The following observations were taken for determining surface tension 𝑇of water by capillary method:
diameter of capillary, 𝐷= 1.25 $\times$ 10 $^{-2}$ m
rise of water, ℎ= 1.45 $\times$ 10 $^{-2}$ m
Using 𝑔= 9.80 m s $^{-2}$ and the simplified relation 𝑇= $\frac{𝑟ℎ𝑔}{2}$ $\times$ 10 $^{3}$ N m $^{-1}$ the possible error in surface tension
is closest to:
a.
10%
b.
0 . 15%
c.
1 . 5%
Correct Answer
d.
2 . 4%
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Q2mcq
A slender uniform rod of mass 𝑀and length 𝑙is pivoted at one end so that it can rotate in a vertical plane (see
figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released.
The angular acceleration of the rod when it makes an angle 𝜃with the vertical is:
a.
$\frac{2𝑔}{3𝑙}$ cos𝜃
b.
$\frac{3𝑔}{2𝑙}$ sin𝜃
Correct Answer
c.
$\frac{2𝑔}{3𝑙}$ sin𝜃 $\frac{3𝑔}{2𝑙}$ cos𝜃
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Q3mcq
$\rightarrow$
An electric dipole has fixed dipole moment 𝑝 , which makes angle 𝜃with respect to 𝑥-axis. When subjected
$\rightarrow$ ^ $\rightarrow$ ^
to an electric field 𝐸 $_{1}$ = 𝐸𝑖, it experiences a torque 𝑇 $_{1}$ = 𝜏𝑘. When subjected to another electric field
$\rightarrow$𝐸 ^𝑗it experiences a torque $\rightarrow$𝑇 = - $\rightarrow$𝑇 . The angle 𝜃is:
$_{2}$ = $\sqrt$3 𝐸 $_{1}_{2}_{1}$
a.
90 $^{𝑜}$
b.
30 $^{𝑜}$
c.
45 $^{𝑜}$
d.
60 $^{𝑜}$
Correct Answer
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Q4mcq
The temperature of an open room of volume 30 m $^{3}$ increases from 17$^{\circ}$Cto 27$^{\circ}$Cdue to the sunshine. The
atmospheric pressure in the room remains 1 $\times$ 10 $^{5}$ Pa. If 𝑛 $_{𝑖}$ and 𝑛 $_{𝑓}$ are the number of molecules in the room
before and after heating, then 𝑛 $_{𝑓}$ - 𝑛 $_{𝑖}$ will be:
a.
-2.5 $\times$ 10 $^{25}$
Correct Answer
b.
-1.61 $\times$ 10 $^{23}$
c.
1.38 $\times$ 10 $^{23}$
d.
2.5 $\times$ 10 $^{25}$
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Q5mcq
When a current of 5 mAis passed through a galvanometer having a coil of resistance 15 $\Omega$, it shows full-
scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a
voltmeter of range 0 - 10 Vis:
a.
4.005 $\times$ 10 $^{3}$ $\Omega$
b.
1.985 $\times$ 10 $^{3}$ $\Omega$
Correct Answer
c.
2.045 $\times$ 10 $^{3}$ $\Omega$
d.
2.535 $\times$ 10 $^{3}$ $\Omega$
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Q6mcq
A diverging lens with magnitude of focal length 25 cmis placed at a distance of 15 cmfrom a converging
lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image
formed is:
a.
Real and at a distance of 6 cmfrom the
convergent lens
b.
Real and at a distance of 40 cmfrom
convergent lens
Correct Answer
c.
Virtual and at a distance of 40 cmfrom
convergent lens
d.
Real and at a distance of 40 cmfrom the
divergent lens
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Q7mcq
Which of the following statements is false?
a.
Kirchhoff's second law represents energy
conservation
b.
Wheatstone bridge is the most sensitive when all
the four resistances are of the same order of
magnitude
c.
In a balanced Wheatstone bridge if the cell and
the galvanometer are exchanged, the null point is
disturbed
Correct Answer
d.
A rheostat can be used as a potential divider
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Q8mcq
In amplitude modulation, the sinusoidal carrier frequency used is denoted by 𝜔 $_{𝑐}$ and the signal frequency is
denoted by 𝜔 $_{𝑚}$ . The bandwidth $\Delta$𝜔 $_{𝑚}$ of the signal is such that $\Delta$𝜔 $_{𝑚}$ $\ll$𝜔 $_{𝑐}$ . Which of the following frequencies
is not contained in the modulated wave?
a.
𝜔 $_{𝑐}$ - 𝜔 $_{𝑚}$
b.
