A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other.
The man pushes his son so that he starts moving at a speed of 0.70 m s $^{-1}$ with respect to the man. The speed of
the man with respect to the surface is:
a.
0.20 m s $^{-1}$
Correct Answer
b.
0.14 m s $^{-1}$
c.
0.47 m s $^{-1}$
d.
0.28 m s $^{-1}$
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Q2mcq
In a double slit experiment, when a thin film of thickness thaving refractive index $\mu$is introuduced in front of
one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of tis ( $\lambda$
is the wavelength of the light used):
a.
$\frac{$\lambda$}{2 ( $\mu$ - 1 )}$
b.
$\frac{$\lambda$}{( 2$\mu$ - 1 )}$
c.
$\frac{2$\lambda$}{( $\mu$ - 1 )}$
d.
$\frac{$\lambda$}{( $\mu$ - 1 )}$
Correct Answer
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Q3mcq
A uniform rod of length π is being rotated in a horizontal plane with a constant angular speed about an axis
passing through one of its ends. If the tension generated in the rod due to rotation is T ( π₯) at a distance π₯from
the axis, then which of the following graphs depicts it most closely?
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Q4mcq
A progressive wave travelling along the positive π₯- direction is represented by π¦π₯, t = A sin ( kπ₯- $\omega$t + $\phi$ ) .
Its snapshot at t = 0is given in the figure.
For this wave, the phase $\phi$is:
a.
$\frac{$\pi$}{2}$
b.
0
c.
$\pi$
Correct Answer
d.
- $\frac{$\pi$}{2}$
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Q5mcq
The trajectory of a projectile near the surface of the earth is given as π¦= 2π₯- 9π₯ $^{2}$ . If it were launched at an
angle $\theta$ $_{0}$ with speed π£ $_{0}$ then g = 10 m s $^{-2}$ :
a.
$\theta$ $_{0}$ = cos $^{-1}$ β‘ $\frac{1}{$\sqrt{\,}$5}$ and π£ $_{0}$ = $\frac{5}{3}$ ms $^{-1}$
Correct Answer
b.
$\theta$ $_{0}$ = cos $^{-1}$ β‘ $\frac{2}{$\sqrt{\,}$5}$ and π£ $_{0}$ = $\frac{3}{5}$ ms $^{-1}$
c.
$\theta$ $_{0}$ = sin $^{-1}$ β‘ $\frac{1}{$\sqrt{\,}$5}$ and π£ $_{0}$ = $\frac{5}{3}$ ms $^{-1}$
d.
$\theta$ $_{0}$ = sin $^{-1}$ β‘ $\frac{2}{$\sqrt{\,}$5}$ and π£ $_{0}$ = $\frac{3}{5}$ ms $^{-1}$
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Q6mcq
An excited He $^{+}$ ion emits two photons in succession, with wavelengths 108.5 nmand 30.4 nmin making a
transition to the ground state. The quantum number n, corresponding to its initial excited state is
(for a photon of wavelength $\lambda$, energy E = $\frac{1240 eV}{$\lambda$ ( in nm )}$ )
a.
n = 6
b.
n = 5
Correct Answer
c.
n = 7
d.
n = 4
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Q7mcq
The resistive network shown below is connected to a D . C . source of 16 V . The power consumed by the
network is 4Watt. The value of Ris:
a.
16 $\Omega$
b.
8 $\Omega$
Correct Answer
c.
6 $\Omega$
d.
1 $\Omega$
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Q8mcq
At 40$^{\circ}$C, a brass wire of 1 mmradius is hung from the ceiling. A small mass, Mis hung from the free end of the
wire. When the wire is cooled down from 40$^{\circ}$C to 20$^{\circ}$Cit regains its original length of 0.2 m . The value of M
is close to:
(Coefficient of linear expansion and Youngβs modulus of brass are 10 $^{-5}$ / $^{$^{\circ}$}$ Cand 10 $^{11}$ N / m $^{2}$ , respectively;
g = 10 m s $^{-2}$ )
a.
0.9 kg
b.
0.5 kg
c.
1.5 kg
d.
9 kg
Correct Answer
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Q9mcq
The truth table for the circuit given in the figure is:
a.
