A plane is inclined at an angle $\alpha$ = 30$^{\circ}$with respect to the horizontal. A particle is projected with a speed
u = 2 m s $^{-1}$ , from the base of the plane, making an angle $\theta$ = 15$^{\circ}$with respect to the plane as shown in the
figure. The distance from the base, at which the particle hits the plane is close to:
(Take g = 10 m s $^{-2}$ )
a.
20 cm
Correct Answer
b.
18 cm
c.
14 cm
d.
26 cm
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Q2mcq
The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 mwhich is
carrying a current of 10 Ais:
[Take $\mu$ $_{0}$ = 4$\pi$ $\times$ 10 $^{-7}$ N A $^{-2}$ ]
a.
3 $\mu$T
b.
1 $\mu$T
c.
18 $\mu$T
Correct Answer
d.
9 $\mu$T
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Q3mcq
A coil of self inductance 10 mHand resistance of 0.1 $\Omega$is connected through a switch to a battery of internal
resistance 0.9 $\Omega$. After the switch is closed, the time taken for the current to attain 80%of the saturation value
is: [ln5 = 1.6]
a.
0.103 s 0.002 s
c.
0.324 s
d.
0.016 s
Correct Answer
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Q4mcq
Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm $^{-2}$ . If the surface
has an area of 25 cm $^{2}$ , the momentum transferred to the surface in 40βmintime duration will be:
a.
6.3 $\times$ 10 $^{-4}$ N s
b.
5.0 $\times$ 10 $^{-3}$ N s
Correct Answer
c.
3.5 $\times$ 10 $^{-6}$ N s
d.
1.4 $\times$ 10 $^{-6}$ N s
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Q5mcq
A metal coin of mass 5 gand radius 1 cmis fixed to a thin stick ABof negligible mass as shown in the figure.
The system is initially at rest. The constant torque, that will make the system rotate about ABat 25rotations per
second in 5 s, is close to:
a.
1.6 $\times$ 10 $^{-5}$ N m
b.
2.0 $\times$ 10 $^{-5}$ N m
Correct Answer
c.
7.9 $\times$ 10 $^{-6}$ N m
d.
4.0 $\times$ 10 $^{-6}$ N m
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Q6mcq
The correct figure that shows, schematically, the wave pattern produced by the superposition of two waves of
frequencies 9 Hzand11 Hz, is
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Q7mcq
The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener
diode is 6 Vand the load resistance is, R $_{L}$ = 4 k$\Omega$. The series resistance of the circuit is R $_{i}$ = 1 k$\Omega$. If the
battery voltage V $_{B}$ varies from 8 V to 16 V, what are the minimum and maximum values of the current
through Zener diode?
a.
0.5 mA; 6 mA
b.
1 mA; 8.5 mA
c.
0.5 mA; 8.5 mA
Correct Answer
d.
1.5 mA; 8.5 mA
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Q8mcq
One mole of an ideal gas passes through a process where pressure and volume obey the relation
P = P $_{o}$ 1 - $\frac{1}{2} \frac{Vo}{V}^{2}$ . Here P $_{o}$ and V $_{o}$ are constants. Calculate the change in the temperature of the gas if its volume
changes from V $_{o}$ to 2V $_{o}$ .
a.
$\frac{1}{4} \frac{P0V0}{R}$
b.
$\frac{5}{4} \frac{P0V0}{R}$
Correct Answer
c.
$\frac{1}{2} \frac{P0V0}{R}$
d.
$\frac{3}{4} \frac{P0V0}{R}$
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Q9mcq
A bullet of mass 20 ghas an initial speed of 1 m s $^{-1}$ , just before it starts penetrating a mud wall of thickness
20 cm. If the wall offers a mean resistance of 2.5 $\times$ 10 $^{-2}$ N, the speed of the bullet after emerging from the
other side of the wall is close to:
a.
0.7 m s $^{-1}$
Correct Answer
b.
0.3 m s $^{-1}$
c.
0.1 m s $^{-1}$
d.
