1
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A block $$M$$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to fixed rigid support at $$O.$$ A transverse wave pulse (Pulse 1) of wavelength $${\lambda _0}$$ is produced at point $$O$$ on the rope. The pulse takes time $${T_{OA}}$$ to reach point $$A.$$ If the wave pulse of wavelength $${\lambda _0}$$ is produced at point $$A$$ (Pulse 2) without disturbing the position of $$M$$ it takes time $${T_{AO}}$$ to reach point $$O.$$ which of the following options is/are correct?

A
The time $${T_{AO}} = {T_{OA}}$$
B
The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
C
The wavelength of Pulse 1 becomes longer when it reaches point $$A$$
D
The velocity of any pulse along the rope is independent of its frequency and wavelength
2
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Two loudspeakers M and N are located 20m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car in initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/h along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q.

Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vP, vQ and vR be the beat frequencies measured at locations P, Q and R respectively. The speed of sound in air is 330 ms$$-$$1. Which of the following statement(s) is (are) true regarding the sound heard by the person?
A
The plot below represents schematically the variation of beat frequency with time
B
The rate of change in beat frequency is maximum when the car passes through Q
C
vP + vR = 2vQ
D
The plot below represents schematically the variations of beat frequency with time

3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
One end of a taut string of length 3 m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms$$-$$1. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary wave is (are)
A
$$y(t) = A\sin {{\pi x} \over 6}\cos {{50\pi t} \over 3}$$
B
$$y(t) = A\sin {{\pi x} \over 3}\cos {{100\pi t} \over 3}$$
C
$$y(t) = A\sin {{5\pi x} \over 6}\cos {{250\pi t} \over 3}$$
D
$$y(t) = A\sin {{5\pi x} \over 2}\cos 250\pi t$$
4
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s$$-$$1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 $$\pm$$ 0.005) m, the gas in the tube is

(Useful information : $$\sqrt {167RT}$$ = 640 J1/2 mol$$-$$1/2; $$\sqrt {140RT}$$ = 590 J1/2 mol$$-$$1/2. The molar mass M in grams is given in the options. Take the values of $$\sqrt {10/M}$$ for each gas as given there.)
A
Neon $$\left( {M = 20,\sqrt {{{10} \over {20}}} = {7 \over {10}}} \right)$$
B
Nitrogen $$\left( {M = 28,\sqrt {{{10} \over {28}}} = {3 \over 5}} \right)$$
C
Oxygen $$\left( {M = 32,\sqrt {{{10} \over {32}}} = {9 \over {16}}} \right)$$
D
Argon $$\left( {M = 36,\sqrt {{{10} \over {36}}} = {{17} \over {32}}} \right)$$
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