Joint Entrance Examination

Graduate Aptitude Test in Engineering

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

1

MCQ (Single Correct Answer)

A block of mass $$m$$ is placed on a surface with a vertical cross section given by $$y = {{{x^3}} \over 6}.$$ If the coefficient of friction is $$0.5,$$ the maximum height above the ground at which the block can be placed without slipping is:

A

$${1 \over 6}m$$

B

$${2 \over 3}m$$

C

$${1 \over 3}m$$

D

$${1 \over 2}m$$

At limiting equilibrium, $$\mu = \tan \theta $$

Equation of the surface,

$$y = {{{x^3}} \over 6}$$

Slope, $$\tan \theta = \mu = {{dy} \over {dx}} = {{{x^2}} \over 2}$$

Given that, Coefficient of friction $$\mu = 0.5$$

$$\therefore$$ $$\,\,\,\,0.5 = {{{x^2}} \over 2}$$

$$ \Rightarrow \,\,\,x = \pm \,1$$

Now, $$y = {{{x^3}} \over 6} = {1 \over 6}m$$

Equation of the surface,

$$y = {{{x^3}} \over 6}$$

Slope, $$\tan \theta = \mu = {{dy} \over {dx}} = {{{x^2}} \over 2}$$

Given that, Coefficient of friction $$\mu = 0.5$$

$$\therefore$$ $$\,\,\,\,0.5 = {{{x^2}} \over 2}$$

$$ \Rightarrow \,\,\,x = \pm \,1$$

Now, $$y = {{{x^3}} \over 6} = {1 \over 6}m$$

2

MCQ (Single Correct Answer)

Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown in the figure. Two blocks $$A$$ and $$B$$ are placed on the two planes. What is the relative vertical acceleration of $$A$$ with respect to $$B$$ ?

A

$$4.9m{s^{ - 2}}$$ in horizontal direction

B

$$9.8m{s^{ - 2}}$$ in vertical direction

C

Zero

D

$$4.9m{s^{ - 2}}$$ in vertical direction

Along inclined plane the equation of motion of the body

$$mg\,\sin \,\theta = ma$$ $$\,\,\,\,\,\,\,\,$$ $$\therefore$$ $$a = g\,\sin \,\theta $$

where $$a$$ is along the inclined plane.

$$\therefore$$ vertical component of acceleration is $$\left( {g\sin \theta } \right)\sin \theta $$ = $$g\,{\sin ^2}\theta $$ (Along vertical)

For block A,

$${a_{A\left( {along\,vertical} \right)}} = g{\sin ^2}60^\circ $$

For block B,

$${a_{B\left( {along\,vertical} \right)}} = g{\sin ^2}30^\circ $$

$$\therefore$$ relative vertical acceleration of $$A$$ with respect to $$B$$ is

$$g{\sin ^2}60^\circ $$ - $$g{\sin ^2}30^\circ $$

=$$g\left( {{{\sin }^2}60 - {{\sin }^2}\left. {30} \right]} \right.$$

$$= 4.9$$ $$\,\,m/{s^2}$$ in vertical direction

$$mg\,\sin \,\theta = ma$$ $$\,\,\,\,\,\,\,\,$$ $$\therefore$$ $$a = g\,\sin \,\theta $$

where $$a$$ is along the inclined plane.

$$\therefore$$ vertical component of acceleration is $$\left( {g\sin \theta } \right)\sin \theta $$ = $$g\,{\sin ^2}\theta $$ (Along vertical)

For block A,

$${a_{A\left( {along\,vertical} \right)}} = g{\sin ^2}60^\circ $$

For block B,

$${a_{B\left( {along\,vertical} \right)}} = g{\sin ^2}30^\circ $$

$$\therefore$$ relative vertical acceleration of $$A$$ with respect to $$B$$ is

$$g{\sin ^2}60^\circ $$ - $$g{\sin ^2}30^\circ $$

=$$g\left( {{{\sin }^2}60 - {{\sin }^2}\left. {30} \right]} \right.$$

$$= 4.9$$ $$\,\,m/{s^2}$$ in vertical direction

3

MCQ (Single Correct Answer)

A block of mass $$m$$ is connected to another block of $$mass$$ $$M$$ by a spring (massless) of spring constant $$k.$$ The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $$F$$ starts acting on the block of mass $$M$$ to pull it. Find the force of the block of mass $$m.$$

A

$${{MF} \over {\left( {m + M} \right)}}$$

B

$${{mF} \over M}$$

C

$${{\left( {M + m} \right)F} \over m}$$

D

$${{mF} \over {\left( {m + M} \right)}}$$

we get $$T = ma$$

we get $$F-T=Ma$$

where $$T$$ is force due to spring

$$ \Rightarrow F - ma = Ma$$

$$ \Rightarrow$$ $$F=Ma+ma$$

$$\therefore$$ $$a = {F \over {M + m}}$$

Now, force acting on the block of mass $$m$$ is

$$ma = m\left( {{F \over {M + m}}} \right) = {{mF} \over {m + M}}.$$

4

MCQ (Single Correct Answer)

A player caught a cricket ball of mass $$150$$ $$g$$ moving at a rate of $$20$$ $$m/s.$$ If the catching process is completed in $$0.1s,$$ the force of the blow exerted by the ball on the hand of the player is equal to

A

$$150$$ $$N$$

B

$$3$$ $$N$$

C

$$30$$ $$N$$

D

$$300$$ $$N$$

We know, Force$$ \times $$ time = Impulse = Change in momentum

$$\therefore$$ $$F \times t = m\left( {v - u} \right)$$

$$ \Rightarrow $$ $$F = {{m\left( {v - u} \right)} \over t} = {{0.15\left( {0 - 20} \right)} \over {0.1}} = 30N$$

$$\therefore$$ $$F \times t = m\left( {v - u} \right)$$

$$ \Rightarrow $$ $$F = {{m\left( {v - u} \right)} \over t} = {{0.15\left( {0 - 20} \right)} \over {0.1}} = 30N$$

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 (2) *keyboard_arrow_right*

JEE Main 2021 (Online) 31st August Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 27th August Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 26th 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) 20th July Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 20th July Morning Shift (2) *keyboard_arrow_right*

JEE Main 2021 (Online) 18th March Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 17th March Evening Shift (1) *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 (1) *keyboard_arrow_right*

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

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

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

JEE Main 2020 (Online) 4th September Evening Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 2nd September Morning Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 8th January Evening Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 7th January Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 12th April Evening Slot (1) *keyboard_arrow_right*

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

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

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

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

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

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

JEE Main 2018 (Offline) (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 2016 (Online) 10th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2016 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

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

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

AIEEE 2010 (1) *keyboard_arrow_right*

AIEEE 2007 (1) *keyboard_arrow_right*

AIEEE 2006 (1) *keyboard_arrow_right*

AIEEE 2005 (5) *keyboard_arrow_right*

AIEEE 2004 (2) *keyboard_arrow_right*

AIEEE 2003 (7) *keyboard_arrow_right*

AIEEE 2002 (7) *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*