0.4 m s $^{-1}$
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Q10mcq
A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this
square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole
moment of circular loop will be:
a.
$\frac{4m}{$\pi$}$
Correct Answer
b.
$\frac{3m}{$\pi$}$
c.
$\frac{2m}{$\pi$}$
d.
$\frac{m}{$\pi$}$
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Water from a tap emerges vertically downwards with an initial speed of 1.0 ms $^{-1}$ . The cross - sectional area
of the tap is 10 $^{-4}$ m $^{2}$ . Assume that the pressure is constant throughout the stream of water and that the flow is
streamlined. The cross - sectional area of the stream, 0.15 mbelow the tap would be:
(Take g = 10 ms $^{-2}$ )
a.
1 $\times$ 10 $^{-5}$ m $^{2}$
b.
5 $\times$ 10 $^{-4}$ m $^{2}$
c.
2 $\times$ 10 $^{-5}$ m $^{2}$
d.
5 $\times$ 10 $^{-5}$ m $^{2}$
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When heat Qis supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by
βT. The heat required to produce the same change in temperature, at a constant pressure is:
a.
$\frac{3}{2}$ Q
b.
$\frac{7}{5}$ Q
c.
$\frac{5}{3}$ Q
d.
$\frac{2}{3}$ Q
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A source of sound Sis moving with a velocity of 50 m s $^{-1}$ towards a stationary observer. The observer
measures the frequency of the source as 1000 Hz . What will be the apparent frequency of the source when it
is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m s $^{-1}$ )
a.
750 Hz
b.
857 Hz
c.
1143 Hz
d.
807 Hz
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A simple pendulum of length Lis placed between the plates of a parallel plate capacitor having electric field E
, as shown in figure. Its bob has mass mand charge q. The time period of the pendulum is given by:
In an experiment, brass and steel wires of length 1 meach with areas of cross section 1 mm $^{2}$ are used. The
wires are connected in series and one end of the combined wire is connected to a rigid support and other end is
subjected to elongation. The stress required to produce a net elongation of 0.2 mmis,
[Given, the Young's Modulus for steel and brass are, respectively, 120 $\times$ 10 $^{9}$ N / m $^{2}$ and 60 $\times$ 10 $^{9}$ N / m $^{2}$ ]
a.
8.0 $\times$ 10 $^{6}$ N / m $^{2}$
b.
1.2 $\times$ 10 $^{6}$ N / m $^{2}$
c.
0.2 $\times$ 10 $^{6}$ N / m $^{2}$
d.
1.8 $\times$ 10 $^{6}$ N / m $^{2}$
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$\rightarrow$ ^ 2^
The time dependence of the position of a particle of mass m = 2is given by r t = 2t i - 3t j . Its angular
momentum, with respect to the origin, at time t = 2 is:
a.
^ ^ + ^
36 k 48 i j
c.
^
-48 k
d.
^k - ^
-34 i
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InLi $^{+ +}$ ,electron in first Bohr orbit is excited to a level by a radiation of wavelength$\lambda$.When the ion gets de
excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines
are observed. What is the value of $\lambda$?
(Given: β= 6.63 $\times$ 10 $^{-34}$ J s ; π= 3 $\times$ 10 $^{8}$ m s $^{-1}$ )
a.
10.8 nm
b.
9.4 nm
c.
11.4 nm
d.
12.3 nm
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A 2 mWlaser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is:
[Given Planck's constant h = 6.6 $\times$ 10 $^{-34}$ J s, speed of light c = 3.0 $\times$ 10 $^{8}$ m / s]
a.
1.5 $\times$ 10 $^{16}$
b.
5 $\times$ 10 $^{15}$
c.
2 $\times$ 10 $^{16}$
d.
1 $\times$ 10 $^{16}$
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In a Young's double-slit experiment, the ratio of the slit's width is 4 : 1. The ratio of the intensity of maxima to
minima, close to the central fringe on the screen, will be
a.
25 : 9
4
b.
