\,u$
c.
$4\,u$
d.
$u/2$
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The rate law for the reaction below is given by the expression $k[A][B]$
$A + B \rightarrow Product\rightarrow$
If the concentration of $B$ is increased from $0. 1\, to \,0. 3\, mol$ , keeping the value of $A$ at $0. 1\, mol$ , the rate
constant will be:
a.
$3k$
b.
$9k$
c.
$k/3$
d.
$k$
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If $\,100\, mole$ of $H_{2}O_{2}$ decompose at $1\, bar$ and $300\,K$ , the work is done ( $kJ$ ) by one mole of $O_{2}(g)$ as it
expands against $1\, bar$ pressure is:
$2H_{2}O_{2}(l) \rightleftharpoons 2H_{2}O(l) + O_{2}(g)$
$(R = 8 .3 \,J\,K^{-1}\, mol^{-1})$
a.
$124. 50$
b.
$249. 00$
c.
$498. 00$
d.
$62. 25$
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Let $A$ , be a $3\, \times 3$ matrix, such that $A^{2} -5A+ 7I =O.$
Statement - I : $A^{-1} = \frac{1}{7}\,(5I- A).$
Statement - II : The polynomial $A^{3} -2A^{2} -3A+I$ ,can be reduced to $5(A-4I).$ Then :
a.
Both the statements are true
b.
Both the statements are false
c.
Statement - I is true, but Statement - II is false
d.
Statement - I is false, but Statement - II is true
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The mean of $5$ observations is $5$ and their variance is $12. 4$ . If three of the observations are $1, 2\,&\,6$ ; then the
value of the remaining two is :
a.
$1, 11$
b.
$5, 5$
c.
$5, 11$
d.
None of these
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The solution of the differential equation $\frac{dy}{dx} + \frac{y}{2}secx= \frac{tanx}{2y}$ , where $0 \leq x< \frac{\pi}{2}$ and $y(0) = 1$ , is given by
a.
$y^{2} = 1 + \frac{x}{secx+tanx}$
b.
$y= 1 + \frac{x}{secx+tanx}$
c.
$y= 1 - \frac{x}{secx+tanx}$
d.
$y^{2} = 1 - \frac{x}{secx+tanx}$
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$x x$
For $x\in R, \,x\neq 0,$ if $y(x)$ is a differentiable function such that $x \int y(t)dt= (x+ 1)\, \int ty(t)dt,$ then $y(x)$
$1 1$
equals (where $C$ is a constant)
a.
$Cx^{3} e\frac{1}{x}$
b.
$\frac{C}{x^{2}} e^{-}\frac{1}{x}$
c.
$\frac{C}{x} e^{-}\frac{1}{x}$
d.
$\frac{C}{x^{3}} e^{-}\frac{1}{x}$
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Equation of the tangent to the circle, at the point $(1, \, -1)$ , whose center, is the point of intersection of the
straight lines $x- y= 1$ and $2x+y= 3$ is:
a.
$x+ 4y+ 3 = 0$
b.
$3x- y-4 = 0$
c.
$x-3y-4 = 0$
d.
$4x+y-3 = 0$
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The angle of elevation of the top of a vertical tower from a point A, due east of it is $45^{o}$ . The angle of
elevation of the top of the same tower from a point B, due south of A is $30^{o}$ . If the distance between A and B
is $54\sqrt{2}m$ , then the height of the tower (in meters), is:
a.
$108$
b.
$36\sqrt{3}$
c.
$54\sqrt{3}$
d.
$54$
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$P$ and $Q$ are two distinct points on the parabola, $y^{2} = 4x$ , with parameters $t$ and $t_{1}$ , respectively. If the normal
at $P$ passes through $Q$ , then the minimum value of $t^{2}_{1}$ , is
a.
$8$
b.
$4$
c.
$6$
d.
$2$
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$10$
The value of the integral $\int \frac{[x^{2}]}{[x^{2}-28x+196]+[x^{2}]}dx,$ where $[x]$ denotes the greatest integer less than or equal to $x$ , is
$4$
a.