A B Y
0 0 0
0 1 0
1 0 1
1 1 1
b.
A B Y
0 0 1
0 1 0
1 0 0
1 1 0
c.
A B Y
0 0 1
0 1 1
1 0 1
1 1 1
d.
A B Y
0 0 1
0 1 1
1 0 0
1 1 0
Correct Answer
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Q10mcq
Which of the following combinations has the dimension of electrical resistance ( $\epsilon$ $_{0}$ is the permittivity of
vacuum and $\mu$ $_{0}$ is the permeability of vacuum)?
A galvanometer of resistance 100 $\Omega$has 50 divisions on its scale and has sensitivity of 20$\mu$A / division. It is
to be converted to voltmeter with three ranges, of 0 - 2 V, 0 - 10 Vand 0 - 20 V . The appropriate circuit to do
so is:
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A sample of an ideal gas is taken through the cyclic process abcaas shown in the figure. The change in the
internal energy of the gas along the path cais -180 J . The gas absorbs 250 Jof heat along the path aband 60 J
along the path bc. The work done by the gas along the path abcis:
a.
130 J
b.
100 J
c.
120 J
d.
140 J
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When π $_{1}$ gram of ice at -10 $^{o}$ C(specific heat = 0.5 cal g $^{-1}$ β $^{-1}$ ) is added to π $_{2}$ gram of water at 50 $^{o}$ C, finally
no ice is left and the water is at 0 $^{o}$ C. The value of latent heat of ice, in cal g $^{-1}$ is:
a.
$\frac{50π2}{π1}$
b.
$\frac{5π1}{π2}$ - 50
c.
$\frac{5π2}{π1}$ - 5
d.
$\frac{50π2}{π1}$ - 5
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$\rightarrow$ ^
A Point dipole p = - p $_{0}$ π₯is kept at the origin. The potential and electric field due to this dipole on the π¦- axis
at a distance dare, respectively: (Taken V = 0at infinity)
A thin ring of 10 cmradius carries a uniformly distributed charge. The ring rotates at a constant angular speed
of 40$\pi$ rads $^{-1}$ about its axis, perpendicular to its plane. Is the magnetic field its centre is 3.8 $\times$ 10 $^{-9}$ T, then the
charge carried by the ring is close to $\mu$ $_{0}$ = 4$\pi$ $\times$ 10 $^{-7}$ N / A $^{2}$ .
a.
4 $\times$ 10 $^{-5}$ C
b.
3 $\times$ 10 $^{-5}$ C
c.
2 $\times$ 10 $^{-6}$ C
d.
7 $\times$ 10 $^{-6}$ C
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A circular disc of radius πhas a hole of radius aat its centre(see figure). If the mass per unit area of the disc
varies as $\frac{π0}{π}$ then, the radius of gyration of the disc about its axis passing through the center is
a.
$\frac{π+ π}{3}$
b.
$\sqrt$ $\frac{π2+ π2+ ππ}{3}$
c.
$\frac{π+ π}{2}$
d.
$\sqrt$ $\frac{π2+ π2+ ππ}{2}$
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The transfer characteristic curve of a transistor, having input and output resistance 100 $\Omega$and 100 k$\Omega$
respectively, is shown in the figure. The voltage and power gain, are respectively:
a.
5 $\times$ 10 $^{4}$ , 2.5 $\times$ 10 $^{6}$
b.
2.5 $\times$ 10 $^{4}$ , 2.5 $\times$ 10 $^{6}$
c.
5 $\times$ 10 $^{4}$ , 5 $\times$ 10 $^{6}$
d.
5 $\times$ 10 $^{4}$ , 5 $\times$ 10 $^{5}$
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$\rightarrow$
An electromagnetic wave is represented by the electric filed E = E $_{0}$ ^nsinβ‘$\omega$t + 6π¦- 8π§. Taking unit vectors in
and directions to be ^π, ^π, ^ the directions of propogations ^ is:
π₯, π¦ π§ π, s,
a.
^s = $\frac{3^π- 4^π}{5}$
^
b.
^s = $\frac{-3^π+ 4^π}{5}$
^
c.
