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

The electric field component of a monochromatic radiation is given by

$$\overrightarrow E $$ = 2 E_{0} $$\widehat i$$ cos kz cos $$\omega $$t

Its magnetic field $$\overrightarrow B $$ is then given by :

$$\overrightarrow E $$ = 2 E

Its magnetic field $$\overrightarrow B $$ is then given by :

A

$${{2{E_0}} \over c}$$ $$\widehat j$$ sin kz cos $$\omega $$t

B

$$-$$ $${{2{E_0}} \over c}$$ $$\widehat j$$ sin kz sin $$\omega $$t

C

$${{2{E_0}} \over c}$$ $$\widehat j$$ sin kz sin $$\omega $$t

D

$${{2{E_0}} \over c}$$ $$\widehat j$$ cos kz cos $$\omega $$t

2

In an a.c. circuit, the instantaneous e.m.f. and current are given by

e = 100 sin 30 t

i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$

In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

e = 100 sin 30 t

i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$

In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

A

50, 0

B

50, 10

C

$${{1000} \over {\sqrt 2 }},10$$

D

$${{50} \over {\sqrt 2 }}$$

Wattless current,

here $$\phi $$ is the angle between i and e.

Average power,

P_{av} = V_{rms} I_{rms} cos$$\phi $$

= $${{100} \over {\sqrt 2 }} \times {{20} \over {\sqrt 2 }}$$ cos$${\pi \over 4}$$

= $${{1000} \over {\sqrt 2 }}$$ watt.

here $$\phi $$ is the angle between i and e.

Average power,

P

= $${{100} \over {\sqrt 2 }} \times {{20} \over {\sqrt 2 }}$$ cos$${\pi \over 4}$$

= $${{1000} \over {\sqrt 2 }}$$ watt.

3

For an RLC circuit driven with voltage of amplitude vm and frequency $${\omega _0}$$ = $${1 \over {\sqrt {LC} }}$$ the current exhibits resonance. The quality factor, Q is given by :

A

$${{CR} \over {{\omega _0}}}$$

B

$${{{\omega _0}L} \over R}$$

C

$${{{\omega _0}R} \over L}$$

D

$${R \over {\left( {{\omega _0}C} \right)}}$$

Quality factor (Q) = $${{Angular\,\,{\mathop{\rm Re}\nolimits} sonance} \over {Bandwith}}$$

= $${{{1 \over {\sqrt {LC} }}} \over {{R \over L}}}$$

= $${{{\omega _0}} \over {{R \over L}}}$$

= $${{{\omega _0}L} \over R}$$

= $${{{1 \over {\sqrt {LC} }}} \over {{R \over L}}}$$

= $${{{\omega _0}} \over {{R \over L}}}$$

= $${{{\omega _0}L} \over R}$$

4

An EM wave from air enters a medium. The electric fields are

$$\overrightarrow {{E_1}} $$ = $${E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]$$ in air and $$\overrightarrow {{E_2}} $$ = $${E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$ in medium, where the wave number k and frequency $$\nu $$ refer to their values in air. The medium is non-magnetic. If $${\varepsilon _{{r_1}}}$$ and $${\varepsilon _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

$$\overrightarrow {{E_1}} $$ = $${E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]$$ in air and $$\overrightarrow {{E_2}} $$ = $${E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$ in medium, where the wave number k and frequency $$\nu $$ refer to their values in air. The medium is non-magnetic. If $${\varepsilon _{{r_1}}}$$ and $${\varepsilon _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

A

$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = 4$$

B

$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = 2$$

C

$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = {1 \over 4}$$

D

$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = {1 \over 2}$$

Electric field in air,

$$\overrightarrow {{E_1}} $$ = E_{01} $$\widehat x$$ cos ( $${{2\pi vz} \over c}$$ $$-$$ 2$$\pi $$vt )

$$\therefore\,\,\,$$ Velocity in air = $${{2\pi v} \over {{{2\pi v} \over c}}}$$ = c

Also, c = $${1 \over {\sqrt {\mu \varepsilon {r_1}{\varepsilon _0}} }}$$ . . . . . . (1)

$$\overrightarrow {{E_2}} $$ = E_{02} $$\widehat x$$ cos(2kz $$-$$ kct)

$$\therefore\,\,\,$$ Velocity in medium = $${{kc} \over {2k}}$$ = $${c \over 2}$$

Also, $${c \over 2}$$ = $${1 \over {\sqrt {\mu {\varepsilon _{r2}}\,{\varepsilon _0}} }}$$ . . . . . (2)

As, medium is non magnetic,

So, $$\mu $$_{medium} = $$\mu $$_{air} = $$\mu $$

Dividing (1) by (2), we get

2 = $$\sqrt {{{{\varepsilon _{r2}}} \over {{\varepsilon _{r1}}}}} $$

$$ \Rightarrow $$$$\,\,\,$$ $${{{{\varepsilon _{r1}}} \over {{\varepsilon _{r2}}}}}$$ = $${1 \over 4}$$

$$\overrightarrow {{E_1}} $$ = E

$$\therefore\,\,\,$$ Velocity in air = $${{2\pi v} \over {{{2\pi v} \over c}}}$$ = c

Also, c = $${1 \over {\sqrt {\mu \varepsilon {r_1}{\varepsilon _0}} }}$$ . . . . . . (1)

$$\overrightarrow {{E_2}} $$ = E

$$\therefore\,\,\,$$ Velocity in medium = $${{kc} \over {2k}}$$ = $${c \over 2}$$

Also, $${c \over 2}$$ = $${1 \over {\sqrt {\mu {\varepsilon _{r2}}\,{\varepsilon _0}} }}$$ . . . . . (2)

As, medium is non magnetic,

So, $$\mu $$

Dividing (1) by (2), we get

2 = $$\sqrt {{{{\varepsilon _{r2}}} \over {{\varepsilon _{r1}}}}} $$

$$ \Rightarrow $$$$\,\,\,$$ $${{{{\varepsilon _{r1}}} \over {{\varepsilon _{r2}}}}}$$ = $${1 \over 4}$$

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (5) *keyboard_arrow_right*

AIEEE 2003 (4) *keyboard_arrow_right*

AIEEE 2004 (6) *keyboard_arrow_right*

AIEEE 2005 (5) *keyboard_arrow_right*

AIEEE 2006 (6) *keyboard_arrow_right*

AIEEE 2007 (2) *keyboard_arrow_right*

AIEEE 2008 (1) *keyboard_arrow_right*

AIEEE 2009 (1) *keyboard_arrow_right*

AIEEE 2010 (3) *keyboard_arrow_right*

AIEEE 2011 (3) *keyboard_arrow_right*

AIEEE 2012 (1) *keyboard_arrow_right*

JEE Main 2013 (Offline) (4) *keyboard_arrow_right*

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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*

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*