JEE Mains Previous Years Questions with Solutions Android App

Download our App

JEE Mains Previous Years Questions with Solutions

4.5 
star star star star star
  (100k+ download)
1

AIEEE 2006

MCQ (Single Correct Answer)
Starting from the origin a body oscillates simple harmonically with a period of $$2$$ $$s.$$ After what time will its kinetic energy be $$75\% $$ of the total energy?
A
$${1 \over 6}s$$
B
$${1 \over 4}s$$
C
$${1 \over 3}s$$
D
$${1 \over 12}s$$

Explanation

$$K.E.\,$$ of a body undergoing $$SHM$$ is given by,

$$K.E. = {1 \over 2}m{a^2}{\omega ^2}{\cos ^2}\,\omega t,$$

$$T.E. = {1 \over 2}m{a^2}{\omega ^2}$$

Given $$K.E.=0.75T.E.$$

$$ \Rightarrow 0.75 = {\cos ^2}\omega t \Rightarrow \omega t = {\pi \over 6}$$

$$ \Rightarrow t = {\pi \over {6 \times \omega }} \Rightarrow t = {{\pi \times 2} \over {6 \times 2\pi }} \Rightarrow t = {1 \over 6}s$$
2

AIEEE 2006

MCQ (Single Correct Answer)
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A
at the mean position of the platform
B
for an amplitude of $${g \over {{\omega ^2}}}$$
C
For an amplitude of $${{{g^2}} \over {{\omega ^2}}}$$
D
at the height position of the platform

Explanation

Coin $$A$$ is moving in simple harmonic motion in vertical direction. Now we are assuming coin will leave contact with the platform when platform is at a distance of $$x$$ from the mean position which is also called amplitude.
At distance $$x$$ the force acting on the coin is

$$mg - N = m{\omega ^2}x$$

For coin to leave contact $$N=0$$

$$ \Rightarrow mg = m{\omega ^2}x \Rightarrow x = {g \over {{\omega ^2}}}$$

$$\therefore$$ Option (B) is correct.
3

AIEEE 2005

MCQ (Single Correct Answer)
If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is
A
$${{2\pi } \over {\sqrt \alpha }}$$
B
$${{2\pi } \over \alpha }$$
C
$$2\pi \sqrt \alpha $$
D
$$2\pi \alpha $$

Explanation

$${{{d^2}x} \over {d{t^2}}} = - \alpha x = - {\omega ^2}x$$

$$ \Rightarrow \omega = \sqrt \alpha $$ $$\,\,\,\,$$ or $$\,\,\,\,$$ $$T = {{2\pi } \over \omega } = {{2\pi } \over {\sqrt \alpha }}$$
4

AIEEE 2005

MCQ (Single Correct Answer)
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
A
first decrease and then increase to the original value
B
first increase and then decrease to the original value
C
increase towards a saturation value
D
remain unchanged

Explanation

Center of mass of combination of liquid and hollow portion (at position $$\ell $$ ), first goes down (to $$\ell + \Delta \ell $$) and when total water is drained out, center of mass regain its original position (to $$\ell $$), $$$T = 2\pi \sqrt {{\ell \over g}} $$$

$$\therefore$$ $$'T'$$ first increases and then decreases to original value.

Questions Asked from Simple Harmonic Motion

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2021 (Online) 1st September Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 31st August Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 22th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th February Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Evening Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Evening Shift (2)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (3)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2018 (Online) 16th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Online) 8th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2016 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2016 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2016 (Offline) (1)
keyboard_arrow_right
JEE Main 2015 (Offline) (2)
keyboard_arrow_right
JEE Main 2014 (Offline) (1)
keyboard_arrow_right
JEE Main 2013 (Offline) (2)
keyboard_arrow_right
AIEEE 2012 (1)
keyboard_arrow_right
AIEEE 2011 (2)
keyboard_arrow_right
AIEEE 2009 (1)
keyboard_arrow_right
AIEEE 2007 (4)
keyboard_arrow_right
AIEEE 2006 (3)
keyboard_arrow_right
AIEEE 2005 (4)
keyboard_arrow_right
AIEEE 2004 (5)
keyboard_arrow_right
AIEEE 2003 (5)
keyboard_arrow_right
AIEEE 2002 (3)
keyboard_arrow_right

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE ME GATE PI GATE EE GATE CE GATE IN

Medical

NEET

CBSE

Class 12