^s = $\frac{4^π- 3π}{5}$
d.
^s = $\frac{-4^π- 3π}{5}$
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The stopping potential V $_{o}$ (in volt) as a function of frequency ( π£) for a sodium emitter, is shown in the figure.
The work function of sodium, form the data plotted in the figure, will be:
(Given: Planckβs constant h = 6.63 $\times$ 10 $^{-34}$ J s, electron charge ( e ) = 1.6 $\times$ 10 $^{-19}$ C)
a.
2.12 eV
b.
1.82 eV
c.
1.95 eV
d.
1.66 eV
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The figure shows a square loop πΏof side 5 cmwhich is connected to a network of resistances. The whole setup
is moving towards the right with a constant speed of 1 cm s $^{-1}$ . At some instant, a part of πΏis in a uniform
magnetic field of 1Tperpendicular to the plane of the loop. If the resistance of πΏis 1 . 7 $\Omega$, the current in the
loop at that instant will be close to:
a.
115 $\mu$A
b.
60 $\mu$A
c.
150 $\mu$A
d.
170 $\mu$A
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Two identical parallel plate capacitors, of capacitance Ceach, have plates of area A, separated by a distance d.
The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and
dielectric constants K $_{1}$ , K $_{2}$ and K $_{3}$ . The first capaciitor is filled as shown in figure I, and the second one is
filled as shown in figure II .
If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two,
would be ( E $_{1}$ refers to capacitor Iand E $_{2}$ to capacitor ( II ) ):
9K K K
A magnetic compass needle oscillates 30times per minute at a place where the dip is 45$^{\circ}$and 40times per
minute where the dip is 30$^{\circ}$. If π΅ $_{1}$ and π΅ $_{2}$ are the net magnetic fields due to the earth at the two places
respectively, then the ratio B $_{1}$ / B $_{2}$ is approximately equal to
a.
3.6
b.
1.8
c.
1.2
d.
0.7
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The value of numerical aperture of the objective lens of a microscope is 1.25 . If light of wavelength 5000 β«is
used, the minimum separation between two points, to be seen as distinct, will be:
a.
0.48 $\mu$m
b.
0.24 $\mu$m
c.
0.38 $\mu$m
d.
0.12 $\mu$m
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A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a
distance Rfrom it. If t $_{1}$ and t $_{2}$ are the values of the time taken by it to hit the target in two possible ways, the
product t $_{1}$ t $_{2}$ is:
a.
R / 2g
b.
R / g
c.
2R / g
d.
R / 4g
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Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the
molar specific heat of mixture at constant volume? R = 8.3 J / mol K
a.
17.4 J / mol K
b.
19.7 J / mol K
c.
15.7 J / mol K
d.
21.6 J / mol K
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A concave mirror has radius of curvature of 40 cm . It is at the bottom of a glass that has water filled up to
5 cm(see figure). If a small particle is floating on the surface of water, its image as seen, from directly above
the glass, is at a distance dfrom the surface of water. The value of dis close to: (Refractive index of water
= 1.33 )
a.
13.4 cm
b.
8.8 cm
c.
6.7 cm
d.
11.7 cm
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A submarine Atravelling at 18km hr $^{-1}$ is being chased along the line of its velocity by another submarine B
travelling at 27 km hr $^{-1}$ . Bsends a sonar signal of 500 Hzto detect Aand receives a reflected sound of
frequency v. The value of vis closed to (Speed of sound in water 1500 m s $^{-1}$ )
a.
504 Hz
b.
499 Hz
c.
502 Hz
d.
507 Hz
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To verify Ohmβs law, a student connects the voltmeter across the battery as shown in the figure. The measured
voltage is plotted as a function of the current, and the following graph is obtained:
If V $_{o}$ is almost zero, identify the correct statement:
a.
The emf of the battery is 1.5 Vand its internal
resistance is 1.5 $\Omega$
b.
The value of the resistance Ris 1.5 $\Omega$
c.
The potential difference across the battery is
1.5 Vwhen it sends a current of 1000 mA
d.
