Ship Ais sailing towards north-east with velocity) π£= 30i + 50j km h where ipoints east and j, north.
The ship Bis at a distance of 80 kmeast and 150 kmnorth of Ship Aand is sailing towards the west at
10 km h $^{-1}$ . Awill be at the minimum distance from Bin:
a.
4.2 h
b.
3.2 h
c.
2.6 h
Correct Answer
d.
2.2 h
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Q2mcq
A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the
wave at a particular point of space and time is E = 6 V m $^{-1}$ along y-direction. Its corresponding magnetic field
component, Bwould be:
a.
2 $\times$ 10 $^{-8}$ T along z- 2 $\times$ 10 $^{-8}$ Talongβy- 6 $\times$ 10 $^{-8}$ Talongβz- 6 $\times$ 10 $^{-8}$ Talongβx-
direction direction direction direction
Correct Answer
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Q3mcq
The wavelength of the carrier waves in a modern optical fiber communication network is close to:
a.
2400 nm
b.
900 nm
c.
600 nm
d.
1500 nm
Correct Answer
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Q4mcq
Two identical beakers Aand Bcontain equal volumes of two different liquids at 60$^{\circ}$Ceach and left to cool
down. Liquid in Ahas density of 8 $\times$ 10 $^{2}$ kg m $^{-3}$ and specific heat of 2000 J kg $^{-1}$ K $^{-1}$ while the liquid in Bhas
density 10 $^{3}$ kg m $^{-3}$ and specific heat of 4000 J kg $^{-1}$ K $^{-1}$ . Which of the following best describes their
temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)
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Q5mcq
An alternating voltage π( π‘) = 220sin100ππ‘volt is applied to a purely resistive load of 50 $\Omega$. The time
taken for the current to rise from half of the peak value to the peak value is:
a.
7.21 ms
b.
5 . 25 ms
c.
2.24 ms
d.
3.33 ms
Correct Answer
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Q6mcq
A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled
by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 mis:
a.
4 J
b.
2.5 J
c.
6.5 J
Correct Answer
d.
5 J
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Q7mcq
A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical
shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the
hollow shell be V . If the shell is now given a charge of - 4Q, the new potential difference between the same
two surfaces is:
a.
- 2V
b.
2 V
c.
V
Correct Answer
d.
4 V
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Q8mcq
In figure, the optical fiber is π= 2 mlong and has a diameter of d = 20 $\mu$m . If a ray of light is incident on one
end of the fiber at angle $\theta$ $_{1}$ = 40$^{\circ}$, the number of reflections it makes before emerging from the other end is
close to:
(refractive index of fiber is 1.31, sin 40$^{\circ}$ = 0.64and sin $^{-1}$ β‘0.49 = 30$^{\circ}$.)
a.
55000
b.
57000
Correct Answer
c.
45000
d.
66000
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Q9mcq
Two particles move at right angle to each other. Their de Broglie wavelengths are π $_{1}$ and π $_{2}$ respectively. The
particles suffer perfectly inelastic collision. The de Broglie wavelength πof the final particle, is given by:
An upright object is placed at a distance of 40 cmin front of a convergent lens of focal length 20 cm . A
convergent mirror of focal length 10 cmis placed at a distance of 60 cmon the other side of the lens. The
position and size of the final image will be:
a.
40 cm from the 20 cmfrom the 40 cm from the 20 cm from the
convergent lens, twice convergent mirror, convergent lens, same convergent mirror,
the size of the object twice the size of the size of the object same size of the object
object
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Water from a pipe is coming at a rate of 100liters per minute. If the radius of the pipe is 5 cm, the Reynolds
number for the flow is of the order of: (density of water = 100 kg / m $^{3}$ , coefficient of viscosity of water
= 1 mPa s )
a.
10 $^{2}$
b.
10 $^{4}$
c.
10 $^{3}$
d.
10 $^{6}$
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For the circuit shown, with π $_{1}$ = 1.0 $\Omega$, π $_{2}$ = 2.0 $\Omega$, πΈ $_{1}$ = 2 Vand πΈ $_{2}$ = πΈ $_{3}$ = 4 V, the potential difference
between the points βaβand βbβis approximately ( in V):
a.
3.3
b.
2.3
c.
2.7
d.
