| 1.
Given,
R1 = 1Ω
C1 = 2μF
R2 = 2Ω
C2 = 4μF
The time constants (in μS) for the circuits I, II, III are respectively
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| 2.
Two blocks A and B of masses 2m and m, respectively, are connected by
a massless and inextensible string. The whole system is suspended by a
massless spring as shown in the figure. The magnitudes of acceleration
of A and B, immediately after the string is cut, are respectively
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| 3.
A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal
length 15 cm, if the plane surface is silvered. The image will form at
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| 4.
A biconvex lens of focal length f forms a circular image of sun of radius r in focal plane. Then
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C
)
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if lower half part is covered by black sheet, then area of the image is equal to
πr2/2
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D
)
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if f is doubled, intensity will increase
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| 5.
Given a sample of Radium-226 having half-life of 4 days.
Find the probability, a nucleus disintegrates after
2 half lives.
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| 6.
Graph of position of image vs position of point object
from a convex lens is shown. Then, focal length of the
lens is
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| 7.
A massless rod is suspended by two identical strings AB and CD of equal
length. A block of mass m is suspended from point O such that BO is
equal to 'x'. Further, it is observed that the frequency of 1st harmonic
(fundamental frequency) in AB is equal to 2nd harmonic frequency in CD.
Then, length of BO is
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| 8.
A system of binary stars of masses mA and mB are moving in
circular orbits of radii rA and rB respectively. If
TA and TB are the time periods of
masses mA and mB respectively, then
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| 9.
A solid sphere of mass M, radius R and having moment of
inertia about an axis passing through the centre of
mass as I, is recast into a disc of thickness t, whose moment
of inertia about an axis passing through its edge
and perpendicular to its plane remains I. Then, radius of the disc will be
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A
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2R
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B
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C
)
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4R
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| 10.
A student performs an experiment for determination of
and he commits an error of Δl.
For T he takes the time of n oscillations with the stop watch of least
count ΔT and he commits a human error
of 0.1sec. For which of the following data,
the measurement of g will be most accurate?
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A
)
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Δl
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ΔT
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n
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Amplitude of oscillation
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5 mm
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0.2 sec
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10
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5 mm
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B
)
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Δl
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ΔT
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n
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Amplitude of oscillation
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5 mm
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0.2 sec
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20
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5 mm
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C
)
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Δl
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ΔT
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n
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Amplitude of oscillation
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5 mm
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0.1 sec
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20
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1 mm
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D
)
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Δl
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ΔT
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n
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Amplitude of oscillation
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1 mm
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0.1 sec
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50
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1 mm
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| 11.
The circular divisions of shown screw gauge are 50. It moves 0.5 mm on
main scale in one rotation. The diameter of the ball is
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| 12.
Consider a cylindrical element as shown in the figure. Current flowing
the through element is I and resistivity of material of the cylinder is ρ .
Choose the correct option out the following.
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A
)
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Power loss in first half is four times the power loss in second half.
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B
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Voltage drop in first half is twice of voltage drop in second half.
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C
)
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Current density in both halves are equal.
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D
)
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Electric field in both halves is equal.
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| 13.
In the given diagram, a line of force of a particular force field is shown. Out of the
following options, it can never represent
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A
)
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an electrostatic field
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B
)
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a magnetostatic field
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C
)
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a gravitational field of a mass at rest
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D
)
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an induced electric field
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| 14.
The electrostatic potential (&phir) of a spherical symmetric system, kept at
origin, is shown in the adjacent figure, and given as
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&phir=
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q
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(r &ge R0)
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4πε0r
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&phir=
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q
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(r &le R0)
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4πε0R0
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Which of the following option(s) is/are correct?
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A
)
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For spherical region r ≤ R0 , total electrostatic energy stored is zero.
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B
)
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Within r = 2R0 , total charge is q.
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C
)
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There will be no charge anywhere except at r = R0.
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D
)
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Electric field is discontinuous at r = R0.
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| 15.
A solid cylinder of mass m and radius r is rolling on a
rough inclined plane of inclination θ. The coefficient
of friction between the cylinder and incline is μ . Then
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A
)
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frictional force is always μmgcosθ
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B
)
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friction is a dissipative force
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C
)
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by decreasing θ, frictional force decreases
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D
)
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friction opposes translation and supports
rotation.
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| 16.
Function x = A sin2ωt + B cos2ωt + C sin ωt cos ωt represents SHM
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A
)
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for any value of A, B and C (except C = 0)
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B
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if A = -B; C = 2B, amplitude = |B |
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D
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if A = B; C = 2B, amplitude = |B|
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| 17.