9 : 1
c.
$\sqrt$3 + 1 : 16
d.
4 : 1
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Space between two concentric conducting spheres of radii aand b ( b > a ) is filled with a medium of
resistivity $\rho$. The resistance between the two spheres will be:
A solid sphere of mass Mand radius Ris divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is
converted into uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I $_{1}$ be
the moment of inertia of the disc about its axis and I $_{2}$ be the moment of inertia of the new sphere about its axis.
The ratio I $_{1}$ / I $_{2}$ is given by:
a.
140
b.
185
c.
65
d.
285
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A spaceship orbits around a planet at a height of 20 kmfrom its surface. Assuming that only gravitational field
of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in
24hours around the planet?
[Given: Mass of planet = 8 $\times$ 10 $^{22}$ kg,
Radius of planet = 2 $\times$ 10 $^{6}$ m,
Gravitational constant G = 6.67 $\times$ 10 $^{-11}$ Nm $^{2}$ / kg $^{2}$ ]
a.
17
b.
9
c.
13
d.
11
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A submarine experiences a pressure of 5.05 $\times$ 10 $^{6}$ Paat a depth of d $_{1}$ in a sea. When it goes further to a depth
of d $_{2}$ , it experiences a pressure of 8.08 $\times$ 10 $^{6}$ Pa. Then d $_{2}$ - d $_{1}$ is approximately (density of water
= 10 $^{3}$ kg / m $^{3}$ and acceleration due to gravity = 10 ms $^{-2}$ ):
a.
600 m
b.
500 m
c.
300 m
d.
400 m
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Two blocks Aand Bof masses m $_{A}$ = 1 kgand m $_{B}$ = 3 kgare kept on the table as shown in figure. The
coefficients of friction between Aand Bis 0.2and between Band the surface of the table is also 0.2 . The
maximum force Fthat can be applied on Bhorizontally, so that the block Adoes not slide over the block Bis :
[Take g = 10 m / s $^{2}$ ]
a.
16 N
b.
12 N
c.
40 N
d.
8 N
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In free space, a particle π΄of charge 1 $\mu$Cis held fixed at point π. Another particle π΅of the same charge and
mass 4 $\mu$gis kept at a distance of 1 mmfrom π. If π΅is released, then its velocity at a distance of 9 mmfrom
πis:
[Take $\frac{1}{4$\pi$$\epsilon$0}$ = 9 $\times$ 10 $^{9}$ N m $^{2}$ C $^{-2}$ ]
a.
1.0 m s $^{-1}$
b.
1.5 $\times$ 10 $^{2}$ m s $^{-1}$
c.
2.0 $\times$ 10 $^{3}$ m s $^{-1}$
d.
3.0 $\times$ 10 $^{4}$ m s $^{-1}$
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A cubical block of side 0.5 mfloats on water with 30%of its volume under water. What is the maximum
weight that can be put on the block without fully submerging it under water?
[Take, density of water = 10 $^{3}$ kg / m $^{3}$ ]
a.
87.5 kg
b.
65.4 kg
c.
30.1 kg
d.
46.3 kg
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Two radioactive substances Aand Bhave decay constants 5$\lambda$and $\lambda$respectively. Att = 0, a sample has the
same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $\frac{1}{e}^{2}$ will be
a.
$\frac{1}{$\lambda$}$
b.
$\frac{1}{2$\lambda$}$
c.
$\frac{2}{$\lambda$}$
d.
$\frac{1}{4$\lambda$}$
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Points I, IIand IIIin the following plot respectively correspond to (V $_{mp}$ :most probable velocity)
a.
V $_{mp}$ of N $_{2}$ 300 K; V $_{mp}$ of H $_{2}$ 300 K; V $_{mp}$ of
O $_{2}$ 400 K;
b.
V $_{mp}$ of H $_{2}$ 300 K; V $_{mp}$ of N $_{2}$ 300 K; V $_{mp}$ of
O $_{2}$ 400 K;
c.
