Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric
field. If, for an N-type semiconductor, the density of electrons is 10 $^{19}$ m $^{-3}$ and their mobility is
1.6 m $^{2}$ V $^{-1}$ s $^{-1}$ , then the resistivity of the semiconductor (since it is an N-type semiconductor contribution of
holes is ignored) is close to:
a.
0.2 $\Omega$ m
b.
4 $\Omega$ m
c.
2 $\Omega$ m
d.
0.4 $\Omega$ m
Correct Answer
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Q2mcq
An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as
shown. The radius of the loop is πand distance of its centre from the wire is π π$\gg$π. If the loop applies a
force πΉon the wire then:
2
Temperature difference of 120 $^{π}$ πΆis maintained between two ends of a uniform rod π΄π΅of length 2πΏ. Another
bent rod ππ, of same cross-section as π΄π΅and length $\frac{3πΏ}{2}$ , is connected across π΄π΅(See figure). In steady state,
temperature difference between πand πwill be close to:
a.
45 $^{π}$ πΆ
Correct Answer
b.
35 $^{π}$ πΆ
c.
60 $^{π}$ πΆ
d.
75 $^{π}$ πΆ
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Q4mcq
For a uniformly charged ring of radius π , the electric field on its axis has the largest magnitude at a distance β
from its centre. Then value of βis:
a.
$\frac{π }{$\sqrt{\,}$2}$
Correct Answer
b.
$\frac{π }{$\sqrt{\,}$5}$
c.
π $\sqrt$2
d.
π
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Q5mcq
A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 π, 100turns, and carrying a
current of 5.2 π΄. The coercivity of the bar magnet is:
a.
285 π΄/ π
b.
2600 π΄/ π
Correct Answer
c.
520 π΄/ π
d.
1200 π΄/ π
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Q6mcq
An πΏ-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure.
If π΄π΅= π΅πΆ, and the angle made by π΄π΅with downward vertical is π, then:
a.
tanβ‘π= $\frac{2}{$\sqrt{\,}$3}$
b.
tanβ‘π= $\frac{1}{3}$
Correct Answer
c.
tanβ‘π= $\frac{1}{2}$
d.
tanβ‘π= $\frac{1}{2$\sqrt{\,}$3}$
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Q7mcq
A block of mass 10 ππis kept on a rough inclined plane as shown in the figure. A force of 3 πis applied on the
block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum
value of force π, such that the block does not move downward? (take π= 10 ππ $^{-2}$ )
a.
23 π
b.
25 π
c.
18 π
d.
32 π
Correct Answer
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Q8mcq
A heavy ball of mass πis suspended from the ceiling of a car by a light string of mass π π$\ll$π. When the
car is at rest, the speed of transverse waves in the string is 60 ms $^{-1}$ . When the car has acceleration π, the wave-
speed increases to 60.5 ms $^{-1}$ . The value of π, in terms of gravitational acceleration π, is closed to
a.
$\frac{π}{10}$
b.
$\frac{π}{20}$
c.
$\frac{π}{5}$
Correct Answer
d.
$\frac{π}{30}$
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Q9mcq
When the switch π, in the circuit shown, is closed, then the value of current πwill be:
a.
2 A
b.
5 A
Correct Answer
c.
3 A
d.
4 A
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Q10mcq
The surface of certain metal is first illuminated with light of wavelength π $_{1}$ = 350 nmand then, by a light of
wavelength π $_{2}$ = 540 nm . It is found that the maximum speed of the photoelectrons in the two cases differ by
a factor of 2. The work function of the metal (in eV) is close to
(Energy of photon = $\frac{1240}{πin nm}$ eV)
a.
2.5
b.
1.8
Correct Answer
c.
5.6
d.
1.4
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Drift speed of electrons, when 1.5 Acurrent flows in a copper wire of cross section 5 mm $^{2}$ is π£ $_{π}$ . If the
electron density in copper is 9 $\times$ 10 $^{28}$ m $^{-3}$ the value of π£ $_{π}$ in mm π $^{-1}$ is close to (Take charge of an electron
to be = 1.6 $\times$ 10 $^{-19}$ C)
a.