𝜔 $_{𝑚}$
Correct Answer
c.
𝜔 $_{𝑐}$
d.
𝜔 $_{𝑚}$ + 𝜔 $_{𝑐}$
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Q9mcq
In a common emitter amplifier circuit using an 𝑛- 𝑝- 𝑛transistor, the phase difference between the input and
the output voltages will be:
a.
180$^{\circ}$
Correct Answer
b.
45$^{\circ}$
c.
90$^{\circ}$
d.
135$^{\circ}$
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Q10mcq
A particle is executing simple harmonic motion with a time period 𝑇. At time 𝑡= 0, it is at its position of
equilibrium. The kinetic energy - time graph of the particle will look like:
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A radioactive nucleus 𝐴with a half-life 𝑇, decays into a nucleus 𝐵. At 𝑡= 0, there is no nucleus 𝐵. At some
time 𝑡, the ratio of the number of 𝐵to that of 𝐴is 0.3. Then, 𝑡is given by: Consider log $_{𝑒}$ 𝑥= log𝑥
a.
𝑡= $\frac{𝑇}{log1.3}$
b.
𝑡= $\frac{𝑇}{2} \frac{log 2}{log 1.3}$
c.
𝑡= 𝑇 $\frac{log 1.3}{log 2}$
d.
𝑡= 𝑇log1.3
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In a coil of resistance 100 $\Omega$, a current is induced by changing the magnetic flux through it as shown in the
figure. The magnitude of change in flux through the coil is:
a.
275 Wb
b.
200 Wb
c.
225 Wb
d.
250 Wb
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A body of mass 𝑚= 10 $^{-2}$ kgis moving in a medium and experiences a frictional force 𝐹= -𝑘𝑣 $^{2}$ . Its initial
speed is 𝑣 $_{0}$ = 10 m s $^{-1}$ .After 10 sits kinetic energy is $\frac{1}{8}$ 𝑚𝑣 $^{2}_{0}$ , then value of 𝑘will be:-
a.
10 $^{-1}$ kg m $^{-1}$ s $^{-1}$
b.
10 $^{-3}$ kg m $^{-1}$
c.
10 $^{-3}$ kg 𝑠 $^{-1}$
d.
10 $^{-4}$ kg m $^{-1}$
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A particle 𝐴of mass 𝑚and initial velocity 𝑣collides with a particle 𝐵of mass $\frac{𝑚}{2}$ which is at rest. The collision
is head on, and elastic. The ratio of the de-Broglie wavelengths 𝜆 $_{𝐴}$ to 𝜆 $_{𝐵}$ after the collision is:
a.
$\frac{𝜆𝐴}{𝜆𝐵}$ = $\frac{1}{2}$
b.
$\frac{𝜆𝐴}{𝜆𝐵}$ = $\frac{1}{3}$
c.
$\frac{𝜆𝐴}{𝜆𝐵}$ = 2
d.
$\frac{𝜆𝐴}{𝜆𝐵}$ = $\frac{2}{3}$
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A copper ball of mass 100 gis at a temperature 𝑇. It is dropped in a copper calorimeter of mass 100 g,filled
with 170 gof water at room temperature. Subsequently, the temperature of the system is found to be 75$^{\circ}$C. 𝑇is
given by:
(Given: room temperature = 30$^{\circ}$C, specific heat of copper = 0.1 cal g $^{-1}$ $^{\circ}$C $^{-1}$ )
a.
825$^{\circ}$C
b.
800$^{\circ}$C
c.
885$^{\circ}$C
d.
1250$^{\circ}$C
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In a Young's double slit experiment, slits are separated by 0 . 5 mm, and the screen is placed 150 cmaway.
A beam of light consisting of two wavelengths, 650 nmand 520 nm, is used to obtain interference fringes
on the screen. The least distance from the common central maximum to the point where the bright fringes due
to both the wavelengths coincide is:
a.
15 . 6 mm
b.
1 . 56 mm
c.
7 . 8 mm
d.
9 . 75 mm
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A time dependent force 𝐹= 6𝑡acts on a particle of mass 1 kg. If the particle starts from the rest, the work
done by the force during the first 1 secwill be:
a.
18 J
b.
4.5 J
c.
22 J
d.
9 J
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𝐶 $_{𝑝}$ - 𝐶 $_{𝑣}$ = $\frac{𝑅}{𝑀}$ and 𝐶 $_{𝑣}$ are specific heats at constant pressure and constant volume respectively. It is observed that,
𝐶 $_{𝑝}$ - 𝐶 $_{𝑣}$ = 𝑎for hydrogen gas and 𝐶 $_{𝑝}$ - 𝐶 $_{𝑣}$ = 𝑏for nitrogen gas. The correct relation between 𝑎and 𝑏is:
a.