3.7
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A wire of length 2L, is made by joining two wires Aand Bof same length but different radii rand 2rand
made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If
the number of antinodes in wire Ais pand that in Bis qthen ratio p: qis:
a.
3 : 5
b.
4 : 9
c.
1 : 4
d.
1 : 2
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If 10 $^{22}$ gas molecules each of mass 10 $^{-26}$ kg collides with a surface (perpendicular to it) elastically per second
over an area 1 m $^{2}$ with a speed 10 $^{4}$ m / s, the pressure exerted by the gas molecules will be of the order of:
a.
2 Pa
b.
4 Pa
c.
6 Pa
d.
8 Pa
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A boyβs catapult is made of rubber cord which is 42 cmlong, with 6 mmdiameter of cross-section and of
negligible mass. The boy keeps a stone weighing 0.02 kgon it and stretches the cord by 20 cmby applying a
constant force. When released, the stone flies off with a velocity of 20 ms $^{-1}$ . Neglect the change in the area of
cross-section of the cord while stretched. The Youngβs modulus of rubber is closest to:
a.
10 $^{6}$ N m $^{-2}$
b.
10 $^{4}$ N m $^{-2}$
c.
10 $^{8}$ N m $^{-2}$
d.
10 $^{3}$ N m $^{-2}$
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Four identical particles of mass Mare located at the corners of a square of side βπβ. What should be their speed
if each of them revolves under the influence of otherβs gravitational field in a circular orbit circumscribing the
square?
a.
1.35$\sqrt$ $\frac{GM}{a}$
b.
1.21$\sqrt$ $\frac{GM}{a}$
c.
1.41$\sqrt$ $\frac{GM}{a}$
d.
1.16$\sqrt$ $\frac{GM}{a}$
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A thin circular plate of mass πand radius π has its density varying as $\rho$ ( π) =$\rho$ $_{0}$ rwith π $_{0}$ as constant and πis
the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate
and passing through its edge is πΌ= πππ $^{2}$ . The value of the coefficient πis:
a.
$\frac{3}{5}$
b.
$\frac{1}{2}$
c.
$\frac{8}{5}$
d.
$\frac{3}{2}$
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A thermally insulated vessel contains 150 gof water at 0$^{\circ}$C. Then the air from the vessel is pumped out
adiabatically. A fraction of water turns into ice and the rest evaporates at 0$^{\circ}$Citself. The mass of evaporated
water will be closest to: (Latent heat of vaporization of water = 2.10 $\times$ 10 $^{6}$ J kg $^{-1}$ and Latent heat of Fusion of
water = 3.36 $\times$ 10 $^{5}$ J kg $^{-1}$ )
a.
35 g
b.
20 g
c.
130 g
d.
150 g
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A thin strip 10 cmlong is on a Ushaped wire of negligible resistance and it is connected to a spring of spring
constant 0.5 N m $^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of 0.1 T . If the strip is pulled
from its equilibrium position and released, the number of oscillations it performs before its amplitude
decreases by a factor of eis N. If the mass of the strip is 50grams, its resistance 10$\Omega$and air drag negligible,
Nwill be close to:
a.
1000
b.
5000
c.
10000
d.
50000
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The bob of a simple pendulum has mass 2 gand a charge of 5.0 $\mu$C . It is at rest in a uniform horizontal electric
field of intensity 2000 V / mAt equilibrium, the angle that the pendulum makes with the vertical is:
take β g = 10 m / s $^{2}$
a.
tan $^{-1}$ 0.2
b.
tan $^{-1}$ 2.0
c.
tan $^{-1}$ 0.5
d.
tan $^{-1}$ 5.0
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Radiation coming from transitions π= 2to π= 1of hydrogen atoms fall on He $^{+}$ ions in π= 1and π= 2
states. The possible transition of helium ions as they absorb energy from the radiation is:
a.
π= 2 $\longrightarrow$π= 3
b.
π= 2 $\longrightarrow$π= 4
c.
π= 2 $\longrightarrow$π= 5
d.
π= 1 $\longrightarrow$π= 4
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A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that
g = 3.1$\pi$ m s $^{-2}$ , what will be the tensile stress that would be developed in the wire?
a.
5.2 $\times$ 10 $^{6}$ N m $^{-2}$
b.
6.2 $\times$ 10 $^{6}$ N m $^{-2}$
c.