The emf of the battery is 1.5 Vand the value of R
is 1.5 $\Omega$
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A person of mass πis sitting on a swing of length πΏand swinging with and an angular amplitude $\theta$ $_{0}$ . If the
person stands up when the swing passes through its lowest point, the work done by him, assuming that his
centre of mass moves by a distance π π< < πΏ, is close to:
)
a.
πππ (1 - $\theta$ $^{2}_{0}$
b.
πππ(1 + $\frac{$\theta$0}{2}^{2}$ )
)
c.
πππ
d.
πππ(1 + $\theta$ $^{2}_{0}$
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Shown in the figure is a shell made of a conductor. It has inner radius πand outer radius π, and carries charge
$\rightarrow$
π. At its centre a dipole π is placed as shown then:
a.
Surface charge density on the inner surface of the
shell is zero everywhere.
b.
Electric field outside the shell is the same as that
of a point charge at the centre of the shell.
c.
Surface charge density on the inner surface is
( π
)
uniform and equal to $\frac{2}{4$\pi$π2}$ .
d.
Surface charge density on the outer surface
$\rightarrow$
depends on π.
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An organic compound βAβ is oxidized with Na $_{2}$ O $_{2}$ followed by boiling with HNO $_{3}$ . The resultant solution is
then treated with ammonium molybdate to yield a yellow percipitate. Based on a above observation, the
element present in the given compound is:
a.
Fluorine
b.
Phosphorus
c.
Nitrogen
d.
Sulphur
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Enthalpy of sublimation of iodine is 24 cal g $^{-1}$ at 200$^{\circ}$C. If specific heat of I $_{2}$ (s) and I $_{2}$ (vap) are 0.055and
0.031 cal g $^{-1}$ K $^{-1}$ respectively, then enthalpy of sublimation of iodine at 250$^{\circ}$Cin cal g $^{-1}$ is:
a.
11.4
b.
2.85
c.
22.8
d.
5.7
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In the following reaction; xA $\rightarrow$yB
log $_{10}$ β‘- $\frac{dA}{dt}$ = log $_{10}$ β‘- $\frac{dB}{dt}$ + 0.3010
βAβ and βBβ respectively can be:
a.
C $_{2}$ H $_{4}$ and C $_{4}$ H $_{8}$
b.
C $_{2}$ H $_{2}$ and C $_{6}$ H $_{6}$
c.
n-Butane and Iso-butane
d.
N $_{2}$ O $_{4}$ and NO $_{2}$
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Complete removal of both the axial ligands (along the z - axis) from an octahedral complex leads to which of
the following splitting patterns? (relative orbital energies not on scale).
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An element has a face-centered cubic fccstructure with a cell edge of a. The distance between the centres of
two nearest tetrahedral voids in the lattice is
a.
$\frac{a}{2}$
b.
$\frac{3}{2}$ a
c.
a
d.
$\sqrt$2a
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5moles of AB $_{2}$ weigh 125 $\times$ 10 $^{-3}$ kgand 10moles of A $_{2}$ B $_{2}$ weigh 300 $\times$ 10 $^{-3}$ kg. The molar mass of A
( M $_{A}$ ) in kg mol $^{-1}$ are:
a.
M $_{A}$ = 5 $\times$ 10 $^{-3}$ and M $_{B}$ = 10 $\times$ 10 $^{-3}$
b.
M $_{A}$ = 25 $\times$ 10 $^{-3}$ and M $_{B}$ = 50 $\times$ 10 $^{-3}$
c.
M $_{A}$ = 50 $\times$ 10 $^{-3}$ and M $_{B}$ = 25 $\times$ 10 $^{-3}$
d.
M $_{A}$ = 10 $\times$ 10 $^{-3}$ and M $_{B}$ = 5 $\times$ 10 $^{-3}$
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Given:
Co $^{3 +}$ + e $^{-}$ $\rightarrow$Co $^{2 +}$ ; E$^{\circ}$ = + 1.81V
Pb $^{3 +}$ + 2e $^{-}$ $\rightarrow$Pb $^{2 +}$ ; E$^{\circ}$ = + 1.67V
Ce $^{4 +}$ + e $^{-}$ $\rightarrow$Ce $^{3 +}$ ; E$^{\circ}$ = + 1.61V
Bi $^{3 +}$ + 3e $^{-}$ $\rightarrow$Bi; E$^{\circ}$ = + 0.20V
Oxidizing power of the species will increase in the order:
a.
