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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2009

MCQ (Single Correct Answer)
A motor cycle starts from rest and accelerates along a straight path at $$2m/{s^2}.$$ At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $$94\% $$ of its value when the motor cycle was at rest? (Speed of sound $$ = 330\,m{s^{ - 1}}$$)
A
$$98$$ $$m$$
B
$$147$$ $$m$$
C
$$196\,m$$
D
$$49$$ $$m$$

Explanation



$$v_m^2 - {u^2} = 2as \Rightarrow v_m^2 = 2 \times 2 \times s$$

$$\therefore$$ $${v_m} = 2\sqrt s $$

According to Doppler's effect

$$0.94v = v\left[ {{{330 - 2\sqrt s } \over {330}}} \right] \Rightarrow s = 98.01\,m$$
2

AIEEE 2009

MCQ (Single Correct Answer)
Three sound waves of equal amplitudes have frequencies $$\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$$ They superpose to give beats. The number of beats produced per second will be :
A
$$3$$
B
$$2$$
C
$$1$$
D
$$4$$

Explanation

Maximum number of beats $$ = \left( {v + 1} \right) - \left( {v - 1} \right) = 2$$
3

AIEEE 2008

MCQ (Single Correct Answer)
A wave travelling along the $$x$$-axis is described by the equation $$y(x, t)=0.005$$ $$\cos \,\left( {\alpha \,x - \beta t} \right).$$ If the wavelength and the time period of the wave are $$0.08$$ $$m$$ and $$2.0s$$, respectively, then $$\alpha $$ and $$\beta $$ in appropriate units are
A
$$\alpha = 25.00\pi ,\,\beta = \pi $$
B
$$\alpha = {{0.08} \over \pi },\,\beta = {{2.0} \over \pi }$$
C
$$\alpha = {{0.04} \over \pi },\,\beta = {{1.0} \over \pi }$$
D
$$\alpha = 12.50\pi ,\,\beta = {\pi \over {2.0}}$$

Explanation

$$y\left( {x,t} \right) = 0.005\,\cos \left( {\alpha x - \beta t} \right)$$ (Given)

Comparing it with the standard equation of wave

$$y\left( {x,t} \right) = a\cos \left( {kx - \omega t} \right)$$ we get

$$k = \alpha $$ $$\,\,\,\,\,$$ and $$\,\,\,\,\,$$ $$\omega = \beta $$

$$\therefore$$ $${{2\pi } \over \gamma } = \alpha $$ $$\,\,\,\,\,$$ and $$\,\,\,\,\,$$ $${{2\pi } \over T} = \beta $$

$$\therefore$$ $$\alpha = {{2\pi } \over {0.08}} = 25\pi $$ $$\,\,\,\,\,$$ and $$\,\,\,\,\,$$ $$\beta = {{2\pi } \over 2} = \pi $$
4

AIEEE 2007

MCQ (Single Correct Answer)
A sound absorber attenuates the sound level by $$20$$ $$dB$$. The intensity decreases by a factor of
A
$$100$$
B
$$1000$$
C
$$10000$$
D
$$10$$

Explanation

We have, $${L_1} = 10\log \left( {{{{{\rm I}_1}} \over {{{\rm I}_0}}}} \right);$$

$${L_2} = 10\,\log \left( {{{{{\rm I}_2}} \over {{{\rm I}_0}}}} \right)$$

$$\therefore$$ $$\,\,{L_1} - {L_2} = 10\,\log \left( {{{{{\rm I}_1}} \over {{{\rm I}_0}}}} \right) - 10\,\log \left( {{{{{\rm I}_2}} \over {{{\rm I}_0}}}} \right)$$

or, $$\Delta L = 10\,\log \left( {{{{{\rm I}_1}} \over {{{\rm I}_0}}} \times {{{{\rm I}_0}} \over {{{\rm I}_2}}}} \right)$$

or, $$\Delta L = 10\,\log \left( {{{{{\rm I}_1}} \over {{{\rm I}_2}}}} \right)$$

or, $$20 = 10\log \left( {{{{{\rm I}_1}} \over {{{\rm I}_2}}}} \right)$$

or, $$2 = \log \left( {{{{{\rm I}_1}} \over {{{\rm I}_2}}}} \right)$$

or, $${{{{\rm I}_1}} \over {{{\rm I}_2}}} = {10^2}$$

or, $${{\rm I}_2} = {{{{\rm I}_1}} \over {100}}.$$

$$ \Rightarrow $$ Intensity decreases by a factor $$100.$$

Questions Asked from Waves

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