1
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
$$y(t) = A\sin {{5\pi x} \over 2}\cos 250\pi t$$
2
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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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 $$\left( {M = 36,\sqrt {{{10} \over {36}}} = {{17} \over {32}}} \right)$$
3
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is(are)

A
If the wind blows from the observer to the source, f2 > f1.
B
If the wind blows from the source to the observer, f2 > f1.
C
If the wind blows from the observer to the source, f2 < f1
D
If the wind blows from the source to the observer, f2 < f1.
4
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation

y(x, t) = (0.01 m) sin[(62.8 m$$-$$1)x] cos[(628 s$$-$$1)t]

Assuming $$\pi$$ = 3.14, the correct statement(s) is(are)

A
The number of nodes is 5.
B
The length of the string is 0.25 m.
C
The maximum displacement of the mid-point of the string, from its equilibrium position is 0.01 m.
D
The fundamental frequency is 100 Hz.
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