Co $^{3}$ + < Ce $^{4 +}$ < Bi $^{3 +}$ < Pb $^{4 +}$
b.
Bi $^{3}$ + < Ce $^{4 +}$ < Pb $^{4 +}$ < Co $^{3 +}$
c.
Co $^{3}$ + < Pb $^{4 +}$ < Ce $^{3 +}$ < Bi $^{4 +}$
d.
Ce $^{4}$ + < Pb $^{4 +}$ < Bi $^{3 +}$ < Co $^{3 +}$
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A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate
25cm / sec, then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the
horizontal ground when the top of the ladder is 1m above the ground is:
a.
25
b.
25$\sqrt$3
c.
$\frac{25}{3}$
d.
$\frac{25}{$\sqrt{\,}$3}$
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If the truth value of the statement π$\rightarrow$~π$\vee$πis false πΉ, then the truth values of the statements π, π, πare
respectively
a.
π, πΉ, π
b.
π, πΉ, πΉ
c.
π, π, πΉ
d.
πΉ, π, π
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If the normal to the ellipse 3π₯ $^{2}$ + 4π¦ $^{2}$ = 12at a point πon it is parallel to the line, 2π₯+ π¦= 4and the tangent
to the ellipse at πpasses through π( 4,4 ) then ππis equal to:
a.
$\frac{$\sqrt{\,}$61}{2}$
b.
$\frac{5$\sqrt{\,}$5}{2}$
c.
$\frac{$\sqrt{\,}$157}{2}$
d.
$\frac{$\sqrt{\,}$221}{2}$
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If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle
formed with these chosen vertices is equilateral is:
a.
$\frac{1}{10}$
b.
$\frac{3}{10}$
c.
$\frac{1}{5}$
d.
$\frac{3}{20}$
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If the line $\frac{π₯- 2}{3}$ = $\frac{π¦+ 1}{2}$ = $\frac{π§- 1}{-1}$ intersects the plane 2π₯+ 3π¦- π§+ 13 = 0at a point πand the plane
3π₯+ π¦+ 4π§= 16at a point π, then ππis equal to
a.
2$\sqrt$7
b.
14
c.
2$\sqrt$14
d.
$\sqrt$14
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If the volume of parallelepiped formed by the vectors ^ ^π+ ^π, ^ ^and ^π+ ^is minimum, then is
π+ π π+ ππ π π π
equal to:
a.
- $\frac{1}{$\sqrt{\,}$3}$
b.
-$\sqrt$3
c.
$\sqrt$3
d.
$\frac{1}{$\sqrt{\,}$3}$
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If πis the minimum value of πfor which the function ππ₯= π₯$\sqrt$ππ₯- π₯ $^{2}$ is increasing in the interval [0, 3]
and πis the maximum value of πin [0, 3]when π= π, then the ordered pair ( π, π) is equal to:
a.
4, 3$\sqrt$3
b.
5, 3$\sqrt$6
c.
3, 3$\sqrt$3
d.
4, 3$\sqrt$2
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For π₯ π (0, $\frac{3}{2}$ ), let ππ₯= $\sqrt$π₯, ππ₯= tanπ₯and βπ₯= $\frac{1 - π₯2}{1 + π₯2}$ . If $\phi$π₯= ( hoπ) og ) ( π₯) , then $\phi$ $\frac{π}{3}$ is equal to:
a.
tanβ‘ $\frac{π}{12}$
b.
tanβ‘ $\frac{5π}{12}$
c.
tanβ‘ $\frac{7π}{12}$
d.
tanβ‘ $\frac{11π}{12}$
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Let a random variable πhas a binomial distribution with mean 8and variance 4. If ππ$\leq$2 = $\frac{π}{216}$ , then the
value of πis equal to
a.
121
b.
1
c.
17
d.