In a dark room with ambient temperature T0, a black body is
kept at a temperature T. Keeping the
temperature of the black body constant (at T), sunrays are
allowed to fall on the black body through a hole in
the roof of the dark room. Assuming that there is no
change in the ambient temperature of the room, which of
the following statement(s) is/are correct?
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A
)
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The quantity of radiation absorbed by the black body in unit time will increase.
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B
)
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Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unit time will
increase.
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C
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Black body radiates more energy in unit time in the visible spectrum.
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D
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The reflected energy in unit time by the black body remains same.
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| 18.
The graph between 1/λ and stopping potential (V) of three metals having
work functions φ1, φ2 and φ3
in an experiment of photo-electric effect is
plotted as shown in the figure. Which of the following statement(s) is/are
correct? [Here λ is the wavelength of the incident ray].
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A
)
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Ratio of work functions φ1 : φ2 : φ3 = 1 : 2 : 4
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B
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Ratio of work functions φ1 : φ2 : φ3 = 4 : 2 : 1
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C
)
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tan θ is directly proportional to hc/e, where h is Planck's constant and c is the speed of light.
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D
)
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The violet colour light can eject photoelectrons from metals 2 and 3.
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| 19.
An infinite current carrying wire passes through point O and in
perpendicular to the plane containing a current carrying loop ABCD
as shown in the figure. Choose the correct option (s).
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A
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Net force on the loop is zero.
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B
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Net torque on the loop is zero.
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C
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As seen from O, the loop rotates clockwise.
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D
)
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As seen from O, the loop rotates anticlockwise
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| 20.
A ball moves over a fixed track as shown in the figure. From
A to B the ball rolls without slipping. Surface BC is
frictionless. KA, KB and KC
are kinetic energies of the ball at
A, B and C, respectively. Then
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| 21.
The capacitor of capacitance C can be charged
(with the help of a resistance R) by a
voltage source V, by closing switch S1
while keeping switch S2 open. The capacitor can
be connected in series with an inductor 'L' by closing
switch S2 and opening S1.
Initially, the capacitor was uncharged. Now,
switch S1 is closed and S2 is kept
open. If time constant of this circuit is τ, then
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A
)
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after time interval τ, charge on the capacitor is CV/2
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B
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after time interval 2τ, charge on the capacitor is CV(1-e-2)
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C
)
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the work done by the voltage source will be half of the heat dissipated
when the capacitor is fully charged.
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D
)
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after time interval 2&tau, charge on the capacitor is CV(1-e-1)
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| 22.
The capacitor of capacitance C can be charged
(with the help of a resistance R) by a
voltage source V, by closing switch S1
while keeping switch S2 open. The capacitor can
be connected in series with an inductor 'L' by closing
switch S2 and opening S1.
After the capacitor gets fully charged, S1 is
opened and S2 is closed so that the inductor is connected in series
with the capacitor. Then,
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A
)
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at t = 0, energy stored in the circuit is purely in the form of magnetic energy
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B
)
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at any time t > 0, current in the circuit is in the same direction
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C
)
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at t > 0, there is no exchange of energy between the inductor and capacitor
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D
)
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at any time t > 0, instantaneous current in the circuit may
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| 23.
The capacitor of capacitance C can be charged
(with the help of a resistance R) by a
voltage source V, by closing switch S1
while keeping switch S2 open. The capacitor can
be connected in series with an inductor 'L' by closing
switch S2 and opening S1.
If the total charge stored in the LC
circuit is Q0, then for t ≥ 0
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A
)
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the charge on the capacitor is
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Q = Q0 cos(
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π
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+
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t
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)
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2
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B
)
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the charge on the capacitor is
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Q = Q0 cos(
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π
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-
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t
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)
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2
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C
)
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the charge on the capacitor is
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D
)
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the charge on the capacitor is
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Q = -
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1
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d2Q
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dt2
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| 24.
A wooden cylinder of diameter 4r, height h
and density ρ/3 is kept on a hole of
diameter 2r of a tank, filled with water
of density ρ as shown in the figure. The
height of the base of cylinder from the base of tank is H.
If level of liquid starts decreasing slowly when the level of liquid is at a
height h1 above the cylinder, the block just starts moving up. Then, value
of h1 is
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| 25.
A wooden cylinder of diameter 4r, height h
and density ρ/3 is kept on a hole of
diameter 2r of a tank, filled with water
of density ρ as shown in the figure. The
height of the base of cylinder from the base of tank is H.