0.2
b.
3
c.
2
d.
0.02
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A block of mass π, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring
constant π. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its
equilibrium position. If now the block is pulled with a constant force πΉ, the maximum speed of the block is:
a.
$\frac{πΉ}{$\sqrt{\,}$ππ}$
b.
$\frac{2πΉ}{$\sqrt{\,}$ππ}$
c.
$\frac{ππΉ}{$\sqrt{\,}$ππ}$
d.
$\frac{πΉ}{π$\sqrt{\,}$ππ}$
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A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of
10 π΄. The magnetic field at point πwill be close to:
a.
1.5 $\times$ 10 $^{-7}$ π
b.
1.0 $\times$ 10 $^{-7}$ π
c.
1.5 $\times$ 10 $^{-5}$ π
d.
1.0 $\times$ 10 $^{-5}$ π
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Two masses πand $\frac{π}{2}$ are connected at the two ends of a massless rigid rod of length π. The rod is suspended by
a thin wire of torsional constant πat the centre of mass of the rod-mass system (see figure). Because of torsional
constant π, the restoring torque is π= ππfor angular displacement π. If the rod is rotated by π $_{0}$ and released,
the tension in it when it passes through its mean position will be:
a.
ππ $^{2}_{0}$
b.
$\frac{3ππ02}{π}$
c.
$\frac{2ππ02}{π}$
d.
$\frac{ππ02}{π}$
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A parallel plate capacitor is made of two square plates of side π, separated by a distance π π$\ll$π. The lower
triangular portion filled with a dielectric of dielectric constant πΎ, as shown in the figure. Capacitance of this
capacitor is:
A convex lens is put 10 ππfrom a light source and it makes a sharp image on a screen, kept 10 ππfrom the
lens. Now a glass block (refractive index 1.5) of 1.5 ππthickness is placed in between the light source and the
lens. To get the sharp image again, the screen is shifted by a distance π. Then πis:
a.
0
b.
0.55 ππaway from the lens
c.
0.55 ππtowards the lens
d.
1.1 ππaway from the lens
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A Sample of radioactive material π΄, that has an activity of 10 π Ci 1 πΆπ= 3.7 $\times$ 10 $^{10}$ decays s $^{-1}$ , has
twice the number of nuclei as another sample of a different radioactive material π΅which has an activity of
20 π Ci. The correct choices for half-lives of π΄and π΅would then be, respectively:
a.
5days and 10days
b.
10days and 40days
c.
20days and 10days
d.
20days and 5days
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Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the
maximum intensity to the minimum intensity is 16 . The intensity of the waves are in the ratio:
a.
25: 9
b.
16: 9
c.
5: 3
d.
4: 1
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Three charges +π, π, + πare placed respectively, at distance, 0, π/ 2and πfrom the origin, on the π₯-axis. If
the net force experienced by +π, placed at π₯= 0, is zero, then value of πis:
a.
+π/ 2
b.
+π/ 4
c.
-π/ 4
d.
-π/ 2
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Three blocks A, Band Care lying on a smooth horizontal surface, as shown in the figure. Aand Bhave equal
masses, πwhile Chas mass π. Block Ais given an initial speed π£towards Bdue to which it collides with B
perfectly inelastically. The combined mass collides with πΆ, also perfectly inelastically . $\frac{5}{6}$ thof the initial kinetic
energy is lost in the whole process. What is the value of π/ π?
a.
3
b.
4
c.
5
d.
2
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A conducting circular loop made of a thin wire has area 3.5 $\times$ 10 $^{-2}$ m $^{2}$ and resistance 10 $\Omega$It is placed
perpendicular to a time-dependent magnetic field π΅π‘= 0.4 Tsin50ππ‘The field is uniform in space. Then the
net charge flowing through the loop during π‘= 0 sand π‘= 10 msis close to
a.
