Joint Entrance Examination

Graduate Aptitude Test in Engineering

1

MCQ (Single Correct Answer)

A mixture of hydrogen and oxygen has volume 500 cm^{3}, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

A

3 : 8

B

3 : 16

C

16 : 3

D

8 : 3

PV = nRT

400 $$\times$$ 10^{3} $$\times$$ 500 $$\times$$ 10^{$$-$$6} = n$$\left( {{{25} \over 3}} \right)$$ (300)

n = $${{2 \over {25}}}$$

n = n_{1} + n_{2}

$${{2 \over {25}}}$$ = $${{{M_1}} \over 2} + {{{M_2}} \over {32}}$$

Also, M_{1} + M_{2} = 0.76 gm

$${{{M_2}} \over {{M_1}}} = {{16} \over 3}$$

400 $$\times$$ 10

n = $${{2 \over {25}}}$$

n = n

$${{2 \over {25}}}$$ = $${{{M_1}} \over 2} + {{{M_2}} \over {32}}$$

Also, M

$${{{M_2}} \over {{M_1}}} = {{16} \over 3}$$

2

MCQ (Single Correct Answer)

Two thin metallic spherical shells of radii r_{1} and r_{2} (r_{1} > r_{2}) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$$_{1} and the outer shell at temperature $$\theta$$_{2}($$\theta$$_{1} < $$\theta$$_{2}). The rate at which heat flows radially through the material is :-

A

$${{4\pi K{r_1}{r_2}({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}$$

B

$${{\pi {r_1}{r_2}({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}$$

C

$${{K({\theta _2} - {\theta _1})} \over {{r_2} - {r_1}}}$$

D

$${{K({\theta _2} - {\theta _1})({r_2} - {r_1})} \over {4\pi {r_1}{r_2}}}$$

Thermal resistance of spherical sheet of thickness dr and radius r is

$$dR = {{dr} \over {K(4\pi {r^2})}}$$

$$R = \int\limits_{{r_1}}^{{r_2}} {{{dr} \over {K(4\pi {r^2})}}} $$

$$R = {1 \over {4\pi K}}\left( {{1 \over {{r_1}}} - {1 \over {{r_2}}}} \right) = {1 \over {4\pi K}}\left( {{{{r_2} - {r_1}} \over {{r_1}{r_2}}}} \right)$$

Thermal current (i) $$ = {{{\theta _2} - {\theta _1}} \over R}$$

$$i = {{4\pi K{r_1}{r_2}} \over {{r_2} - {r_1}}}({\theta _2} - {\theta _1})$$

3

MCQ (Single Correct Answer)

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $${{dp} \over {dv}} = - ap$$. If p = p_{0} at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)

A

$${{{p_0}} \over {aeR}}$$

B

$${{a{p_0}} \over {eR}}$$

C

infinity

D

0$$^\circ$$C

$$\int\limits_{{p_0}}^p {{{dp} \over P} = - a\int\limits_0^v {dv} } $$

$$\ln \left( {{p \over {{p_0}}}} \right) = - av$$

$$p = {p_0}{e^{ - av}}$$

For temperature maximum p-v product should be maximum

$$T = {{pv} \over {nR}} = {{{p_0}v{e^{ - av}}} \over R}$$

$${{dT} \over {dv}} = 0 \Rightarrow {{{p_0}} \over R}\{ {e^{ - av}} + v{e^{ - av}}( - a)\} $$ = 0

$${{{p_0}{e^{ - av}}} \over R}\{ 1 - av\} = 0$$

$$v = {1 \over a},\infty $$

$$T = {{{p_0}1} \over {Rae}} = {{{p_0}} \over {Rae}}$$

at v = $$\infty$$

T = 0

Option (a)

$$\ln \left( {{p \over {{p_0}}}} \right) = - av$$

$$p = {p_0}{e^{ - av}}$$

For temperature maximum p-v product should be maximum

$$T = {{pv} \over {nR}} = {{{p_0}v{e^{ - av}}} \over R}$$

$${{dT} \over {dv}} = 0 \Rightarrow {{{p_0}} \over R}\{ {e^{ - av}} + v{e^{ - av}}( - a)\} $$ = 0

$${{{p_0}{e^{ - av}}} \over R}\{ 1 - av\} = 0$$

$$v = {1 \over a},\infty $$

$$T = {{{p_0}1} \over {Rae}} = {{{p_0}} \over {Rae}}$$

at v = $$\infty$$

T = 0

Option (a)

4

MCQ (Single Correct Answer)

A reversible engine has an efficiency of $${1 \over 4}$$. If the temperature of the sink is reduced by 58$$^\circ$$C, its efficiency becomes double. Calculate the temperature of the sink :

