BITSAT Grand Test-3 - sakshieducation.com

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BITSAT Grand Test-3
1.
An equipotential surfaces is shown in figure. Find the magnitude and the direction
of the electric field?
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(A) 200 V/m making an angle 60° with the positive x-axis
(B) 200 V/m making an angle 120° with the positive x-axis
(C) 200 V/m making an angle 120° with the negative x-axis
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(D) 100 V/m making an angle 60° with the x-axis
10V
0
30°
10
20V
30°
20
30V
30°
30
40V
30°
40
x(cm)
2.Three masses A, B and C are connected by string as shown in the figure. The system
moves over a frictionless pulley. The tension in the string connecting A and B is (where g
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is acceleration due to gravity)
3)
8g
9
3 kg
A
1 kg
B
C
5 kg
10 g
9
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4)
g
9
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a
2)
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1) g
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3.Consider earth to be a homogeneous sphere. Scientist A goes deep down in a mine and
scientist B goes high up in a balloon. The value of g measured by
(a) A goes on decreasing and that by B goes on increasing
(b) B goes on decreasing and that by A goes on increasing
(c) Each decreases at the same rate
(d) Each decreases at different rates
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4.In a sample of hydrogen like atoms all of which are in ground state, a photon beam
containing photons of various energies is passed. In absorption spectrum, five dark lines,
are observed. The number of bright lines in the emission spectrum will be (assume that
(b) 10
(c) 15
(d) 19
A physical quantity is represented by x =MaLbT-c. The percentage of errors in the
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5.
(a) 5
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all transitions takes place).
measurements of M, L and T are α , β and γ then the maximum percentage error is
1) α a + β b − cγ
2) α a + β b + γ c
6. If a ball is thrown vertically upwards with speed
t
seconds of its ascent is
1)
7.
1 2
gt
2
2)
ut −
3) α a − β b − γ c
u,
4) α a − β b + γ c
the distance covered during the last
1 2
gt
2
3)
(u − gt)t
4)
ut
Two sirens situated one kilometer apart are producing sound of frequency 330 Hz. An
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observer starts moving from one siren to the other with a speed of 2 m/s. If the speed of
1) 8Hz
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sound be 330 m/s, the beat frequency heard by the observer is
2) 6 Hz
3) 4 Hz
4) 2 Hz
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a
8 .Two rods of equal length and equal area of cross-section are kept parallel and lagged
between temperatures 200C and 800C. The ratio of their thermal conductivities is
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3 : 4. The ratio of the effective thermal conductivity to the conductivity of the first
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rod is
1) 7 : 6
9.
2) 7 : 4
3) 7 :2
4) 7 : 3
A galvanometer having a resistance of 8 ohm is shunted by a wire of resistance 2
ohm. If the total current is one ampere the part of it passing through the shunt is
1) 0.25 amp
2) 0.8 amp
3) 0.2 amp
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4) 0.5 amp
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10. A body is projected vertically up with certain velocity. At a point 'P' in its path, the
ratio of its potential to kinetic energies is 9 : 16. The ratio of velocity of projection to
velocity at 'P' is,
11.
2) 5 : 4
3) 9 : 25
4) 25 : 16
The half life of radon is 1600 yrs. The time after which
1
th part of the radon will
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remain un- disintegrated in the sample is
1) 6400 yrs.
2) 800 yrs.
3) 3200 yrs.
2 × 10 6 N / m
4) 1600 yrs.
times and amplitude 0.01 m
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12.A linear harmonic oscillator of force constant
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1) 3 : 4
has a total mechanical energy of 160 joules. Its
(a) Maximum potential energy is 100 J
(b) Maximum K.E. is 60 J
(c) Maximum P.E. is 160 J
(d) Minimum P.E. is zero
13. The maximum velocity of an electron emitted by light of wavelength
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the surface of a metal of work function
φ,
λ
incident on
is (Where h = Planck's constant, m = mass
1/2
⎡ 2(hc − λφ ) ⎤
⎢ mλ
⎥
⎣
⎦
1/2
(b)
2(hc − λφ )
m
(d)
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(c)
⎡ 2(hc + λφ ) ⎤
⎢ mλ
⎥
⎣
⎦
.s
a
(a)
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of electron and c = speed of light.)
⎡ 2(h λ − φ ) ⎤
⎢
⎥
m
⎣
⎦
1/2
G G
1 − A.B
G
G
14. If θ is the angle between unit vectors A and B , then
G G is equal to
1 + A.B
1) tan2 ( θ / 2)
(
(
2) sin2 ( θ / 2)
3) cot2 ( θ / 2)
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)
)
4) cos2 ( θ / 2)
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15. Two uniform rods A and B of lengths 5 m and 3 m are placed end to end. If their
linear densities are 3 kg/m and 2 kg/m, the position of their centre of mass from their
interface is
3) 2 m on the side of heavier rod
4) 2 m on the side of lighter rod.
