Joint Entrance Examination

Graduate Aptitude Test in Engineering

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

1

MCQ (Single Correct Answer)

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the
particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation
between H, u and n is:

A

2gH = n^{2}u^{2}

B

gH = (n - 2)^{2}u^{2}

C

2gH = nu^{2}(n - 2)

D

gH = (n - 2)u^{2}

Time taken to reach highest point is $$t = {u \over g}$$

Time taken by the particle to reach the ground = $$nt = {nu \over g}$$

Speed on reaching ground $$v = \sqrt {{u^2} + 2gH} $$

Now, $$v = u + at$$

$$ \Rightarrow \sqrt {{u^2} + 2gH} = - u + gt$$

$$ \Rightarrow t = {{u + \sqrt {{u^2} + 2gH} } \over g} = {{nu} \over g}$$ (from question)

$$ \Rightarrow 2gH = n\left( {n - 2} \right){u^2}$$

2

MCQ (Single Correct Answer)

A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ is along the ground and $${\widehat j}$$ is along the
vertical. If g = 10 m/s^{2}, the equation of its trajectory is:

A

y = x - 5x^{2}

B

y = 2x - 5x^{2}

C

4y = 2x - 5x^{2}

D

4y = 2x - 25x^{2}

$$\overrightarrow u = \widehat i + 2\widehat j = {u_x}\widehat i + {u_y}\widehat j$$

$$ \Rightarrow u\cos \theta = 1,u\sin \theta = 2$$

Also $$x = {u_x}t$$ and

$$y = {u_y}t - {1 \over 2}g{t^2}$$

$$ \Rightarrow $$ $$y = x\tan \theta - {1 \over 2}{{g{x^2}} \over {u_x^2}}$$

$$\therefore$$ $$y = 2x - {1 \over 2}g{x^2} = 2x - 5{x^2}$$

$$ \Rightarrow u\cos \theta = 1,u\sin \theta = 2$$

Also $$x = {u_x}t$$ and

$$y = {u_y}t - {1 \over 2}g{t^2}$$

$$ \Rightarrow $$ $$y = x\tan \theta - {1 \over 2}{{g{x^2}} \over {u_x^2}}$$

$$\therefore$$ $$y = 2x - {1 \over 2}g{x^2} = 2x - 5{x^2}$$

3

MCQ (Single Correct Answer)

A particle of mass $$m$$ is at rest at the origin at time $$t=0.$$ It is subjected to a force $$F\left( t \right) = {F_0}{e^{ - bt}}$$ in the $$x$$ direction. Its speed $$v(t)$$ is depicted by which of the following curves?

A

B

C

D

Given that $$F\left( t \right) = {F_0}{e^{ - bt}} $$

$$\Rightarrow m{{dv} \over {dt}} = {F_0}{e^{ - bt}}$$

$${{dv} \over {dt}} = {{{F_0}} \over m}{e^{ - bt}} $$

$$\Rightarrow \int\limits_0^v {dv} = {{{F_0}} \over m}\int\limits_0^t {{e^{ - bt}}} \,dt$$

$$v = {{{F_0}} \over m}\left[ {{{{e^{ - bt}}} \over { - b}}} \right]_0^t = {{{F_0}} \over {mb}}\left[ { - \left( {{e^{ - bt}} - {e^{ - 0}}} \right)} \right]$$

$$ \Rightarrow v = {{{F_0}} \over {mb}}\left[ {1 - {e^{ - bt}}} \right]$$

$$ \Rightarrow v_{max} = {{{F_0}} \over {mb}}$$

$$\Rightarrow m{{dv} \over {dt}} = {F_0}{e^{ - bt}}$$

$${{dv} \over {dt}} = {{{F_0}} \over m}{e^{ - bt}} $$

$$\Rightarrow \int\limits_0^v {dv} = {{{F_0}} \over m}\int\limits_0^t {{e^{ - bt}}} \,dt$$

$$v = {{{F_0}} \over m}\left[ {{{{e^{ - bt}}} \over { - b}}} \right]_0^t = {{{F_0}} \over {mb}}\left[ { - \left( {{e^{ - bt}} - {e^{ - 0}}} \right)} \right]$$

$$ \Rightarrow v = {{{F_0}} \over {mb}}\left[ {1 - {e^{ - bt}}} \right]$$

$$ \Rightarrow v_{max} = {{{F_0}} \over {mb}}$$

4

MCQ (Single Correct Answer)

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy
can throw the same stone up to will be