1.4 ππΆ
b.
7 ππΆ
c.
21 ππΆ
d.
6 ππΆ
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A gas can be taken from Ato Bvia two different processes ACBand ADB.
When path ACBis used 60 Jof heat flows into the system and 30 Jof work is done by the system. If the path
ADBis used then work done by the system is 10 J, the heat flows into the system in the path ADBis:
a.
100 J
b.
20 J
c.
40 J
d.
80 π½
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A rod, of length πΏat room temperature and uniform area of cross section π΄, is made of a metal having
coefficient of linear expansion πΌ / $^{\circ}$πΆIt is observed that an external compressive force πΉis applied on each
of its ends, prevents any change in the length of the rod when its temperature rises by βπ KYoung's modulus,
πfor this metal is:
a.
$\frac{πΉ}{π΄πΌβπ- 273}$
b.
$\frac{2πΉ}{π΄πΌβπ}$
c.
$\frac{πΉ}{π΄πΌβπ}$
d.
$\frac{πΉ}{2π΄ πΌβπ}$
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A plane electromagnetic wave of frequency 50 ππ»π§travels in free space along the positive π₯- direction. At a
$\rightarrow$ ^ $\rightarrow$
particular point in space and time, πΈ= 6.3 π π/ π, The corresponding magnetic field π΅, at that point will be:
a.
-8^
2.1 $\times$ 10 π π
b.
8^
18.9 $\times$ 10 π π
c.
-8^
18.9 $\times$ 10 π π
d.
-8^
6.3 $\times$ 10 π π
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If the angular momentum of a planet of mass π, moving around the Sun in a circular orbit is πΏ, about the center
of the Sun, its areal velocity is:
a.
$\frac{πΏ}{π}$
b.
$\frac{4πΏ}{π}$
c.
$\frac{πΏ}{2π}$
d.
$\frac{2πΏ}{π}$
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A mixture of 2 moles of helium gas (atomic mass = 4u) , and 1 mole of argon gas (atomic mass = 40 u) is kept
at 300 πΎin a container. The ratio of their rms speeds $\frac{ππππ βππππ’π}{ππππ ( πππππ)}$ , is close to:
a.
0.45
b.
2.24
c.
0.32
d.
3.16
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Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive
index π. A student finds that, irrespective of what the incident angle π(see figure) is for a beam of light
entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to
happen, the minimum value of πis:
a.
$\frac{3}{$\sqrt{\,}$5}$
b.
$\frac{4}{3}$
c.
$\frac{5}{$\sqrt{\,}$3}$
d.
$\sqrt$ $\frac{5}{3}$
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Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures
T $_{1}$ and T $_{2}$ T $_{1}$ < T $_{2}$ . The correct graphical depiction of the dependence of work done wvs the final volume V
is:
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20βmlof 0.1βMβH $_{2}$ SO $_{4}$ solution is added to 30βmLof 0 .2 βMβNH $_{4}$ OHsolution. The pHof the resultant mixture
is: pk $_{b}$ of NH $_{4}$ OH = 4 .7
a.
5.0
b.
5.2
c.
9.4
d.
9.0
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0.5moles of gas Aand xmoles of gas Bexert a pressure of 200 Pain a container of volume 10 m $^{3}$ at 1000 K.
Given, Ris the gas constant in JK $^{-1}$ mol $^{-1}$ , xis:
a.
$\frac{4 + R}{2R}$
b.
$\frac{2R}{4 + R}$
c.
$\frac{4 - R}{2R}$
d.
$\frac{2R}{4 - R}$
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Two complexes CrH $_{2}$ O $_{6}$ Cl $_{3}$ Aand CrNH $_{36}$ Cl $_{3}$ Bare violet and yellow coloured, respectively, The incorrect
statement regarding them is:
a.
Both are paramagnetic with three unpaired
electrons
b.
$\Delta$ $_{0}$ value of π΄is less than that of π΅
c.