𝑎= 28 𝑏
b.
𝑎= $\frac{1}{14}$ 𝑏
c.
𝑎= 𝑏
d.
𝑎= 14𝑏
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The moment of inertia of a uniform cylinder of length 𝑙and radius 𝑅about its perpendicular bisector is 𝐼. What
is the ratio 𝑙/ 𝑅such that the moment of inertia is minimum?
a.
$\frac{3}{$\sqrt{\,}$2}$
b.
$\sqrt$ $\frac{3}{2}$
c.
$\frac{$\sqrt{\,}$3}{2}$
d.
1
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An electron beam is accelerated by a potential difference 𝑉to hit a metallic target to produce 𝑋-rays. It
produces continuous as well as characteristic 𝑋-rays. If 𝜆 $_{𝑚𝑖𝑛}$ is the smallest possible wavelength of 𝑋-ray in
the spectrum, the variation of log𝜆 $_{𝑚𝑖𝑛}$ with log𝑉is correctly represented in :
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An external pressure 𝑃is applied on a cube at 0$^{\circ}$Cso that it is equally compressed from all sides. 𝐾is the bulk
modulus of the material of the cube and 𝛼is its coefficient of linear expansion. Suppose we want to bring the
cube to its original size by heating. The temperature should be raised by:
a.
3𝑃𝐾𝛼
b.
$\frac{𝑃}{3𝛼𝐾}$
c.
$\frac{𝑃}{𝛼𝐾}$
d.
$\frac{3𝛼}{𝑃𝐾}$
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A magnetic needle of magnetic moment 6 .7 $\times$ 10 $^{-2}$ A m $^{2}$ and moment of inertia 7 .5 $\times$ 10 $^{-6}$ kg m $^{2}$ is
performing simple harmonic oscillations in a magnetic field of 0 . 01 T. Time taken for 10complete
oscillations is:
a.
8 . 76 s
b.
6 . 65 s
c.
8 . 89 s
d.
6 . 98 s
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A capacitance of 2 $\mu$Fis required in an electrical circuit across a potential difference of 1.0 kV. A large
number of 1 𝜇Fcapacitors are available which can withstand a potential difference of not more than 300 V.
The minimum number of capacitors required to achieve this is:
a.
32
b.
2
c.
16
d.
24
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An observer is moving with half the speed of light towards a stationary microwave source emitting waves at
frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light
= 3 $\times$ 10 $^{8}$ m s $^{-1}$ )
a.
15 . 3 GHz
b.
10 . 1 GHz
c.
12 . 1 GHz
d.
17 . 3 GHz
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A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density
remains same, the stress in the leg will change by a factor of:
a.
$\frac{1}{81}$
b.
9
c.
$\frac{1}{9}$
d.
81
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A metal crystallizes in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest
approach between two atoms in the metallic crystal will be
a.
2$\sqrt$2a
b.
$\sqrt$2a
c.
$\frac{a}{$\sqrt{\,}$2}$
d.
2a
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The sodium salt of an organic acid Xproduces effervescence with concentrated H $_{2}$ SO $_{4}$ . Xreacts with the
acidified aqueous CaCl $_{2}$ solution to give a white precipitate which decolourises acidic solution of KMnO $_{4}$ . Xis
a.
HCOONa
b.
CH $_{3}$ COONa
c.
Na $_{2}$ C $_{2}$ O $_{4}$
d.
C $_{6}$ H $_{5}$ COONa
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Given
E $^{o}_{Cl2/ Cl}$ - = 1 .36 V, E $^{o}_{Cr3 +}_{/ Cr}$ = - 0 .74 V
E $^{o}_{Cr2O2 -}_{/ Cr3 +}$ = 1 .33 V, E $^{o}_{MnO-4}_{/ Mn2 +}$ = 1 .51 V .
7
Among the following, the strongest reducing agent is:
a.
Mn $^{2 +}$
b.
Cr $^{3 +}$
c.
Cl $^{-}$
d.
Cr
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In the following reactions, ZnOis respectively acting as a/an,
(i) ZnO + Na $_{2}$ O $\rightarrow$Na $_{2}$ ZnO $_{2}$
(ii) ZnO + CO $_{2}$ $\rightarrow$ZnCO $_{3}$
a.
base and base.
b.
acid and acid.
c.
acid and base.
d.
base and acid.
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The freezing point of benzene decreases by 0.45 $^{$^{\circ}$}$ Con adding 0 . 2 gof acetic acid to 20 gof benzene. If
acetic acid associates to form a dimer in benzene, then what is the percentage association of acetic acid in
benzene?