Let the cylinder is prevented from moving up,
by applying a force and water level is further decreased. Then,
height of water level (h2 in figure) for which the
cylinder remains in original position without application of
force is
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| 26.
A wooden cylinder of diameter 4r, height h
and density ρ/3 is kept on a hole of
diameter 2r of a tank, filled with water
of density ρ as shown in the figure. The
height of the base of cylinder from the base of tank is H.
If height h2 of water level is further decreased, then
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A
)
|
cylinder will not move up and remains at its original position.
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B
)
|
for h2 = h/3, cylinder again starts moving up
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C
)
|
for h2 = h/4, cylinder again starts moving up
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D
)
|
for h2 = h/5 cylinder again starts moving up
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| 27.
The equation of two plane progressive sound waves are given as
y1 = A cos( 0.5πx-100πt)
and y2 = A cos( 0.46πx-92πt)
Answer the following equations based on nabove equation
Find the number of times
intensity is maximum in time interval of 1 sec.
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| 28.
The equation of two plane progressive sound waves are given as
y1 = A cos( 0.5πx-100πt)
and y2 = A cos( 0.46πx-92πt)
Answer the following equations based on nabove equation
Find wave velocity of louder sound
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| 29.
The equation of two plane progressive sound waves are given as
y1 = A cos( 0.5πx-100πt)
and y2 = A cos( 0.46πx-92πt)
Answer the following equations based on nabove equation
Find the number of times y1 + y2 = 0 at x = 0 in 1 sec
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| 30.
In conventional vehicle, power is dissipated due to friction.
To reduce the loss of power due to friction MAGLEV train using a new
technology called electro dynamic suspension (EDS) was developed by the
Japanese. The magnetized coil running along the track called the guide way,
repels the large magnets on the train's undercarriage, allowing the train
to levitate between 1 to 10cm above the guideway.
The electric current supplied to the coils in the guideway walls is constantly
alternating to change the polarity of the magentized coil. The hchange of the
polarity causes the magnetic field in front of the train to pull the vehicle
forward, while the magnetic field behind the train adds more forward thrust.
It works on the principle of Lenz's law. In this system a train moves without
contact with track or it flots on a cushion of air, eliminating friction.
In this system electromagnets are attached to the train and conducting coils
on the track. When th etrain moves there is a change of flux in the conducting
coil and due to induction the train is repelled by the track which lifts the train
above the track.
It also has stability factor. If the train comes downward the repulsive force
increases to restore its position and if it goes up, then repulsive force
decreases to bring it down..
Due to induced circulating currents an opposing force acts on the train. A
significant power is required to propel the train against the force at low speeds.
Choose the correct statement about MAGLEV train.
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A
)
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It is lifted due to magnetic repulsion
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B
)
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It moves due to magnetic attraction
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C
)
|
It is lifted due to electrostatic repulsion.
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D
)
|
It moves due to electrostatic attraction.
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| 31.
In conventional vehicle, power is dissipated due to friction.
To reduce the loss of power due to friction MAGLEV train using a new
technology called electro dynamic suspension (EDS) was developed by the
Japanese. The magnetized coil running along the track called the guide way,
repels the large magnets on the train's undercarriage, allowing the train
to levitate between 1 to 10cm above the guideway.
The electric current supplied to the coils in the guideway walls is constantly
alternating to change the polarity of the magentized coil. The hchange of the
polarity causes the magnetic field in front of the train to pull the vehicle
forward, while the magnetic field behind the train adds more forward thrust.
It works on the principle of Lenz's law. In this system a train moves without
contact with track or it flots on a cushion of air, eliminating friction.
In this system electromagnets are attached to the train and conducting coils
on the track. When th etrain moves there is a change of flux in the conducting
coil and due to induction the train is repelled by the track which lifts the train
above the track.
It also has stability factor. If the train comes downward the repulsive force
increases to restore its position and if it goes up, then repulsive force
decreases to bring it down..
Due to induced circulating currents an opposing force acts on the train. A
significant power is required to propel the train against the force at low speeds.
The disadvantge of EDS is
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A
)
|
Lot of energy is lost to start the motion as there is more opposition to the motion
at lower speeds
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B
)
|
repulsive force is conservative so it lifts the vehicle and bring down.
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C
)
|
magnetic force tends to bring down the train.
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D
)
|
It cannot overcome the force of gravity.
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| 32.
In conventional vehicle, power is dissipated due to friction.
