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JEE Mains Previous Years Questions with Solutions

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1

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)
The motion of a mass on a spring, with spring constant K is as shown in figure.


The equation of motion is given by
x(t) = A sin$$\omega$$t + B cos$$\omega$$t with $$\omega$$ = $$\sqrt {{K \over m}} $$

Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos($$\omega$$t $$-$$ $$\phi$$), where C and $$\phi$$ are :
A
$$C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{x(0)\omega } \over {2v(0)}}} \right)$$
B
$$C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{x(0)\omega } \over {v(0)}}} \right)$$
C
$$C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} \right)$$
D
$$C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} \right)$$

Explanation

$$C\cos \phi = x(0)$$

$$tC\omega \sin \phi = v(0)$$

$${\left[ {{{v(0)} \over \omega }} \right]^2} + {[x(0)]^2} = {C^2}$$

$$\tan \phi = {{v(0)} \over {x(0)\omega }}$$
2

JEE Main 2021 (Online) 17th March Evening Shift

MCQ (Single Correct Answer)
A sound wave of frequency 245 Hz travels with the speed of 300 ms$$-$$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?
A
Y(x, t) = 0.03 [ sin 5.1x $$-$$ (0.2 $$\times$$ 103)t ]
B
Y(x, t) = 0.03 [ sin 5.1x $$-$$ (1.5 $$\times$$ 103)t ]
C
Y(x, t) = 0.06 [ sin 5.1x $$-$$ (1.5 $$\times$$ 103)t ]
D
Y(x, t) = 0.06 [ sin 0.8x $$-$$ (0.5 $$\times$$ 103)t ]

Explanation

$$Y = A\sin (kx - \omega t)$$

$$A = {6 \over 2}$$ = 3cm = 0.03 m

$$\omega = 2\pi f = 2\pi \times 245$$

$$\omega = 1.5 \times {10^3}$$

$$k = {\omega \over v} = {{1.5 \times {{10}^3}} \over {300}}$$

$$k = 5.1$$

$$y = 0.03\sin (5.1x - (1.5 \times {10^3})t)$$
3

JEE Main 2021 (Online) 17th March Morning Shift

MCQ (Single Correct Answer)
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?
A
x = $${A \over 2}$$
B
x = $$\pm$$ A
C
x = $$\pm$$ $${A \over {\sqrt 2 }}$$
D
x = 0

Explanation

KE = PE

$${1 \over 2}k({A^2} - {X^2}) = {1 \over 2}K{X^2}$$

$$ \Rightarrow $$ $${A^2} - {X^2} = {X^2}$$

$$ \Rightarrow $$ $$2{X^2} = {A^2}$$

$$ \Rightarrow $$ $${X^2} = {{{A^2}} \over {\sqrt 2 }}$$

$$ \Rightarrow $$ $$X = \pm {A \over {\sqrt 2 }}$$
4

JEE Main 2021 (Online) 26th February Evening Shift

MCQ (Single Correct Answer)
A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is field, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?
A
335 Hz
B
345 Hz
C
338 Hz
D
342 Hz

Explanation

Initially beat frequency = 5Hz

so, $$\rho$$A = 340 $$ \pm $$ 5 = 345 Hz, or 335 Hz

after filing frequency increases slightly so, new value of frequency of A > $$\rho$$A

Now, beat frequency = 2Hz

$$ \Rightarrow $$ new $$\rho$$A = 340 $$ \pm $$ 2 = 342 Hz, or 338 Hz

hence, original frequency of A is $$\rho$$A = 335 Hz

Questions Asked from Waves

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2021 (Online) 22th July Evening Shift (1)
JEE Main 2021 (Online) 17th March Evening Shift (1)
JEE Main 2021 (Online) 17th March Morning Shift (1)
JEE Main 2021 (Online) 26th February Evening Shift (1)
JEE Main 2021 (Online) 25th February Morning Shift (1)
JEE Main 2021 (Online) 24th February Evening Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 6th September Morning Slot (1)
JEE Main 2020 (Online) 5th September Evening Slot (2)
JEE Main 2020 (Online) 4th September Evening Slot (1)
JEE Main 2020 (Online) 4th September Morning Slot (1)
JEE Main 2020 (Online) 3rd September Morning Slot (1)
JEE Main 2020 (Online) 2nd September Morning Slot (1)
JEE Main 2020 (Online) 9th January Morning Slot (1)
JEE Main 2020 (Online) 8th January Evening Slot (1)
JEE Main 2020 (Online) 7th January Evening Slot (1)
JEE Main 2020 (Online) 7th January Morning Slot (1)
JEE Main 2019 (Online) 12th April Evening Slot (3)
JEE Main 2019 (Online) 12th April Morning Slot (2)
JEE Main 2019 (Online) 10th April Evening Slot (2)
JEE Main 2019 (Online) 10th April Morning Slot (2)
JEE Main 2019 (Online) 9th April Evening Slot (2)
JEE Main 2019 (Online) 9th April Morning Slot (2)
JEE Main 2019 (Online) 8th April Evening Slot (1)
JEE Main 2019 (Online) 8th April Morning Slot (1)
JEE Main 2019 (Online) 12th January Evening Slot (1)
JEE Main 2019 (Online) 11th January Morning Slot (1)
JEE Main 2019 (Online) 10th January Morning Slot (3)
JEE Main 2019 (Online) 9th January Evening Slot (2)
JEE Main 2019 (Online) 9th January Morning Slot (1)
JEE Main 2018 (Online) 16th April Morning Slot (2)
JEE Main 2018 (Offline) (2)
JEE Main 2018 (Online) 15th April Evening Slot (1)
JEE Main 2018 (Online) 15th April Morning Slot (1)
JEE Main 2017 (Online) 9th April Morning Slot (2)
JEE Main 2017 (Online) 8th April Morning Slot (1)
JEE Main 2017 (Offline) (1)
JEE Main 2016 (Online) 10th April Morning Slot (1)
JEE Main 2016 (Online) 9th April Morning Slot (1)
JEE Main 2016 (Offline) (2)
JEE Main 2015 (Offline) (1)
JEE Main 2014 (Offline) (1)
JEE Main 2013 (Offline) (1)
AIEEE 2012 (1)
AIEEE 2011 (1)
AIEEE 2010 (1)
AIEEE 2009 (2)
AIEEE 2008 (2)
AIEEE 2007 (1)
AIEEE 2006 (2)
AIEEE 2005 (2)
AIEEE 2004 (1)
AIEEE 2003 (3)
AIEEE 2002 (5)

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