K $_{f}$ for benzene = 5 .12 K kg mol $^{-1}$
a.
80 . 4%
b.
74 . 6%
c.
94 . 6%
d.
64 . 6%
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The most abundant elements by mass in the body of a healthy human adult are:
Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75kg person
would gain if all $^{1}$ 𝐻atoms are replaced by $^{2}$ 𝐻atoms is:
a.
37.5 kg
b.
7.5 kg
c.
10 kg
d.
15 kg
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A water sample has ppm level concentration of following anions
F $^{-}$ = 10; SO $^{2 -}_{4}$ = 100; NO $^{-}_{3}$ = 50
The anion/anions that make/makes the water sample unsuitable for drinking is/are
a.
Both SO $^{2 -}_{4}$ and NO $^{-}_{3}$
b.
Only F $^{-}$
c.
Only SO $^{2 -}_{4}$
d.
Only NO $^{-}_{3}$
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The radius of the second Bohr orbit for hydrogen atom is
(Planck's constant, ( h ) = 6 .6262 $\times$ 10 $^{-34}$ Js;mass of electron = 9 .1091 $\times$ 10 $^{-31}$ kg; charge of electron
= 1 .60210 $\times$ 10 $^{-19}$ C;permittivity of vacuum, ( $\in$ $_{0}$ ) = 8 .854185 $\times$ 10 $^{-12}$ kg $^{-1}$ m $^{-3}$ A $^{2}$ )
a.
4 .76 Å
b.
0 .529 Å
c.
2 .12 Å
d.
1 .65 Å
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1gram of a carbonate M $_{2}$ CO $_{3}$ on treatment with excess HClproduces 0.01186moles of CO $_{2}$ . The molar mass
of M $_{2}$ CO $_{3}$ in gmol $^{-1}$ is:
a.
84.3
b.
118.6
c.
11.86
d.
1186
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The Tyndall effect is observed only when the following conditions are satisfied,
iThe diameter of the dispersed particles is much smaller than the wavelength of the light used.
iiThe diameter of the dispersed particle is not much smaller than the wavelength of the light used.
iiiThe refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude.
ivThe refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.
a.
ii and iv
b.
i and iii
c.
ii and iii i and iv
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Given:
Cgraphite + O $_{2}$ g $\rightarrow$CO $_{2}$ g ; $\Delta$ $_{r}$ H $^{o}$ = -393 .5 kJ mol $^{-1}$
H $_{2}$ g + $\frac{1}{2}$ O $_{2}$ g $\rightarrow$H $_{2}$ Ol; $\Delta$ $_{r}$ H $^{o}$ = - 285 .8 kJ mol $^{-1}$
CO $_{2}$ g + 2H $_{2}$ Ol $\rightarrow$CH $_{4}$ g + 2O $_{2}$ g; $\Delta$ $_{r}$ H $^{o}$ = + 890 .3 kJ mol $^{-1}$
Based on the above thermochemical equations, the value of $\Delta$ $_{r}$ H $^{o}$ at 298 Kfor the reaction
Cgraphite + 2H $_{2}$ g $\rightarrow$CH $_{4}$ gwill be:
a.
+144 .0 kJ mol $^{-1}$
b.
-74 .8 kJ mol $^{-1}$
c.
-144 .0 kJ mol $^{-1}$
d.
+74 .8 kJ mol $^{-1}$
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Two reactions A $_{1}$ and A $_{2}$ have identical pre-exponential factors. The activation energy of A $_{1}$ is more than A $_{2}$
by 10 kJ mol $^{-1}$ . If k $_{1}$ and k $_{2}$ are the rate constants for reactions A $_{1}$ and A $_{2}$ , respectively at 300 K, then
ln $\frac{k2}{k1}$ is equal to
R = 8 .314 J mol $^{-1}$ K $^{-1}$
a.
12
b.
6
c.
4
d.
8
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If the image of the point 𝑃1, - 2, 3in the plane, 2𝑥+ 3𝑦- 4𝑧+ 22 = 0measured parallel to the line,
$\frac{𝑥}{1}$ = $\frac{𝑦}{4}$ = $\frac{𝑧}{5}$ is 𝑄, then 𝑃𝑄is equal to:
a.
3$\sqrt$5
b.
2$\sqrt$42
c.
$\sqrt$42
d.
6$\sqrt$5
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Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the
maximum area (in sq. m) of the flower-bed, is:
a.
12 . 5
b.
10
c.
25
d.