Find the equivalent capacitance in the given figure
A
B
C
C
C
(A) 3C/2
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2) 8/7 m on the side of lighter rod
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16.
1) 19/14 m on the side of heavier rod
(B) C/3
(C) 3C
(D) C
17. A body is projected with velocity u such that its horizontal range and
maximum vertical heights are same. The maximum heights is
u
3u
4g
2)
2g
2
2
8u
16 u
3)
17g
4)
2
17 g
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1)
2
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18.A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale reading
has changed from 60 kg to 50kg for a while and then comes back to the original mark.
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a
What should we conclude ?
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(a) The lift was in constant motion upwards
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(b) The lift was in constant motion downwards
(c) The lift while in constant motion upwards, is stopped suddenly
(d) The lift while in constant motion downwards, is suddenly stopped
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19.A particle of mass m is under the influence of a force F which varies with the
displacement x according to the relation
F = −kx + F0
in which k and
F0
are constants. The
particle when disturbed will oscillate
x = 0, with ω ≠ k / m
(b) about
x = 0, with ω = k / m
(c) About
x = F0 / k with ω = k / m
(d) about
x = F0 /k with ω ≠ k / m
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20.
(a) About
A straight line conductor of length 0.4 m is moved with a speed of 7 m/s
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perpendicular to a magnetic field of intensity 0.9 Wb/m2. The induced e.m.f.
across the conductor is
1) 2.52 V
21.
2) 25.2 V
2) 1.26 V
4) 5. 04 V
The inductance L (in mH) of the coil which is to be connected in series with a
capacitor of 0.3pF to get an oscillatory frequency of 1 MHz is
1) 8.44
2) 84. 4
3) 844
4) 8440
22. The electric current in a circular coil of two turns produces a magnetic induction of
0.2T at its centre. The coil is unwound and is rewound into a circular coil of four
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turns and same current is flown through it. The magnetic induction at the centre of
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the coil now in tesla is
2) 0.4
3) 0.6
4) 0.8
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1) 0.2
23. Work done in time t on a body of mass m which is accelerated from rest to a speed v
t1
as a function of time t is given by
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in time
1 v 2
m t
2 t1
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(a)
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(b) m
v 2
t
t1
(c)
2
1 ⎛mv⎞ 2
⎜
⎟ t
2 ⎜⎝ t 1 ⎟⎠
(d)
1 v2 2
m
t
2 t12
A galvanometer of resistance 20Ω gives a full scale deflection when a current of
0.04 A is passed through it. It is desired to convert it into an ammeter reading 20 A
in full scale. The only shunt available is 0.05Ω resistance. The resistance that must
be connected in series with the coil of the galvanometer is
1) 4.95 Ω
2) 5.94 Ω
3) 9.45 Ω
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4) 12.62 Ω
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25. A ball moving with speed v hits another identical ball at rest. The two balls stick
together after collision. If specific heat of the material of the balls is S, the temperature
(a)
v2
8S
(b)
v2
4S
(c)
v2
2S
(d)
v2
S
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rise resulting from the collision is
26.A ball of radius r and density ρ falls freely under gravity through a distance h before
entering water in a beaker. Velocity of ball does not change even on entering water. If
(a)
2 2⎛ 1 − ρ ⎞
⎟g
r ⎜
9 ⎜⎝ η ⎟⎠
(c)
2 4⎛ ρ − 1⎞
⎟ g
r ⎜
81 ⎜⎝ η ⎟⎠
2
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viscosity of water is η, the value of h is given by
(b)
2 2⎛ ρ −1 ⎞
⎟g
r ⎜
81 ⎜⎝ η ⎟⎠
(d)
2 4⎛ ρ −1 ⎞
⎟ g
r ⎜
9 ⎜⎝ η ⎟⎠
2
27. When un polarized light is incident on a glass plate at an angle 600 the reflected
light is found to be completely polarized, then the critical angle of glass - air
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interface is
⎛ 1 ⎞
2) tan-1
( 3)
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1) tan-1 ⎜⎜ ⎟⎟
⎝ 3⎠
⎛ 1 ⎞
⎟⎟
⎝ 3⎠
3) sin-1 ⎜⎜
4) sin-1
( 3)
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a
28. A shell projected from a level ground has a range R, if it did not explode. At the
highest point, the shell explodes into two fragments having masses in the ratio 1:3;
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with each fragment moving horizontally immediately after the explosion. If the
lighter fragment falls at a distance R from the point of projection, behind the point of
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projection, the distance at which the other fragments falls from the point of
projection is
1) 2R
2) 5R/3
3) 4R/3
4) 2R/3
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29.