To reduce the loss of power due to friction MAGLEV train using a new
technology called electro dynamic suspension (EDS) was developed by the
Japanese. The magnetized coil running along the track called the guide way,
repels the large magnets on the train's undercarriage, allowing the train
to levitate between 1 to 10cm above the guideway.
The electric current supplied to the coils in the guideway walls is constantly
alternating to change the polarity of the magentized coil. The hchange of the
polarity causes the magnetic field in front of the train to pull the vehicle
forward, while the magnetic field behind the train adds more forward thrust.
It works on the principle of Lenz's law. In this system a train moves without
contact with track or it flots on a cushion of air, eliminating friction.
In this system electromagnets are attached to the train and conducting coils
on the track. When th etrain moves there is a change of flux in the conducting
coil and due to induction the train is repelled by the track which lifts the train
above the track.
It also has stability factor. If the train comes downward the repulsive force
increases to restore its position and if it goes up, then repulsive force
decreases to bring it down..
Due to induced circulating currents an opposing force acts on the train. A
significant power is required to propel the train against the force at low speeds.
The advantge of EDS is that
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A
)
|
no force is required to overcome gravity
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B
)
|
no power is required to propel the train
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C
)
|
no energy is lost due to conservative force
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D
)
|
no power is dissipated against friction force
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| 33.
Subjective problem
There is a rectangular plate of mass M kg of dimensions (a x b). The plate
is held in horizontal position by striking n small balls each of mass m per
unit area per unit time. These are striking in the shaded half region of the
plate. The balls are colliding elastically with velocity v. What is v?
It is given n = 100, M = 3 kg, m = 0.01 kg; b = 2 m; a = 1 m; g = 10 m/s2.
Answer : 10 m/s
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| 34.
Subjective problem
In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final
temperature of the mixture.
Given, Lfusion = 80 cal/g = 336 J/g, Lvaporization = 540 cal/g = 2268 J/g,
Sice = 2100 J/kg K = 0.5 cal/gK and Swater = 4200 J/kg K = 1 cal /gK
Answer : final temperature of mixture is 0°C.
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| 35.
Subjective problem
In hydrogen-like atom (z = 11), nth line of Lyman
series has wavelength λ equal to the de-Broglie's
wavelength of electron in the level from which it originated.
What is the value of n?
Answer : 24
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| 36.
Subjective problem
A circular disc with a groove along its diameter is placed horizontally. A
block of mass 1 kg is placed as shown. The co-efficient of friction
between the block and all surfaces of groove in contact is μ = 2/5. The
disc has an acceleration of 25 m/s2. Find the acceleration of the block
with respect to disc.
Answer : 10 m/s2
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| 37.
Subjective problem
Heat given to process is positive, match the following option
of column I with the corresponding option of column II
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Column I
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Column II
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(A) JK
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(P) ΔW > 0
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(B) KL
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(Q) ΔQ < 0
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(C) LM
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(R) ΔW < 0
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(D) MJ
|
(S) ΔQ > 0
|
Answer :
(A)→(Q), (B)→(P), (S), (C)→(S), (D)→(Q),(R)
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| 38.
Subjective problem
Match the following Columns
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Column I
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Column II
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(A) Nuclear fusion
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(P) Converts some matter into energy
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(B) Nuclear fission
|
(Q) Generally possible for nuclei with low atomic number
|
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(C) β-decay
|
(R) Generally possible for nuclei with higher atomic number
|
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(D) Exothermic nuclear reaction
|
(S) Essentially proceeds by weak nuclear forces
|
Answer :
(A)→(P,Q), (B)→(P,R) , (C)→(S,P), (D)→(P,Q,R)
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| 39.
Subjective problem
Match the following Columns
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Column I
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Column II
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(A) Dielectric ring uniformly charged
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(P) Time independent electrostatic field out of system
|
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(B) Dielectric ring uniformly charged rotating
with angular velocity ω
|
(Q) Magnetic field
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(C) Constant current in ring i0
|
(R) Induced electric field
|
|
(D) i = i0 cos ωt
|
(S) Magnetic moment
|
Answer :
(A)→(P), (B)→(Q,S) , (C)→(Q,S), (D)→(Q,R,S)
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| 40.
Subjective problem
Match the following Columns
|
Column I
|
Column II
|
|
(A) Intensity of light received by lens
|
(P) Radius of aperture (R)
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(B) Angular magnification
|
(Q) Dispersion of lens
|
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(C) Length of telescope
|
(R) focal length f0, fe
|
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(D) Sharpness of image
|
(S) spherical aberration
|
Answer :
(A)→(P), (B)→(R) , (C)→(R), (D)→(P,Q,S)
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