Joint Entrance Examination

Graduate Aptitude Test in Engineering

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

1

MCQ (Single Correct Answer)

A projectile can have the same range 'R' for two angles of projection. If T_{1} and T_{2} be the time
of flights in the two cases, then the product of the two time of flights is directly proportional to

A

R

B

$${1 \over R}$$

C

$${1 \over {{R^2}}}$$

D

$${R^2}$$

Range is same for angle of projection $$\theta ,$$ and $${90^ \circ } - \theta $$

$${T_1} = {{2u\sin \theta } \over g},\,\,{T_2} = {{2u\cos \theta } \over g}$$

$${T_1}{T_2} =$$ $${{4{u^2}\sin \theta \cos \theta } \over {{g^2}}}$$

= $${2 \over g} \times \left( {{{{u^2}\sin 2\theta } \over g}} \right)$$

= $${{2R} \over g}$$

(as $$R = $$$${{{{u^2}\sin 2\theta } \over g}}$$ )

Hence, $${T_1}{T_2}$$ is proportional to $$R.$$

2

MCQ (Single Correct Answer)

If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetween A and B is

A

$${\pi \over 2}$$

B

$${\pi \over 3}$$

C

$$\pi $$

D

$${\pi \over 4}$$

$$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$

$$\overrightarrow A \times \overrightarrow B - \overrightarrow B \times \overrightarrow A = 0$$

$$ \Rightarrow \overrightarrow A \times \overrightarrow B + \overrightarrow A \times \overrightarrow B = 0$$

$$\therefore$$ $$\overrightarrow A \times \overrightarrow B = 0$$

$$ \Rightarrow AB\sin \theta = 0$$

$$\theta = $$ $$0,\pi ,\,\,$$$$2\pi $$ ........

from the given options, $$\theta = \pi $$

$$\overrightarrow A \times \overrightarrow B - \overrightarrow B \times \overrightarrow A = 0$$

$$ \Rightarrow \overrightarrow A \times \overrightarrow B + \overrightarrow A \times \overrightarrow B = 0$$

$$\therefore$$ $$\overrightarrow A \times \overrightarrow B = 0$$

$$ \Rightarrow AB\sin \theta = 0$$

$$\theta = $$ $$0,\pi ,\,\,$$$$2\pi $$ ........

from the given options, $$\theta = \pi $$

3

MCQ (Single Correct Answer)

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the
ground. What is the position of the ball in $${T \over 3}$$ seconds?

A

$${{8h} \over 9}$$ meters from the ground

B

$${{7h} \over 9}$$ meters from the ground

C

$${h \over 9}$$ meters from the ground

D

$${{7h} \over {18}}$$ meters from the ground

We know that equation of motion, $$s = ut + {1 \over 2}g{t^2},\,\,$$

Initial speed of ball is zero and it take T second to reach the ground.

$$\therefore$$ $$h = {1 \over 2}g{T^2}$$

After $$T/3$$ second, vertical distance moved by the ball

$$h' = {1 \over 2}g{\left( {{T \over 3}} \right)^2} $$

$$\Rightarrow h' = {1 \over 2} \times {{8{T^2}} \over 9}$$

$$ = {h \over 9}$$

$$\therefore$$ Height from ground

$$ = h - {h \over 9} = {{8h} \over 9}$$

Initial speed of ball is zero and it take T second to reach the ground.

$$\therefore$$ $$h = {1 \over 2}g{T^2}$$

After $$T/3$$ second, vertical distance moved by the ball

$$h' = {1 \over 2}g{\left( {{T \over 3}} \right)^2} $$

$$\Rightarrow h' = {1 \over 2} \times {{8{T^2}} \over 9}$$

$$ = {h \over 9}$$

$$\therefore$$ Height from ground

$$ = h - {h \over 9} = {{8h} \over 9}$$

4

MCQ (Single Correct Answer)

The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha $$t^{3} and y = βt^{3}. The speed to the particle at time 't' is given by

A

$$3t\sqrt {{\alpha ^2} + {\beta ^2}} $$

B

$$3{t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $$

C

$${t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $$

D

$$\sqrt {{\alpha ^2} + {\beta ^2}} $$

Given that $$x = \alpha {t^3}\,\,\,\,$$ and $$\,\,\,\,y = \beta {t^3}$$

$$\therefore$$ $${v_x} = {{dx} \over {dt}} = 3\alpha {t^2}\,\,\,\,$$

and$$\,\,\,\,\,{v_y} = {{dy} \over {dt}} = 3\beta {t^2}$$

$$\therefore$$ $$v = \sqrt {v_x^2 + v_y^2} $$

$$ = \sqrt {9{\alpha ^2}{t^4} + 9{\beta ^2}{t^4}} $$

$$ = 3{t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $$

$$\therefore$$ $${v_x} = {{dx} \over {dt}} = 3\alpha {t^2}\,\,\,\,$$

and$$\,\,\,\,\,{v_y} = {{dy} \over {dt}} = 3\beta {t^2}$$

$$\therefore$$ $$v = \sqrt {v_x^2 + v_y^2} $$

$$ = \sqrt {9{\alpha ^2}{t^4} + 9{\beta ^2}{t^4}} $$

$$ = 3{t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $$

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*

Dual Nature of Radiation *keyboard_arrow_right*

Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

Practical Physics *keyboard_arrow_right*