4 . 8 $\times$ 10 $^{6}$ N m $^{-2}$
d.
3.1 $\times$ 10 $^{6}$ N m $^{-2}$
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A 20 Hinductor coil is connected to a 10 $\Omega$resistance in series as shown in figure. The time at which rate of
dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in
the inductor, is:
a.
$\frac{1}{2}$ ln2
b.
2ln2
c.
$\frac{2}{ln2}$
d.
ln2
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Voltage rating of a parallel plate capacitor is 500 V . Its dielectric can withstand a maximum electric field of
10 $^{6}$ V / m . The plate area is 10 $^{-4}$ m $^{2}$ . What is the dielectric constant if the capacitance is 15 pF?
given β $\epsilon$ $_{0}$ = 8.86 $\times$ 10 $^{-12}$ C $^{2}$ / Nm $^{2}$
a.
3.8
b.
8.5
c.
4.5
d.
6.2
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In an interference experiment the ratio of amplitudes of coherent waves is $\frac{π1}{π2}$ = $\frac{1}{3}$ . The ratio of maximum and
minimum intensities of fringes will be:
a.
4
b.
9
c.
2
d.
18
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Four particles A, B, C and Dwith masses m $_{A}$ = m, m $_{B}$ = 2m, m $_{C}$ = 3mand m $_{D}$ = 4mare at the corners of a
square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of
mass of the particles is:
a.
$\frac{a}{5}$ ^i + ^j
b.
$\frac{a}{5}$ ^i - ^j
c.
^ + ^
ai j
d.
Zero
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A circular coil having Nturns and radius rcarries a current I . It is held in the XZplane in a magnetic field B^i.
The torque on the coil due to the magnetic field is:
a.
B$\pi$r $^{2}$ IN
b.
$\frac{Br2I}{$\pi$N}$
c.
$\frac{B$\pi$r2I}{N}$
d.
Zero
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Assertion: Ozone is destroyed by CFCsin the upper stratosphere.
Reason: Ozone holes increase the amount of UVradiation reaching the earth.
a.
Assertion and reason The assertion is false, Assertion and reason Assertion and reason
are correct, but the but the reason is are incorrect. are both correct, and
reason is not the correct. the reason is the
explanation for the correct explanation for
assertion. the assertion.
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The vapour pressures of pure liquids Aand Bare 400and 600 mm Hgrespectively at 298 K . On mixing the
two liquids, the sum of their volumes is equal to the volume of the final mixture. The mole fraction of liquid B
is 0.5in the mixture. The vapour pressure of the final solution, the mole fractions of components Aand Bin
the vapour phase, respectively are
a.
500 mm Hg, 0.5, 0.5
b.
450 mm Hg, 0.4, 0.6
c.
450 mm Hg, 0.5, 0.5
d.
500 mm Hg, 0.4, 0.6
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Given that,
E $^{o}_{O2/ H2O}$ = + 1 .23 V;
E $^{o}_{S2O2 -8}_{/ SO2 -4}$ = 2 .05 V
E $^{o}_{Br2/ Br}$ - = + 1 . 09 V;
E $^{o}_{Au3 +}_{/ Au}$ = 1 .4 V
The strongest oxidizing agent is
a.
O $_{2}$
b.
S $_{2}$ O $^{2 -}_{8}$
c.
Br $_{2}$
d.
Au $^{3 +}$
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If solubility product of Zr $_{3}$ ( PO $_{4}$ ) $_{4}$ is denoted by K $_{sp}$ and its molar solubility is denoted by S, then which of
the following relation between Sand K $_{sp}$ is correct?
a.
S = $\frac{Ksp}{144}\frac{1}{6}$
b.
S = $\frac{Ksp}{6912}\frac{1}{7}$
c.
S = $\frac{Ksp}{929}\frac{1}{9}$
d.
S = $\frac{Ksp}{216}\frac{1}{7}$
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For the reaction 2A + B $\rightarrow$C, the values of initial rate at different reactant concentrations are given in the table
below. The rate law for the reactions is:
[A] (mol β L $^{-1}$ ) [B] (mol β L $^{-1}$ ) Initial Rate
(mol β L $^{-1}$ s $^{-1}$ )
0.05 0.05 0.045
0.10 0.05 0.090
0.20 0.10 0.72
a.