A

$$20\sqrt 2 $$ m

B

10 m

C

$$10\sqrt 2 $$ m

D

20 m

We know, $$R = {{{u^2}{{\sin }2}\theta } \over g}$$ and $$H = {{{u^2}{{\sin }^2}\theta } \over {2g}};$$

$${H_{\max }}\,\,$$ is possible when $$\theta = 90$$$$^\circ $$

$${H_{\max }} = {{{u^2}} \over {2g}} = 10 \Rightarrow {u^2} = 10g \times 2$$

As $$R = {{{u^2}\sin 2\theta } \over g}$$

Range is maximum when projectile is thrown at an angle $$45^\circ $$.

$$ \Rightarrow {R_{\max }} = {{{u^2}} \over g}$$

$${R_{\max }} = {{10 \times g \times 2} \over g} = 20$$ meter

$${H_{\max }}\,\,$$ is possible when $$\theta = 90$$$$^\circ $$

$${H_{\max }} = {{{u^2}} \over {2g}} = 10 \Rightarrow {u^2} = 10g \times 2$$

As $$R = {{{u^2}\sin 2\theta } \over g}$$

Range is maximum when projectile is thrown at an angle $$45^\circ $$.

$$ \Rightarrow {R_{\max }} = {{{u^2}} \over g}$$

$${R_{\max }} = {{10 \times g \times 2} \over g} = 20$$ meter

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 Morning Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 27th August Evening Shift (2) *keyboard_arrow_right*

JEE Main 2021 (Online) 26th August 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 (3) *keyboard_arrow_right*

JEE Main 2021 (Online) 25th July Morning Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 20th July Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 20th July Morning Shift (1) *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) 17th March Morning Shift (1) *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 (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 25th February Morning Shift (2) *keyboard_arrow_right*

JEE Main 2021 (Online) 24th February Morning Shift (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 6th September Evening Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 5th September Evening Slot (2) *keyboard_arrow_right*

JEE Main 2020 (Online) 5th September Morning Slot (2) *keyboard_arrow_right*

JEE Main 2020 (Online) 4th September Morning Slot (2) *keyboard_arrow_right*

JEE Main 2020 (Online) 3rd 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 April Evening Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 12th April Morning Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th April Evening Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 8th April Evening Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 8th April Morning 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 (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 11th January Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th January Evening Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th January Morning Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th January Evening Slot (2) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th January Morning Slot (1) *keyboard_arrow_right*

JEE Main 2018 (Online) 16th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2018 (Online) 15th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2018 (Offline) (1) *keyboard_arrow_right*

JEE Main 2018 (Online) 15th April Morning Slot (2) *keyboard_arrow_right*

JEE Main 2017 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2017 (Online) 8th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2017 (Offline) (1) *keyboard_arrow_right*

JEE Main 2015 (Offline) (1) *keyboard_arrow_right*

JEE Main 2014 (Offline) (1) *keyboard_arrow_right*

JEE Main 2013 (Offline) (1) *keyboard_arrow_right*

AIEEE 2012 (2) *keyboard_arrow_right*

AIEEE 2011 (2) *keyboard_arrow_right*

AIEEE 2010 (4) *keyboard_arrow_right*

AIEEE 2009 (2) *keyboard_arrow_right*

AIEEE 2008 (1) *keyboard_arrow_right*

AIEEE 2007 (2) *keyboard_arrow_right*

AIEEE 2006 (1) *keyboard_arrow_right*

AIEEE 2005 (3) *keyboard_arrow_right*

AIEEE 2004 (6) *keyboard_arrow_right*

AIEEE 2003 (3) *keyboard_arrow_right*

AIEEE 2002 (3) *keyboard_arrow_right*

Units & Measurements *keyboard_arrow_right*

Motion *keyboard_arrow_right*

Laws of Motion *keyboard_arrow_right*

Work Power & Energy *keyboard_arrow_right*

Simple Harmonic Motion *keyboard_arrow_right*

Impulse & Momentum *keyboard_arrow_right*

Rotational Motion *keyboard_arrow_right*

Gravitation *keyboard_arrow_right*

Properties of Matter *keyboard_arrow_right*

Heat and Thermodynamics *keyboard_arrow_right*

Waves *keyboard_arrow_right*

Vector Algebra *keyboard_arrow_right*

Ray & Wave Optics *keyboard_arrow_right*

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*

Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

Practical Physics *keyboard_arrow_right*

Dual Nature of Radiation *keyboard_arrow_right*