A plano convex lens when silvered on the plane side behaves like a concave
mirror of focal length 30 cm. However when silvered on the convex side it
behaves like a concave mirror of focal length 10cm. The true radius of curvature
of the spherical surface of plano-convex lens is
2) 10 cm
3) 60 cm
4) 30 cm
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1) 20 cm
Efficiency of a reversible engine working between temperatures 270C and 9270C is
η1 .
Efficiency of Carnot's engine working between temperatures 270C and 9270C
is
η2
1)
η1 =0.75, η 2 =1
. Then
2)
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30.
η1 < η 2 =0.75
3)
η1 = η 2 =
0.25
4)
η1 < η 2 =
0.25
31. A car is moving with a speed of 30 ms–1 on a circular path of radius 500 m. If its
speed is increasing at the rate of 2 ms–2, the net acceleration of the car is
1) 3.6 ms–2
2) 2.7 ms–2
3) 1.8 ms–2
4) 2 ms–2
32. A uniform circular disc of radius R lies in the XY - plane with its centre at the origin
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of co-ordinate system. Its moment of inertia about an axis, lying in the xy-plane,
parallel to the x-axis and passing through a point on the y-axis at a distance y = 2R is
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I1. Its moment of inertia about an axis lying in a plane perpendicular to xy-plane
‘d’ is
19
R
2
17
R
2
2)
3)
15
R
2
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1)
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passing through a point on the x-axis at a distance x = d is I2. If I1 = I2 , the value of
4)
13
R
2
33.A body falls freely under gravity. Its speed is v when it has lost an amount U of the
gravitational energy. Then its mass is
(a)
Ug
v2
(b)
U2
g
(c)
2U
v2
(d)
2 Ugv 2
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34.If σ be the surface tension, the work done in breaking a big drop of radius R in n drops
of equal radius is
Rn 2 / 3σ
(b) (n 2 / 3 − 1)R σ
(c)
(n1 / 3 − 1)R σ
(d)
4 πR 2 (n 1 / 3 − 1)σ
A rectangular block is 5 cm × 5 cm × 10cm in size. The block is floating in water
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35.
(a)
with 5 cm side vertical. If it floats with 10 cm side vertical, what change will occur in
the level of water?
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a) No change
b) It will rise
c) It will fall
d) It may rise or fall depending on the density of block
36. A battery of emf 4 V is connected across a 10 m long potentiometer wire having a
m–1. A cell of emf 2.4 V is connected so that its
resistance per unit length 1.6
negative terminal is connected to the low potential end of the potentiometer wire and the
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other end is connected through a galvanometer to a sliding contact along the wire. It is
found that the no-deflection point occurs against the balancing length of 8 m. The
c) 18
d)
13
The reading of the ideal voltmeter in the adjoining diagram will be
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37.
b16
.s
a
a) 16/3
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internal resistance of the 4 V battery is
A
10V
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(a) 4 V
(b) 8 V
20Ω
V
4V
10Ω
B
N
C
(c) 12 V
(d) 14 V
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38. Total energy density of electromagnetic waves in vacuum is given by the relation
1 E 2 B2
⋅
+
2 ε 0 2μ 0
(b)
1
1
ε0 E 2 + μ0 B 2
2
2
(c)
E 2 + B2
c
(d)
1
B2
ε0 E 2 +
2
2μ 0
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(a)
If μ o and μ e are the refractive indices of Quartz for ordinary and extraordinary
39.
rays and vo and ve are the speeds of ordinary and extra ordinary rays through
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Quartz, then
1) μ e + μ o and ve > vo
2) μ e = μ o and ve = vo
3) μ e > μ o and ve < vo
40.
4) μ e > μ o and ve > vo
The refractive indices of the material of a lens for violet, yellow and red colours of
light are 1.66, 1.64 and 1.62 respectively.
The mean focal length of the lens is
8cm. The chromatic aberration of the lens between the violet and red colour is :
2) 0.25m
3) 0.625m
4) 0.64 m
KEY
2
4
3
4
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2
4
3
5
2
6
1
7
3
8
1
9
2
10 2
11 1
12 3
13 3
14 1
15 1
16 3
17 4
18 3
19 3
20 1
21 2
22 4
23 4
24 1
25 1
26 3
27 3
28 2
29 4
30 2
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1
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1) 0.5m
33 3
34 4
35 1
36 1
37 2
38 4
39 3
40 1
32 3
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31 2
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