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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2003

MCQ (Single Correct Answer)
A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is
A
12 m
B
18 m
C
24 m
D
6 m

Explanation

For case 1 :
u = 50 km/hr = $${{50 \times 1000} \over {3600}}$$ m/s = $${{125} \over 9}$$ m/s, v = 0, s = 6 m, $$a$$ = ?

$$\therefore$$ 02 = u2 + 2$$a$$s

$$ \Rightarrow $$ $$a = - {{{u^2}} \over {2s}}$$

$$ \Rightarrow $$ $$a = - {{{{\left( {{{125} \over 9}} \right)}^2}} \over {2 \times 6}}$$ = $$-$$16 m/s2

For case 2 :
u = 100 km/hr = $${{100 \times 1000} \over {3600}}$$ m/s = $${{250} \over 9}$$ m/s, v = 0, $$a$$ = $$-$$16, s = ?

$$\therefore$$ 02 = u2 + 2$$a$$s

$$ \Rightarrow $$ $$s = - {{{u^2}} \over {2a}}$$

$$ \Rightarrow $$ $$s = - {{{{\left( {{{250} \over 9}} \right)}^2}} \over {2 \times -16}}$$ = 24 m
2

AIEEE 2002

MCQ (Single Correct Answer)
Speeds of two identical cars are $$u $$ and $$4$$$$u $$ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is
A
$$1:1$$
B
$$1:4$$
C
$$1:8$$
D
$$1:16$$

Explanation

Given that initial speed of two cars $$u$$ and $$4u$$ and final speed $$v$$ is 0 for both car. Both car is gradually slowing down so acceleration = $$(-a)$$

So formula becomes, 0 = $${u^2}$$ - 2$$a$$s.

$$ \Rightarrow {u^2} = 2as$$

For first car $${u^2} = 2a{s_1}$$ ..........(i)

For second car $${\left( {4u} \right)^2} = 2a{s_2}$$ ..........(ii)

Dividing $$(i)$$ and $$(ii),$$

$${{{u^2}} \over {16{u^2}}} = {{2a{s_1}} \over {2a{s_2}}}$$

$$ \Rightarrow {1 \over {16}} = {{{s_1}} \over {{s_2}}}$$
3

AIEEE 2002

MCQ (Single Correct Answer)
From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If vA and vB are their respective velocities on reaching the ground, then
A
$${v_B} > {v_A}$$
B
$${v_A} = {v_B}$$
C
$${v_A} > {v_B}$$
D
their velocities depend on their masses.

Explanation


Assume the initial velocity of each particle is = u

And height of building = h

If final velocity of A is vA then vA2 = u2 + 2(-g)(-h) = u2 + 2gh

If final velocity of B is vB then vB2 = u2 + 2gh

$$\therefore$$ vA = vB

Sign Rule : Take the direction of initial velocity positive opposite direction as negative.

Here for ball A initial velocity u is upward so upward is positive and downward is negative. That is why gravity is = - g and height = - h

And for ball B initial velocity u is downward so downward is positive and upward is negative. That is why gravity is = + g and height = + h
4

AIEEE 2002

MCQ (Single Correct Answer)
A ball whose kinetic energy E, is projected at an angle of $$45^\circ $$ to the horizontal. The kinetic energy of the ball at the highest point of its height will be
A
E
B
$${E \over {\sqrt 2 }}$$
C
$${E \over 2}$$
D
zero

Explanation

Assume the ball of mass m is projected with a speed u. Then the kinetic energy(E) at the point of projection = $${1 \over 2}m{u^2}$$

At highest point of flight only horizontal component of velocity $$u\cos \theta $$ present as at highest point vertical component of velocity is = 0.

Note : The horizontal component of velocity does not change in entire projectile motion.

At highest point the velocity is = $$u\cos \theta $$ = $$u\cos 45^\circ $$ = $${u \over {\sqrt 2 }}$$

$$\therefore$$ The kinetic energy at the height point = $${1 \over 2}m{\left( {{u \over {\sqrt 2 }}} \right)^2}$$

= $${1 \over 2}m{u^2} \times {1 \over 2}$$ = $${E \over 2}$$

Questions Asked from Motion

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
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JEE Main 2021 (Online) 25th July Evening Shift (3)
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JEE Main 2021 (Online) 18th March Evening Shift (1)
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JEE Main 2021 (Online) 17th March Evening Shift (2)
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JEE Main 2021 (Online) 17th March Morning Shift (1)
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JEE Main 2021 (Online) 16th March Evening Shift (1)
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JEE Main 2021 (Online) 16th March Morning Shift (1)
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JEE Main 2021 (Online) 26th February Evening Shift (2)
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JEE Main 2021 (Online) 25th February Evening Shift (1)
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JEE Main 2021 (Online) 25th February Morning Shift (2)
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JEE Main 2021 (Online) 24th February Morning Shift (1)
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JEE Main 2020 (Online) 6th September Evening Slot (1)
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JEE Main 2020 (Online) 5th September Evening Slot (2)
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JEE Main 2020 (Online) 5th September Morning Slot (2)
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JEE Main 2020 (Online) 4th September Morning Slot (2)
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JEE Main 2020 (Online) 3rd September Evening Slot (1)
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JEE Main 2020 (Online) 2nd September Morning Slot (1)
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JEE Main 2020 (Online) 9th January Evening Slot (1)
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JEE Main 2020 (Online) 8th January Evening Slot (1)
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JEE Main 2019 (Online) 12th April Evening Slot (2)
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JEE Main 2019 (Online) 12th April Morning Slot (2)
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JEE Main 2019 (Online) 10th April Evening Slot (1)
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JEE Main 2019 (Online) 10th April Morning Slot (1)
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JEE Main 2019 (Online) 9th April Evening Slot (2)
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JEE Main 2019 (Online) 9th April Morning Slot (1)
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JEE Main 2019 (Online) 8th April Evening Slot (2)
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JEE Main 2019 (Online) 8th April Morning Slot (1)
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JEE Main 2019 (Online) 12th January Morning Slot (2)
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JEE Main 2019 (Online) 11th January Evening Slot (1)
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JEE Main 2019 (Online) 11th January Morning Slot (1)
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JEE Main 2019 (Online) 10th January Evening Slot (2)
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JEE Main 2019 (Online) 10th January Morning Slot (2)
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JEE Main 2019 (Online) 9th January Evening Slot (2)
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JEE Main 2019 (Online) 9th January Morning Slot (1)
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JEE Main 2018 (Online) 16th April Morning Slot (1)
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JEE Main 2018 (Online) 15th April Evening Slot (1)
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JEE Main 2018 (Offline) (1)
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JEE Main 2018 (Online) 15th April Morning Slot (2)
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JEE Main 2017 (Online) 9th April Morning Slot (1)
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JEE Main 2017 (Online) 8th April Morning Slot (1)
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JEE Main 2017 (Offline) (1)
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JEE Main 2015 (Offline) (1)
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JEE Main 2014 (Offline) (1)
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JEE Main 2013 (Offline) (1)
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AIEEE 2012 (2)
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AIEEE 2011 (2)
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AIEEE 2010 (4)
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AIEEE 2009 (2)
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AIEEE 2008 (1)
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AIEEE 2007 (2)
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AIEEE 2006 (1)
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AIEEE 2005 (3)
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AIEEE 2004 (6)
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AIEEE 2003 (3)
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AIEEE 2002 (3)
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