Rate = k[A] $^{2}$ [B]
b.
Rate = k[A] $^{2}$ [B] $^{2}$
c.
Rate = k[A][B]
d.
Rate = k[A][B] $^{2}$
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In order to oxidize a mixture of one mole of each of FeC $_{2}$ O $_{4}$ , Fe $_{2}$ ( C $_{2}$ O $_{4}$ ) $_{3}$ , FeSO $_{4}$ and Fe $_{2}$ ( SO $_{4}$ ) $_{3}$ in acidic
medium, the number of moles of KMnO $_{4}$ is:
a.
1
b.
2
c.
3
d.
1.5
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An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however,
reacts with Grignard reagent and given positive iodoform test. The compound is:
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Element Bforms ccp structure and Aoccupies half of the octahedral voids, while oxygen atoms occupy all the
tetrahedral voids. The structure of bimetallic oxide is:
a.
A $_{2}$ BO $_{4}$
b.
AB $_{2}$ O $_{4}$
c.
A $_{2}$ B $_{2}$ O
d.
A $_{4}$ B $_{2}$ O
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The correct order of the spin -only magnetic moment of metal ions in the following low-spin complexes,
[V ( CN ) $_{6}$ ] $^{4 -}$ , [Fe ( CN ) $_{6}$ ] $^{4 -}$ , [Ru ( NH $_{3}$ ) $_{6}$ ] $^{3 +}$ and [Cr ( NH $_{3}$ ) $_{6}$ ] $^{2 +}$ , is:
The quantum number of four electrons are given below:
I . n = 4, l = 2, m $_{l}$ = - 2, m $_{s}$ = - 1 / 2
II . n = 3, l = 2, m $_{l}$ = 1, m $_{s}$ = + 1 / 2
III . n = 4, l = 1, m $_{l}$ = 0, m $_{s}$ = + 1 / 2
IV . n = 3, l = 1, m $_{l}$ = 1, m $_{s}$ = - 1 / 2
The correct order of their increasing energies will be:
a.
I < III < II < IV
b.
IV < II < III < I
c.
I < II < III < II
d.
IV < III < II < I
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For silver, C $_{p}$ (JK $^{-1}$ mol $^{-1}$ ) = 23 + 0.01T . If the temperature Tof 3moles of silver is raised from
300 K to 1000 K at 1 atmpressure, the value of $\Delta$Hwill be close to:
a.
16 kJ
b.
62 kJ
c.
13 kJ
d.
21 kJ
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Which one of the following equations does not correctly represent the first law of thermodynamics for the
given processes involving an ideal gas? (Assume non- expansion work is zero)
a.
Isochoric process :
$\Delta$U = q
b.
Isochoric process :
q = - w
c.
Cyclic process :
q = - w
d.
Adiabatic process :
$\Delta$U = - w
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100 mL of a water sample contains 0.81 gof calcium bicarbonate and 0.73g of magnesium bicarbonate. The
hardness of this water sample expressed in terms of equivalents of CaCO $_{3}$ is:
(molar mass of calcium bicarbonate is 162 gm mol $^{-1}$ and magnesium bicarbonate is 146 g mol $^{-1}$ )
a.
100 ppm
b.
1,000 ppm
c.
5,000 ppm
d.
10,000 ppm
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Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass mof
the adsorbent. The plot of log $\frac{x}{m}$ vs logpis shown in the given graph. $\frac{x}{m}$ is proportional to,
a.
p $^{3}$
b.
p $^{2}$
c.
p $^{2 / 3}$
d.
p $^{3 / 2}$
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If 2π¦= cot $\frac{-1$\sqrt{\,}$3cosπ₯+ sinπ₯}{cosπ₯- $\sqrt{\,}$3sinπ₯}^{2}$ $\forall$π₯$\in$0, $\frac{π}{2}$ , then $\frac{ππ¦}{ππ₯}$ is equal to
a.
$\frac{π}{6}$ - π₯
b.
2π₯- $\frac{π}{3}$
c.
π₯- $\frac{π}{6}$
d.
None of these
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The magnitude of the projection of the vector ^ ^π+ ^on the vector perpendicular to the plane containing
2π+ 3 π
the vectors ^π+ ^π+ ^and ^ ^ ^ is:
π π+ 2π+ 3π,
a.