V $_{mp}$ of N $_{2}$ 300 K; V $_{mp}$ of O $_{2}$ 400 K; V $_{mp}$ of V $_{mp}$ of O $_{2}$ 400 K; V $_{mp}$ of N $_{2}$ 300 K; V $_{mp}$ of
H $_{2}$ 300 K; H $_{2}$ 300 K;
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The correct match between Item - I and Item - II is:
Item - I Item - II
(a) High density polythene (I) Peroxide catalyst
(b) Polyacrylonitrile (II) Condensation at high temperature & pressure
(c) Novolac (III) Ziegler-Natta catalyst
(d) Nylon 6 (IV) Acid or base catalyst
a.
a $\rightarrow$IV, b $\rightarrow$( II ) , ( c ) $\rightarrow$( I ) , ( d ) $\rightarrow$( III )
b.
( a ) $\rightarrow$III, ( b ) $\rightarrow$( I ) , ( c ) $\rightarrow$( IV ) , ( d ) $\rightarrow$( II )
c.
( a ) $\rightarrow$III, ( b ) $\rightarrow$ ( I ) , ( c ) $\rightarrow$( II ) , ( d ) $\rightarrow$( IV )
d.
( a ) $\rightarrow$II, b $\rightarrow$IV, c $\rightarrow$I, d $\rightarrow$III
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For the reaction,
2SO $_{2}$ g + O $_{2}$ g $\rightleftharpoons$2SO $_{3}$ g,
βH = - 57.2 kJ mol $^{-1}$ and K $_{c}$ = 1.7 $\times$ 10 $^{16}$ .
Which of the following statements is incorrect?
a.
The equilibrium constant is large suggestive of
reaction going to completion and so, no catalyst
is required.
b.
The equilibrium will shift in forward direction as
the pressure increases.
c.
The equilibrium constant decreases as the
temperature increases.
d.
The addition of inert gas at constant volume will
not affect the equilibrium constant.
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For the reaction of H $_{2}$ with I $_{2}$ , the rate constant is 2.5 $\times$ 10 $^{-4}$ dm $^{3}$ mol $^{-1}$ s $^{-1}$ at 327 $^{o}$ Cand 1.0 dm $^{3}$ mol-1s $^{-1}$ at
527$^{\circ}$C. The activation energy for the reaction, in kJ mol-1is:
R = 8.314 JK $^{-1}$ mol $^{-1}$
a.
166
b.
59
c.
72
d.
150
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The correct statements among ato dare:
aSaline hydrides produce H $_{2}$ gas when reacted with H $_{2}$ O .
bReaction of LiAlH $_{4}$ with BF $_{3}$ leads to B $_{2}$ H $_{6}$ .
c PH $_{3}$ and CH $_{4}$ are electron - rich and electron - precise hydrides, respectively.
d HFand CH $_{4}$ are called as molecular hydrides.
a.
a, band conly.
b.
a, cand donly.
c.
cand donly.
d.
a, b, cand d
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1 gof a non-volatile non-electrolyte solute is dissolved in 100 gof two different solvents Aand B whose
ebullioscopic constants are in the ratio of 1: 5. The ratio of the elevation in their boiling points, $\frac{βTbA}{βTbB}$ , is:
(assuming they have the same molar mass)
a.
10: 1
b.
1: 5
c.
1: 0.2
d.
5: 1
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The minimum amount of O $_{2}$ gconsumed per gram of reactant is for the reaction:
(Given atomic mass: Fe = 56, O = 16, Mg = 24, P = 31, C = 12, H = 1)
a.
P $_{4}$ s + 5O $_{2}$ g $\rightarrow$P $_{4}$ O $_{10}$ s
b.
2 Mgs + O $_{2}$ g $\rightarrow$2MgOs
c.
4Fes + 3O $_{2}$ g $\rightarrow$2Fe $_{2}$ O $_{3}$ s
d.
