Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geomatics Engineering Or Surveying

Engineering Mechanics

Hydrology

Transportation Engineering

Strength of Materials Or Solid Mechanics

Reinforced Cement Concrete

Steel Structures

Irrigation

Environmental Engineering

Engineering Mathematics

Structural Analysis

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

General Aptitude

1

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is given an initial speed $$\upsilon $$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically $${5 \over 6}$$th of the initial kinetic energy is lost in whole process. What is value of M/m ?

A

5

B

2

C

4

D

3

As in elastic or in elastic clollision, momentum is conserved.

$$ \therefore $$ P_{i} = P_{f}

P_{i} = Initial momentum

P_{f} = Final Momentum

mv = (2m + m) V_{f}

$$ \Rightarrow $$ V_{f} = $${{mv} \over {2m + M}}$$

Here due to collision $${5 \over 6}$$th of kinetic energy is lost.

$$ \therefore $$ Remaining kinetic energy,

K_{f} = $${1 \over 6}$$ Ki

$$ \Rightarrow $$ $${1 \over 2}$$(2m + M) $$ \times $$ $${{{{\left( {mv} \right)}^2}} \over {{{\left( {2m + M} \right)}^2}}}$$ = $${1 \over 6} \times {1 \over 2}m{v^2}$$

$$ \Rightarrow $$ $${{{m^2}{v^2}} \over {2m + M}}$$ = $${1 \over 6}m{v^2}$$

$$ \Rightarrow $$ $${m \over {2m + M}}$$ = $${1 \over 6}$$

$$ \Rightarrow $$ 6m = 2m + M

$$ \Rightarrow $$ M = 4m

$$ \Rightarrow $$ $${M \over m}$$ = 4

$$ \therefore $$ P

P

P

mv = (2m + m) V

$$ \Rightarrow $$ V

Here due to collision $${5 \over 6}$$th of kinetic energy is lost.

$$ \therefore $$ Remaining kinetic energy,

K

$$ \Rightarrow $$ $${1 \over 2}$$(2m + M) $$ \times $$ $${{{{\left( {mv} \right)}^2}} \over {{{\left( {2m + M} \right)}^2}}}$$ = $${1 \over 6} \times {1 \over 2}m{v^2}$$

$$ \Rightarrow $$ $${{{m^2}{v^2}} \over {2m + M}}$$ = $${1 \over 6}m{v^2}$$

$$ \Rightarrow $$ $${m \over {2m + M}}$$ = $${1 \over 6}$$

$$ \Rightarrow $$ 6m = 2m + M

$$ \Rightarrow $$ M = 4m

$$ \Rightarrow $$ $${M \over m}$$ = 4

2

A force acts on a 2 kg object so that its position is given as a function of time as x = 3t^{2} + 5. What is the work done by this force in first 5 seconds ?

A

850 J

B

950 J

C

875 J

D

900 J

Displacement,

x = 3t^{2} + 5

$$ \therefore $$ v = $${{dx} \over {dt}} = 6t$$

At t = 0, velocity = 6 $$ \times $$ 0 = 0

at t = 5, velocity = 5 $$ \times $$ 6 = 30 m/s

we know from work energy theorem,

Work (W) = change in kinetic energy ($$\Delta $$K)

= $${1 \over 2}mv_F^2 - {1 \over 2}mv_i^2$$

= $${1 \over 2}$$ $$ \times $$ 2 $$ \times $$ (30)^{2} $$-$$ 0

= 900 J

x = 3t

$$ \therefore $$ v = $${{dx} \over {dt}} = 6t$$

At t = 0, velocity = 6 $$ \times $$ 0 = 0

at t = 5, velocity = 5 $$ \times $$ 6 = 30 m/s

we know from work energy theorem,

Work (W) = change in kinetic energy ($$\Delta $$K)

= $${1 \over 2}mv_F^2 - {1 \over 2}mv_i^2$$

= $${1 \over 2}$$ $$ \times $$ 2 $$ \times $$ (30)

= 900 J

3

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time is -

A

$${{m{g^2}{t^2}} \over 8}$$

B

$${{3m{g^2}{t^2}} \over 8}$$

C

$$-$$ $${{m{g^2}{t^2}} \over 8}$$

D

0

N $$-$$ mg = $${{mg} \over 2}$$ $$ \Rightarrow $$ N = $${{3mg} \over 2}$$

The distance travelled by the system in time t is

S = ut + $${1 \over 2}a{t^2} = 0 + {1 \over 2}\left( {{g \over 2}} \right){t^2} = {1 \over 2}{g \over 2}{t^2}$$

Now, work done

W = N.S = $$\left( {{3 \over 2}mg} \right)\left( {{1 \over 2}{g \over 2}{t^2}} \right)$$

$$ \Rightarrow $$ W = $${{3m{g^2}{t^2}} \over 8}$$

The distance travelled by the system in time t is

S = ut + $${1 \over 2}a{t^2} = 0 + {1 \over 2}\left( {{g \over 2}} \right){t^2} = {1 \over 2}{g \over 2}{t^2}$$

Now, work done

W = N.S = $$\left( {{3 \over 2}mg} \right)\left( {{1 \over 2}{g \over 2}{t^2}} \right)$$

$$ \Rightarrow $$ W = $${{3m{g^2}{t^2}} \over 8}$$

4

A particle which is experiencing a force, given by $$\overrightarrow F = 3\widehat i - 12\widehat j,$$ undergoes a displacement of $$\overrightarrow d = 4\overrightarrow i $$ particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?

A

9 J

B

10 J

C

12 J

D

15 J

Work done = $$\overrightarrow F \cdot \overrightarrow d $$

$$=$$ 12 J

work energy theorem

w_{net} $$=$$ $$\Delta $$K.E.

12 $$=$$ K_{f} $$-$$ 3

K_{f} = 15 J

$$=$$ 12 J

work energy theorem

w

12 $$=$$ K

K

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (2) *keyboard_arrow_right*

AIEEE 2003 (4) *keyboard_arrow_right*

AIEEE 2004 (5) *keyboard_arrow_right*

AIEEE 2005 (5) *keyboard_arrow_right*

AIEEE 2006 (4) *keyboard_arrow_right*

AIEEE 2007 (1) *keyboard_arrow_right*

AIEEE 2008 (2) *keyboard_arrow_right*

AIEEE 2010 (1) *keyboard_arrow_right*

AIEEE 2012 (1) *keyboard_arrow_right*

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

JEE Main 2016 (Offline) (2) *keyboard_arrow_right*

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

JEE Main 2016 (Online) 10th April Morning Slot (3) *keyboard_arrow_right*

JEE Main 2017 (Offline) (2) *keyboard_arrow_right*

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

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

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

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

JEE Main 2018 (Online) 16th April Morning Slot (2) *keyboard_arrow_right*

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

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

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

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

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

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

JEE Main 2019 (Online) 12th January Evening Slot (2) *keyboard_arrow_right*

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

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

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

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

JEE Main 2020 (Online) 7th January Morning Slot (2) *keyboard_arrow_right*

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

JEE Main 2020 (Online) 9th January Morning Slot (1) *keyboard_arrow_right*

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

JEE Main 2020 (Online) 3rd September Evening Slot (1) *keyboard_arrow_right*

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

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

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

JEE Main 2021 (Online) 26th February Morning Shift (1) *keyboard_arrow_right*

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

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

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

JEE Main 2021 (Online) 22th July Evening Shift (1) *keyboard_arrow_right*

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

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

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*

Ray & Wave Optics *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*