3$\sqrt$6
b.
$\sqrt$ $\frac{3}{2}$
c.
$\sqrt$6
d.
$\frac{$\sqrt{\,}$3}{2}$
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The sum of the co-efficient of all even degree terms in π₯in the expansion of
π₯+ $\sqrt$π₯ $^{3}$ - 1 $^{6}$ +π₯- $\sqrt$π₯ $^{3}$ - 1 $^{6}$ , π₯> 1is equal to
a.
26
b.
32
c.
24
d.
29
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$\frac{π}{4}$
If ππ₯= $\frac{2 - π₯cosπ₯}{2 + π₯cosπ₯}$ and π(π₯) = log $_{π}$ β‘π₯, then the value of the integral $\int$ πππ₯ππ₯is
- $\frac{π}{4}$
a.
log $_{π}$ β‘π
b.
log $_{π}$ β‘2
c.
log $_{π}$ β‘1
d.
log $_{π}$ β‘3
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If π $_{1}$ and π $_{2}$ are respectively the sets of local minimum and local maximum points of the function,
ππ₯= 9π₯ $^{4}$ + 12π₯ $^{3}$ - 36π₯ $^{2}$ + 25, π₯$\in$π , then
a.
π $_{1}$ = -2; π $_{2}$ = {0,1}
b.
π $_{1}$ = -1; π $_{2}$ = 0,2
c.
π $_{1}$ = -2,0; π $_{2}$ = {1}
d.
π $_{1}$ = -2,1; π $_{2}$ = {0}
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The contrapositive of the statement βIf you are born in India, then you are a citizen of Indiaβ, is
a.
If you are not born in
India, then you are not
a citizen of India.
b.
If you are a citizen of If you are born in If you are not a citizen
India, then you are India, then you are not of India, then you are
born in India. a citizen of India. not born in India.
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If the tangents on the ellipse 4π₯ $^{2}$ + π¦ $^{2}$ = 8at the points 1, 2and ( π, π) are perpendicular to each other,
then π $^{2}$ is equal to
a.
$\frac{2}{17}$
b.
$\frac{4}{17}$
c.
$\frac{64}{17}$
d.
$\frac{128}{17}$
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The equation of a plane containing the line of intersection of the planes 2π₯- π¦- 4 = 0and π¦+ 2π§- 4 = 0and
passing through the point 1,1, 0is
a.
π₯- 3π¦- 2π§= - 2
b.
π₯+ 3π¦+ π§= 4
c.
π₯- π¦- π§= 0
d.
2π₯- π§= 2
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Let π: 0, 2 $\rightarrow$π be a twice differentiable function such that π $''$ π₯> 0, for all π₯$\in$0, 2 . If ππ₯= ππ₯+ π2 - π₯,
then πis
a.
decreasing on 0,2 increasing on 0,2 increasing on ( 0,1 ) decreasing on 0,1 and
and decreasing on 1,2 increasing on ( 1,2 )
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The mean and variance for seven observations are 8and 16respectively. If 5of the observations are
2, 4, 10, 12, 14, then the product of the remaining two observations is
a.
48
b.
45
c.
49
d.
40
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The sum of the squares of the lengths of the chords intercepted on the circle, π₯ $^{2}$ + π¦ $^{2}$ = 16, by the lines,
π₯+ π¦= π, π$\in$π, where πis the set of all natural numbers is:
a.
210 105 320 160
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Let π¦= π¦( π₯) be the solution of the differential equation, π₯ $^{2}$ + 1 $^{2} \frac{ππ¦}{ππ₯}$ + 2π₯(π₯ $^{2}$ + 1)π¦= 1such that π¦0 = 0 .
If $\sqrt$π π¦1 = $\frac{π}{32}$ , then the value of πis
a.
$\frac{1}{16}$
b.
$\frac{1}{2}$
c.
$\frac{1}{4}$
d.
1
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All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of
such numbers in which the odd digits occupy even places is
a.
175
b.
162
c.
180
d.
160
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The greatest value of π$\in$π for which the system of linear equations π₯- ππ¦- ππ§= 0, ππ₯- π¦+ ππ§= 0,
ππ₯+ ππ¦- π§= 0has a non-trivial solution, is
a.
-1
b.
2
c.
$\frac{1}{2}$
d.
0
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