$\Delta$ $_{0}$ values of π΄and π΅are calculated from the
energies violet and yellow light, respectively.
d.
Both absorb energies corresponding to their
complementary colors.
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For emission line of atomic hydrogen from n $_{i}$ = 8to n $_{f}$ = n, the plot of wave number v $^{-}$ against $\frac{1}{n2}$ will be:
(The Rydberg constant, R $_{H}$ is in wave number unit)
a.
Linear with slope -R $_{H}$
b.
Non linear
c.
Linear with slope R $_{H}$
d.
Linear with intercept -R $_{H}$
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A water sample has ppm level concentration of the following metals:
Fe = 0 .2 ; Mn = 5 .0 ; Cu = 3 .0 ; Zn = 5 .0 .
The metal that makes the water sample unsuitable for drinking is
a.
Zn
b.
Fe
c.
Mn
d.
Cu
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A solution of sodium sulphate contains 92 πof Na $^{+}$ ions per kilogram of water. The molality of Na $^{+}$ ions in
that solution in mol kg $^{-1}$ is:
a.
16
b.
4
c.
12
d.
8
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The anodic half-cell of lead-acid battery is recharged using electricity of 0 .05 Faraday. The amount of PbSO $_{4}$
electrolyzed in gduring the process is: (Molar mass of PbSO $_{4}$ = 303g mol $^{-1}$ )
a.
22.8
b.
15.2
c.
11.4
d.
7.6
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The correct match between column-Iand column-IIis
Column-I(drug) Column-II(test)
(A) Chloroxylenol (P) Carbylamine test
(B) Norethindrone (Q) Sodium hydrogen carbonate test
(C) Sulphapyridine (R) Ferric chloride test
(D) Penicillin (S) Baeyerβs test
The following results were obtained during kinetic studies of the reaction.
2A + B $\rightarrow$ product
Experiment A in mol L $^{-1}$ B in mol L $^{-1}$ Initial rate of reaction in mol L $^{-1}$ min $^{-1}$
I 0 . 10 0 . 20 6.93 $\times$ 10 $^{-3}$
II 0 . 10 0 . 25 6.93 $\times$ 10 $^{-3}$
III 0 . 20 0 . 30 1.386 $\times$ 10 $^{-2}$
The time (in minutes) required to consume half of Ais
a.
100
b.
10
c.
5
d.
1
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Correct statements among regarding silicones are:
( π) They are polymers with hydrophobic character.
( π) They are biocompatible.
( π) In general, they have high thermal stability and low dielectric strength.
( π) Usually, they are resistant to oxidation and used as greases.
a.
( π) , ( π) and ( π) only
b.
( π) and ( π) only
c.
( π) , ( π) , ( π) and ( π)
d.
( π) , ( π) and ( π) only
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Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, π₯is the mass of the gas
adsorbed on mass mof the adsorbent at pressure P . $\frac{x}{m}$ is proportional to:
a.
π $\frac{1}{4}$ π
c.
π $^{2}$
d.
π $\frac{1}{2}$
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For, π₯ $^{2}$ $\neq$ππ+ 1, π$\in$π(the set of natural numbers), the integral $\int$π₯$\sqrt$ $\frac{2sinπ₯2- 1 - sin2π₯2- 1}{2sinπ₯2- 1 + sin2π₯2- 1}$ ππ₯, is equal to
(where πis a constant of integration).
Let π΄= π$\in$- $\frac{π}{2}$ , π: $\frac{3 + 2πβ sinπ}{1 - 2π sinπ}$ is purely imaginary . Then the sum of the elements in π΄is:
a.
$\frac{5π}{6}$
b.
$\pi$
c.
$\frac{2π}{3}$
d.
$\frac{3π}{4}$
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Axis of a parabola lies along π₯-axis. If its vertex and focus are at distances 2and 4respectively from the
origin, on the positive π₯-axis then which of following points does not lie on it?
a.
6, 4$\sqrt$2
b.
5, 2$\sqrt$6
c.