C $_{3}$ H $_{8}$ g + 5O $_{2}$ g $\rightarrow$3CO $_{2}$ g + 4H $_{2}$ O ( l )
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A hydrated solid X on heating initially gives a monohydrated compound Y. Y upon heating above 373 Kleads
to an anhydrous white powder Z. X and Z, respectively, are;
a.
washing soda and soda ash.
b.
baking soda and soda ash.
c.
washing soda and dead burnt plaster.
d.
baking soda and dead burnt plaster.
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Compound AC $_{9}$ H $_{10}$ Oshows positive iodoform test. Oxidation of A with KMnO $_{4}$ / KOHgives acid BC $_{8}$ H $_{6}$ O $_{4}$ .
Anhydride of B is used for the preparation of phenolphthalein. Compound A is:
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A perpendicular is drawn from a point on the line $\frac{π₯- 1}{2}$ = $\frac{π¦+ 1}{-1}$ = $\frac{π§}{1}$ to the plane π₯+ π¦+ π§= 3such that the
foot of the perpendicular πalso lies on the plane π₯- π¦+ π§= 3. Then the coordinates of πare
a.
2, 0, 1
b.
- 1, 0, 4
c.
4, 0, - 1 1, 0, 2
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The tangent and normal to the ellipse 3π₯ $^{2}$ + 5π¦ $^{2}$ = 32at the point π2, 2meet the π₯-axis at πand π ,
respectively. Then the area (in sq. units) of the triangle πππ is:
a.
$\frac{68}{15}$
b.
$\frac{16}{3}$
c.
$\frac{14}{3}$
d.
$\frac{34}{15}$
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Let π $_{1}$ , π $_{2}$ , π $_{3}$ . . . be an π΄. π. with π $_{6}$ = 2 .Then, the common difference of this π΄. π. ,which maximise
the product π $_{1}$ Β· π $_{4}$ Β· π $_{5}$ ,is :
a.
$\frac{2}{3}$
b.
$\frac{3}{2}$
c.
$\frac{6}{5}$
d.
$\frac{8}{5}$
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The distance of the point having position vector ^ ^ ^from the straight line passing through the point
-π+ 2π+ 6π
and parallel to the vector, ^ ^ ^is
2, 3, - 4 6π+ 3π- 4π
a.
4$\sqrt$3
b.
6
c.
2$\sqrt$13
d.
7
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A spherical iron ball of radius 10 ππis coated with a layer of ice of uniform thickness that melts at a rate of
50 ππ $^{3}$ / πππ.When the thickness of the ice is 5 ππ,then the rate at which the thickness (in ππ/ πππ)
of the ice decreases, is :
a.
$\frac{1}{9$\pi$}$
b.
$\frac{1}{36$\pi$}$
c.
$\frac{1}{18$\pi$}$
d.
$\frac{5}{6$\pi$}$
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If the tangent to the curve π¦= $\frac{π₯}{π₯2- 3}$ , π₯$\in$π , π₯$\neq$$\pm$ $\sqrt$3,at a point πΌ, π½$\neq$0, 0on it is parallel to the line
2π₯+ 6π¦- 11 = 0,then:
a.
2πΌ+ 6π½= 19
b.
2πΌ+ 6π½= 11
c.
6πΌ+ 2π½= 19
d.
6πΌ+ 2π½= 9
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Lines are drawn parallel to the line 4π₯- 3π¦+ 2 = 0,at a distance $\frac{3}{5}$ units from the origin. Then which one of
the following points lies on any of these lines?
a.
$\frac{1}{4}$ , - $\frac{1}{3}$
b.
- $\frac{1}{4}$ , $\frac{2}{3}$
c.
- $\frac{1}{4}$ , - $\frac{2}{3}$
d.
$\frac{1}{4}$ , $\frac{1}{3}$
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If both the mean and the standard deviation of 50observations π₯ $_{1}$ , π₯ $_{2}$ , β¦ , π₯ $_{50}$ are equal to 16, then the mean
of π₯ $_{1}$ - 4 $^{2}$ , π₯ $_{2}$ - 4 $^{2}$ , β¦ , π₯ $_{50}$ - 4 $^{2}$ is
a.