30
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The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$ . If one of its directrices is 𝑥= - 4, then the
equation of the normal to it at 1, $\frac{3}{2}$ is:
a.
2𝑦- 𝑥= 2
b.
4𝑥- 2𝑦= 1
c.
4𝑥+ 2𝑦= 7
d.
𝑥+ 2𝑦= 4
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The distance of the point 1, 3, - 7from the plane passing through the point 1, - 1, - 1, having normal
perpendicular to both the lines $\frac{𝑥- 1}{1}$ = $\frac{𝑦+ 2}{-2}$ = $\frac{𝑧- 4}{3}$ and $\frac{𝑥- 2}{2}$ = $\frac{𝑦+ 1}{-1}$ = $\frac{𝑧+ 7}{-1}$ , is:
a.
$\frac{20}{$\sqrt{\,}$74}$
b.
$\frac{10}{$\sqrt{\,}$83}$
c.
$\frac{5}{$\sqrt{\,}$83}$
d.
$\frac{10}{$\sqrt{\,}$74}$
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A hyperbola passes through the point 𝑃$\sqrt$2, $\sqrt$3and has foci at $\pm$ 2, 0. Then the tangent to this hyperbola at 𝑃
also passes through the point
a.
3$\sqrt$2, 2$\sqrt$3
b.
2$\sqrt$2, 3$\sqrt$3
c.
$\sqrt$3, $\sqrt$2
d.
-$\sqrt$2, - $\sqrt$3
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Let a vertical tower 𝐴𝐵have its end 𝐴on the level ground. Let 𝐶be the mid-point of 𝐴𝐵and 𝑃be a point on
the ground such that 𝐴𝑃= 2𝐴𝐵. If $\angle$𝐵𝑃𝐶= 𝛽, then tan𝛽is equal to:
a.
$\frac{6}{7}$
b.
$\frac{1}{4}$
c.
$\frac{2}{9} \frac{4}{9}$
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If, for a positive integer 𝑛, the quadratic equation,
𝑥𝑥+ 1 + 𝑥+ 1𝑥+ 2 + . .. + 𝑥+ 𝑛- 1𝑥+ 𝑛= 10𝑛-
has two consecutive integral solutions, then 𝑛is equal to:
a.
12
b.
9
c.
10
d.
11
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Let 𝑘be an integer such that the triangle with vertices 𝑘, - 3𝑘, 5, 𝑘and -𝑘, 2has area 28sq. units. Then the
orthocenter of this triangle is at the point:
a.
2, - $\frac{1}{2}$
b.
1, $\frac{3}{4}$
c.
1, - $\frac{3}{4}$
d.
2, $\frac{1}{2}$
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If 𝑆is the set of distinct values of 𝑏for which the following system of linear equations
𝑥+ 𝑦+ 𝑧= 1
𝑥+ 𝑎𝑦+ 𝑧= 1
𝑎𝑥+ 𝑏𝑦+ 𝑧= 0
has no solution, then 𝑆is:
a.
An empty set
b.
An infinite set
c.
A finite set containing two or more elements
d.
A singleton
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For three events, 𝐴, 𝐵and 𝐶, 𝑃(Exactly one of 𝐴or 𝐵occurs)
= 𝑃(Exactly one of 𝐵or 𝐶occurs)
= 𝑃(Exactly one of 𝐶or 𝐴occurs) = $\frac{1}{4}$ and 𝑃(All the three events occur simultaneously) = $\frac{1}{16}$ .
Then the probability that at least one of the events occurs, is:
a.
$\frac{7}{32}$
b.
$\frac{7}{16}$
c.
$\frac{7}{64}$
d.
$\frac{3}{16}$
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A man 𝑋has 7friends, 4of them are ladies and 3are men. His wife 𝑌also has 7friends, 3of them are ladies
and 4are men. Assume 𝑋and 𝑌have no common friends. Then the total number of ways in which 𝑋and 𝑌
together can throw a party inviting 3ladies and 3men, so that 3friends of each of 𝑋and 𝑌are in this party is:
a.
485
b.
468
c.
469
d.
484
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A box contains 15green and 10yellow balls. If 10balls are randomly drawn, one-by-one, with replacement,
then the variance of the number of green balls drawn is:
a.
$\frac{12}{5}$
b.
6
c.
4
d.
$\frac{6}{25}$
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If two different numbers are taken from the set 0, 1, 2, 3, . . . . . , 10; then the probability that their sum
as well as absolute difference are both multiple of 4, is:
a.
$\frac{6}{55}$
b.
$\frac{12}{55}$
c.
$\frac{14}{45}$
d.
$\frac{7}{55}$
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