$\frac{1}{3}$
b.
$6$
c.
$7$
d.
$3$
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A hyperbola whose transverse axis is along the major axis of the conic $\frac{x^{2}}{3} + \frac{y^{2}}{4} = 4$ and has vertices at the
foci of the conic. If the eccentricity of the hyperbola is $\frac{3}{2}$ , then which of the following points does not lie on
the hyperbola $?$
a.
$(\sqrt{5}, 2\sqrt{2})$
b.
$(0, 2)$
c.
$(5, 2\sqrt{3})$
d.
$(\sqrt{10}, 2\sqrt{3})$
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Let $a,b\in R, (a\neq 0).$ If the function $f$ , defined as
$\{ \frac{2x^{2}}{a}, \,0 \leq x< 1$
$f(x) = a, \,1 \leq x< \sqrt{2}$ ,is continuous in the interval $[0, \,\infty )$ , then an ordered pair $(a,b)$ can be
$\{$
$\frac{2b^{2}-4b}{x^{3}}, \,\sqrt{2}\leq x< 8$
a.
$(-\sqrt{2}, 1 - \sqrt{3})$
b.
$(\sqrt{2}, -1 + \sqrt{3})$
c.
$(\sqrt{2}, 1 - \sqrt{3})$
d.
$(-, \,1 + \,\sqrt{2} \sqrt{3})$
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Let $ABC$ be a triangle whose circumcentre is at $P$ . If the position vectors $A, \,B, \,C$ and $P$ are $\vec{a}, \vec{b}, \vec{c}$ and $\frac{\vec{a}+\vec{b}+\vec{c}}{4}$
respectively, then the position vector of the orthocentre of this triangle, is :
Let C be a curve given by $y(x) = 1 + \,\sqrt{4x-3}x$ , $> \frac{3}{4}$ . If $P$ is a point on C, such that the tangent at $P$ has
slope $\frac{2}{3}$ , then a point through which the normal at $P$ passes, is :
a.
$(1, \,7)$
b.
$(3, \, -4)$
c.
$(4, \, -3)$
d.
$(2, \,3)$
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$18$
If the coefficients of $x^{-2}$ and $x^{-4}$ , in the expansion of $(x\frac{1}{3} + \frac{1}{1} ) , (x> 0)$ , are $m$ and $n$ respectively, then
$2x 3$
$\frac{m}{n}$ is equal to
a.
$27$
b.
$182$
c.
$\frac{5}{4}$
d.
$\frac{4}{5}$
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The number of distinct real values of $\lambda$ , for which the lines $\frac{x-1}{1} = \frac{y-2}{2} = \frac{z+3}{\lambda ^{2}}$ and $\frac{x-3}{1} = \frac{y-2}{\lambda ^{2}} = \frac{z-1}{2}$ , are
coplanar is
a.
$2$
b.
$4$
c.
$3$
d.
$1$
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A straight line through origin $O$ meets the lines $3y= 10 -4x$ and $8x+ 6y+ 5 = 0$ at points $A$ and $B$
respectively. Then, $O$ divides the segment $AB$ in the ratio
a.
$2 : 3$
b.
$1 : 2$
c.
$4 : 1$
d.
$3 : 4$
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$ABC$ is a triangle in a plane with vertices $A(2, \,3, \,5), \,B(-1, \,3, \,2)$ and $C(\lambda , \,5, \,\mu )$ . If the median through $A$
is equally inclined to the coordinate axes, then the value of $(\lambda ^{3} +\mu ^{3} + 5)$ is
a.
$1130$
b.
$1348$
c.
$1077$
d.
$676$
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A ray of light is incident along a line which meets another line $7x- y+ 1 = 0$ at the point $(0, 1)$ . The ray is
then reflected from this point along the line $y+ 2x= 1$ . Then the equation of the line of incidence of the ray
of light is :
a.
$41x-25y+ 25 = 0$
b.
$41x+ 25y-25 = 0$
c.
$41x-38y+ 38 = 0$
d.
$41x+ 38y-38 = 0$
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