A

174$$^\circ$$C

B

280$$^\circ$$C

C

180.4$$^\circ$$C

D

382$$^\circ$$C

T_{2} = sink temperature

$$\eta = 1 - {{{T_2}} \over {{T_1}}}$$

$${1 \over 4} = 1 - {{{T_2}} \over {{T_1}}}$$

$${{{T_2}} \over {{T_1}}} = {3 \over 4}$$ .... (i)

$${1 \over 2} = 1 - {{{T_2} - 58} \over {{T_1}}}$$

$${{{T_2}} \over {{T_1}}} = {{58} \over {{T_1}}} = {1 \over 2}$$

$${3 \over 4} = {{58} \over {{T_1}}} + {1 \over 2}$$

$${1 \over 4} = {{58} \over {{T_1}}} \Rightarrow {T_1} = 232$$

$${T_2} = {3 \over 4} \times 232$$

$${T_2} = 174$$ K

$$\eta = 1 - {{{T_2}} \over {{T_1}}}$$

$${1 \over 4} = 1 - {{{T_2}} \over {{T_1}}}$$

$${{{T_2}} \over {{T_1}}} = {3 \over 4}$$ .... (i)

$${1 \over 2} = 1 - {{{T_2} - 58} \over {{T_1}}}$$

$${{{T_2}} \over {{T_1}}} = {{58} \over {{T_1}}} = {1 \over 2}$$

$${3 \over 4} = {{58} \over {{T_1}}} + {1 \over 2}$$

$${1 \over 4} = {{58} \over {{T_1}}} \Rightarrow {T_1} = 232$$

$${T_2} = {3 \over 4} \times 232$$

$${T_2} = 174$$ K

On those following papers in MCQ (Single Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2021 (Online) 31st August Evening Shift (2)

JEE Main 2021 (Online) 31st August Morning Shift (2)

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

JEE Main 2021 (Online) 27th August Morning Shift (2)

JEE Main 2021 (Online) 26th August Evening Shift (3)

JEE Main 2021 (Online) 26th August Morning Shift (2)

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

JEE Main 2021 (Online) 27th July Morning Shift (3)

JEE Main 2021 (Online) 25th July Evening Shift (2)

JEE Main 2021 (Online) 25th July Morning Shift (3)

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

JEE Main 2021 (Online) 20th July Evening Shift (2)

JEE Main 2021 (Online) 20th July Morning Shift (3)

JEE Main 2021 (Online) 18th March Evening Shift (3)

JEE Main 2021 (Online) 18th March Morning Shift (2)

JEE Main 2021 (Online) 17th March Evening Shift (2)

JEE Main 2021 (Online) 17th March Morning Shift (4)

JEE Main 2021 (Online) 16th March Evening Shift (2)

JEE Main 2021 (Online) 16th March Morning Shift (2)

JEE Main 2021 (Online) 26th February Evening Shift (1)

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

JEE Main 2021 (Online) 25th February Evening Shift (2)

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

JEE Main 2021 (Online) 24th February Evening Shift (2)

JEE Main 2021 (Online) 24th February Morning Shift (3)

JEE Main 2020 (Online) 6th September Evening Slot (2)

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

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

JEE Main 2020 (Online) 5th September Morning Slot (3)

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

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

JEE Main 2020 (Online) 3rd September Evening Slot (3)

JEE Main 2020 (Online) 3rd September Morning Slot (2)

JEE Main 2020 (Online) 2nd September Evening Slot (3)

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

JEE Main 2020 (Online) 9th January Evening Slot (1)

JEE Main 2020 (Online) 9th January Morning Slot (2)

JEE Main 2020 (Online) 8th January Evening Slot (2)

JEE Main 2020 (Online) 8th January Morning Slot (2)

JEE Main 2020 (Online) 7th January Evening Slot (2)

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

JEE Main 2019 (Online) 12th April Evening Slot (3)

JEE Main 2019 (Online) 12th April Morning Slot (3)

JEE Main 2019 (Online) 10th April Evening Slot (3)

JEE Main 2019 (Online) 10th April Morning Slot (3)

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

JEE Main 2019 (Online) 9th April Morning Slot (3)

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

JEE Main 2019 (Online) 8th April Morning Slot (2)

JEE Main 2019 (Online) 12th January Evening Slot (1)

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

JEE Main 2019 (Online) 11th January Evening Slot (5)

JEE Main 2019 (Online) 11th January Morning Slot (3)

JEE Main 2019 (Online) 10th January Evening Slot (3)

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

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

JEE Main 2019 (Online) 9th January Morning Slot (3)

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

JEE Main 2018 (Offline) (2)

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

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

JEE Main 2017 (Online) 9th April Morning Slot (2)

JEE Main 2017 (Online) 8th April Morning Slot (2)

JEE Main 2017 (Offline) (2)

JEE Main 2016 (Online) 10th April Morning Slot (2)

JEE Main 2016 (Online) 9th April Morning Slot (2)

JEE Main 2016 (Offline) (3)

JEE Main 2015 (Offline) (3)

JEE Main 2014 (Offline) (4)

JEE Main 2013 (Offline) (2)

AIEEE 2012 (4)

AIEEE 2011 (4)

AIEEE 2010 (1)

AIEEE 2009 (6)

AIEEE 2008 (2)

AIEEE 2007 (4)

AIEEE 2006 (3)

AIEEE 2005 (4)

AIEEE 2004 (5)

AIEEE 2003 (6)

AIEEE 2002 (10)

Units & Measurements

Motion

Laws of Motion

Work Power & Energy

Simple Harmonic Motion

Impulse & Momentum

Rotational Motion

Gravitation

Properties of Matter

Heat and Thermodynamics

Waves

Vector Algebra

Ray & Wave Optics

Electrostatics

Current Electricity

Magnetics

Alternating Current and Electromagnetic Induction

Atoms and Nuclei

Dual Nature of Radiation

Electronic Devices

Communication Systems