8, 6
d.
4, - 4
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If π¦= π¦( π₯) is the solution of the differential equation, π₯ $\frac{ππ¦}{ππ₯}$ + 2π¦= π₯ $^{2}$ satisfying π¦1 = 1, then π¦ $\frac{1}{2}$ is equal to
a.
$\frac{7}{64}$
b.
$\frac{1}{4}$
c.
$\frac{13}{16}$
d.
$\frac{49}{16}$
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The plane through the intersection of the planes π₯+ π¦+ π§= 1and 2π₯+ 3π¦- π§+ 4 = 0and parallel to π¦-
axis also passes through the point
a.
3, 3, - 1
b.
-3, 1, 1
c.
3, 2, 1
d.
-3, 0, - 1
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Let π: π $\rightarrow$π be a function defined as
5, ππ π₯$\leq$1
π+ ππ₯, ππ 1 < π₯< 3
ππ₯=
π+ 5π₯, ππ 3 $\leq$π₯< 5
30, ππ π₯$\geq$5
Then πis:
a.
continuous if π= - 5and π= 10
b.
continuous if π= 0and π= 5
c.
not continuous for any values of πand π
d.
continuous if π= 5and π= 5
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Consider a class of 5girls and 7boys. The number of different teams consisting of 2girls and 3boys that can
be formed from this class, if there are two specific boys π΄and π΅, who refuse to be the members of the same
team, is:
a.
300
b.
200
c.
500
d.
350
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If the Boolean expression π$\oplus$π$\wedge$~πβπis equivalent to π$\wedge$π, where $\oplus$, β$\in$$\wedge$, $\vee$, then the ordered
pair $\oplus$, β is
a.
$\vee$, $\wedge$
b.
$\wedge$, $\wedge$
c.
$\vee$, $\vee$
d.
$\wedge$, $\vee$
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Two cards are drawn successively with replacement from a well-shuffled deck of 52cards. Let πdenote the
random variable of number of aces obtained in the two drawn cards. Then ππ= 1 + ππ= 2equals:
a.
$\frac{24}{169}$
b.
$\frac{52}{169}$
c.
$\frac{49}{169}$
d.
$\frac{25}{169}$
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The equation of the line passing through -4, 3, 1, parallel to the plane π₯+ 2π¦- π§- 5 = 0and intersecting the
line $\frac{π₯ + 1}{-3}$ = $\frac{π¦- 3}{2}$ = $\frac{π§- 2}{-1}$ is
Let 0 < π< $\frac{π}{2}$ . If the eccentricity of the hyperbola $\frac{π₯2}{cos2β‘π}$ - $\frac{π¦2}{sin2β‘π}$ = 1is greater than 2, then the length of its
latus rectum lies in the interval:
a.
3, $\infty$
b.
1, $\frac{3}{2}$
c.
2, 3
d.
$\frac{3}{2}$ , 2
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5students of a class have an average height 150 ππand variance 18 ππ $^{2}$ . A new student, whose height is
156 ππ, joined them. The variance in ππ $^{2}$ of the height of these six students is:
a.
22
b.
16
c.
18
d.
20
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$\rightarrow$ $\rightarrow$ $\rightarrow$ $\rightarrow$ $\rightarrow$π+ $\rightarrow$π= $\rightarrow$ $\rightarrow$ $\rightarrow$ $\rightarrow$ $^{2}$
Let π= ^π- ^π, π= ^π+ ^π+ ^πand π be a vector such that π$\times$ 0and π. π= 4, then | π| is
equal to:
a.
$\frac{19}{2}$
b.
9
c.
$\frac{17}{2}$
d.
8
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If πdenotes the acute angle between the curves, π¦= 10 - π₯ $^{2}$ and π¦= 2 + π₯ $^{2}$ at a point of their intersection,
then tanβ‘πis equal to:
a.
$\frac{4}{9}$
b.
$\frac{8}{17}$
c.
$\frac{7}{17}$
d.
$\frac{8}{15}$
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