137
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For π₯$\in$π , Let [π₯]denotes the greatest integer $\leq$π₯, then the sum of the series
- $\frac{1}{3}$ + - $\frac{1}{3}$ - $\frac{1}{100}$ + - $\frac{1}{3}$ - $\frac{2}{100}$ + . . . . . + - $\frac{1}{3}$ - $\frac{99}{100}$ is
a.
-131
b.
-153
c.
-135
d.
-133
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If πΌ and π½are the roots of the equation 375 π₯ $^{2}$ - 25π₯- 2 = 0, then
$_{π$\rightarrow$$\infty$}$ lim $\sum$ $_{π= 1}^{π}$ πΌ $^{π}$ + $_{π$\rightarrow$$\infty$}$ lim $\sum$ $_{π= 1}^{π}$ π½ $^{π}$ is equal to:
a.
$\frac{1}{12}$
b.
$\frac{21}{346}$
c.
$\frac{7}{116}$
d.
$\frac{29}{358}$
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If the area (in sq. units) of the region π₯, π¦: π¦ $^{2}$ $\leq$4π₯, π₯+ π¦$\leq$1, π₯$\geq$0, π¦$\geq$0is π$\sqrt$2 + π, then π- πis
equal to
a.
6
b.
$\frac{10}{3}$
c.
- $\frac{2}{3}$
d.
$\frac{8}{3}$
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Let π: π $\rightarrow$π be a continuous and differentiable function such that π2 = 6and π $'$ 2 = $\frac{1}{48}$ . If
$\int$ $^{π( π₯)}_{6}$ 4π‘ $^{3}$ ππ‘= π₯- 2ππ₯, then $_{π₯$\rightarrow$2}$ lim ππ₯is equal to
a.
24
b.
18
c.
12
d.
36
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5 2πΌ 1
If π΅= 0 2 1 is the inverse of a 3 $\times$ 3matix π΄, then the sum of all values of πΌfor which πππ‘π΄+ 1 = 0,
πΌ 3 -1
is:
a.
2
b.
1
c.
0
d.
-1
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If the data π₯ $_{1}$ , π₯ $_{2}$ , β¦ π₯ $_{10}$ is such that the mean of first four of these is 11, the mean of the remaining six is 16
and the sum of squares of all of these is 2000, then the standard deviation of this data is:
a.
2$\sqrt$2
b.
4
c.
2
d.
$\sqrt$2
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Let πbe the point of intersection of the common tangents to the parabola π¦ $^{2}$ = 12π₯and the hyperbola
8π₯ $^{2}$ - π¦ $^{2}$ = 8. If πand π $'$ denote the foci of the hyperbola where πlies on the positive π₯-axis then πdivides ππ $'$
in a ratio:
a.
5: 4
b.
2: 1
c.
13: 11
d.
14: 13
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Consider the differential equation, π¦ $^{2}$ ππ₯+ π₯- $\frac{1}{π¦}$ ππ¦= 0. If value of π¦is 1when π₯= 1, then the value of π₯for
which π¦= 2, is
a.
$\frac{3}{2}$ - $\frac{1}{$\sqrt{\,}$π}$
b.
$\frac{3}{2}$ - π
$\sqrt$
c.
$\frac{1}{2}$ + $\frac{1}{$\sqrt{\,}$π}$
d.
$\frac{5}{2}$ + $\frac{1}{$\sqrt{\,}$π}$
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$\rightarrow$ ^ ^ ^ $\rightarrow$ ^ ^ ^
Let π= 3π+ 2π+ 2πand π= π+ 2π- 2πbe two vectors. If a vector perpendicular to both the vectors
$\rightarrow$π+ $\rightarrow$ $\rightarrow$π- $\rightarrow$
π and π has the magnitude 12then one such vector is:
a.
^ ^π+ ^
4(2π+ 2 π)
b.
^ ^π- ^
4(2π- 2 π)
c.
^ ^π+ ^
4( - 2π- 2 π)
d.
^ ^π- ^
4(2π+ 2 π)
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If the angle of intersection at a point where the two circles with radii 5 cmand 12 cmintersect is 90$^{\circ}$, then the
length (in cm) of their common chord is:
a.
$\frac{120}{13}$
b.
$\frac{60}{13}$
c.
$\frac{13}{5}$
d.
$\frac{13}{2}$
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