525
b.
480
c.
400
d.
380
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Suppose that 20pillars of the same height have been erected along the boundary of circular stadium. If the top
of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of
beams is:
a.
170
b.
180
c.
210
d.
190
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If cos $^{-1}$ π₯- cos $^{- 1 π¦}_{2}$ = πΌ,where -1 $\leq$π₯$\leq$1, - 2 $\leq$π¦$\leq$2, π₯$\leq$ $\frac{π¦}{2}$ ,then for all π₯, π¦, 4π₯ $^{2}$ - 4π₯π¦cosπΌ+ π¦ $^{2}$ is
equal to :
a.
4cos $^{2}$ πΌ+ 2π₯ $^{2}$ π¦ $^{2}$
b.
4sin $^{2}$ πΌ- 2π₯ $^{2}$ π¦ $^{2}$
c.
2sin $^{2}$ $\alpha$
d.
4sin $^{2}$ $\alpha$
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Let πbe a real number for which the system of linear equations
π₯+ π¦+ π§= 6,
4π₯+ ππ¦- ππ§= π- 2and
3π₯+ 2π¦- 4π§= - 5
has infinitely many solutions. Then πis a root of the quadratic equation:
a.
π $^{2}$ + 3π- 4 = 0
b.
π $^{2}$ - π- 6 = 0
c.
π $^{2}$ - 3π- 4 = 0
d.
π $^{2}$ + π- 6 = 0
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If the plane 2π₯- π¦+ 2π§+ 3 = 0has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the planes 4π₯- 2π¦+ 4π§+ π= 0and
2π₯- π¦+ 2π§+ π= 0, respectively, then the maximum value of π+ πis equal to:
a.
9
b.
15
c.
13
d.
5
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Let ππ₯= log $_{π}$ sinπ₯, 0 < π₯< πand ππ₯= sin $^{-1}$ ( π $^{-π₯}$ ) , (π₯$\geq$0) .If πΌis a positive real number such that
π= πππ $'$ (πΌ)and π= πππ( πΌ) ,then
a.
ππΌ $^{2}$ + ππΌ+ π= 0
b.
ππΌ $^{2}$ + ππΌ- π= - 2πΌ
c.
ππΌ $^{2}$ - ππΌ- π= 0
d.
ππΌ $^{2}$ - ππΌ- π= 1
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Let π, πand πbe in πΊ. π. with common ratio π,where π$\neq$0and 0 < π$\leq$ $\frac{1}{2}$ .If 3π, 7πand 15πare the
first three terms of an π΄. π. ,then the 4 $^{π‘β}$ term of this π΄. π. is :
a.
π
b.
$\frac{7}{3}$ π
c.
5π
d.
$\frac{2}{3}$ π
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The angles π΄, π΅ & πΆof a βπ΄π΅πΆare in π΄. π. and π: π= 1: $\sqrt$3 .If π= 4 ππ,then the area (in π π. ππ)
of this triangle is:
a.
2$\sqrt$3
b.
$\frac{2}{$\sqrt{\,}$3}$
c.
$\frac{4}{$\sqrt{\,}$3}$
d.
4$\sqrt$3
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The locus of the centres of the circles, which touch the circle, π₯ $^{2}$ + π¦ $^{2}$ = 1externally, also touch the π¦-axis and
lie in the first quadrant, is:
a.
π¦= $\sqrt$1 + 2π₯, π₯$\geq$0
b.
π¦= $\sqrt$1 + 4π₯, π₯$\geq$0
c.
π₯= $\sqrt$1 + 2π¦, π¦$\geq$0
d.
π₯= $\sqrt$1 + 4π¦, π¦$\geq$0
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The smallest natural number π, such that the coefficient of π₯in the expansion of π₯ $^{2}$ + $\frac{1}{π₯3}^{π}$ is $^{π}$ πΆ $_{23}$ , is
a.
58
b.
38
c.
35
d.
23
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