Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geotechnical Engineering

Transportation Engineering

Irrigation

Engineering Mathematics

Construction Material and Management

Fluid Mechanics and Hydraulic Machines

Hydrology

Environmental Engineering

Engineering Mechanics

Structural Analysis

Reinforced Cement Concrete

Steel Structures

Geomatics Engineering Or Surveying

General Aptitude

1

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

A

$${{{h^2}} \over {{\pi ^2}{m^2}{r^3}}}$$

B

$${{{h^2}} \over {{8\pi ^2}{m^2}{r^3}}}$$

C

$${{{h^2}} \over {{4\pi ^2}{m^2}{r^3}}}$$

D

$${{{h^2}} \over {{4\pi }{m^2}{r^3}}}$$

2

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 10^{9} watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is
3×10^{8} m/s)

A

0.96 gm

B

0.8 gm

C

4 $$ \times $$ 10^{$$-$$2} gm

D

6.6 $$ \times $$ 10^{$$-$$5} gm

3

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let
$${\lambda _n}$$, $${\lambda _g}$$ be the de Broglie wavelength of the electron in the n^{th} state and the ground state respectively. Let
$${\Lambda _n}$$ be the wavelength of the emitted photon in the transition from the n^{th} state to the ground state. For large n, (A, B are constants)

A

$${\Lambda _n} \approx A + {B \over {\lambda _n^2}}$$

B

$${\Lambda _n} \approx A + B{\lambda _n}$$

C

$$\Lambda _n^2 \approx A + B\lambda _n^2$$

D

$$\Lambda _n^2 \approx \lambda$$

We know,

Wavelength of emitted photon from n_{2} state to n_{1} state is

$${1 \over \lambda }$$ = RZ^{2} $$\left( {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right)$$

Here electron comes from n^{th} state to ground state (n = 1),

then the wavelength of photon is ,

$${1 \over {{\Lambda _n}}}$$ = RZ^{2} $$\left( {{1 \over {{1^2}}} - {1 \over {{n^2}}}} \right)$$

$$ \Rightarrow $$$$\,\,\,$$ $$\Lambda $$_{n} = $${1 \over {R{Z^2}}}{\left( {1 - {1 \over {{n^2}}}} \right)^{ - 1}}$$

As n is very large, so using binomial theorem

$$\Lambda $$_{n} = $${1 \over {R{Z^2}}}\left( {1 + {1 \over {{n^2}}}} \right)$$

$$ \Rightarrow $$$$\,\,\,$$ $$\Lambda $$_{n} = $${1 \over {R{Z^2}}} + {1 \over {R{Z^2}}}\left( {{1 \over {{n^2}}}} \right)$$

We know,

$$\lambda $$_{n} = $${{2\pi r} \over n}$$

= 2$$\pi $$ $${\left( {{{{n^2}{h^2}} \over {4{\pi ^2}mZ{C^2}}}} \right)\times{{1 \over n}}}$$

$$\therefore\,\,\,$$ $$\lambda $$_{n} $$ \propto $$ n

$$ \Rightarrow $$$$\,\,\,$$ n = K $$\lambda $$_{n}

$$\therefore\,\,\,$$ $$\Lambda $$_{n} = $${1 \over {R{Z^2}}} + {1 \over {R{Z^2}}}\left( {{1 \over {{{\left( {K\,{\lambda _n}} \right)}^2}}}} \right)$$

Let A = $${1 \over {R{Z^2}}}$$ and B = $${1 \over {{K^2}R{Z^2}}}$$

$$ \Rightarrow $$$$\,\,\,$$ $$\Lambda $$_{n} = A + $${B \over {\lambda _n^2}}$$

Wavelength of emitted photon from n

$${1 \over \lambda }$$ = RZ

Here electron comes from n

then the wavelength of photon is ,

$${1 \over {{\Lambda _n}}}$$ = RZ

$$ \Rightarrow $$$$\,\,\,$$ $$\Lambda $$

As n is very large, so using binomial theorem

$$\Lambda $$

$$ \Rightarrow $$$$\,\,\,$$ $$\Lambda $$

We know,

$$\lambda $$

= 2$$\pi $$ $${\left( {{{{n^2}{h^2}} \over {4{\pi ^2}mZ{C^2}}}} \right)\times{{1 \over n}}}$$

$$\therefore\,\,\,$$ $$\lambda $$

$$ \Rightarrow $$$$\,\,\,$$ n = K $$\lambda $$

$$\therefore\,\,\,$$ $$\Lambda $$

Let A = $${1 \over {R{Z^2}}}$$ and B = $${1 \over {{K^2}R{Z^2}}}$$

$$ \Rightarrow $$$$\,\,\,$$ $$\Lambda $$

4

If the series limit frequency of the Lyman series is $${\nu _L}$$, then the series limit frequency of the Pfund series is:

A

$${\nu _L}/25$$

B

$$25{\nu _L}$$

C

$$16{\nu _L}$$

D

$${\nu _L}/16$$

(1) In Lyman Series, transition happens in n = 1 state

from n = 2, 3, . . . . . $$ \propto $$

(2) In Balmer Series, transition happens in n = 2 state

from n = 3, 4, . . . . . $$ \propto $$

(3) In Paschen Series, transition happens in n = 3 state

from n = 4, 5, . . . . . $$ \propto $$

(4) In Bracktt Series, transition happens in n = 4 state

from n = 5, 6 . . . . . . $$ \propto $$

(5) In Pfund Series, transition happens in n = 5 state

from n = 6, 7, . . . . $$ \propto $$

We know,

$${1 \over \lambda }$$ = RZ

Series limit means transition happens

from n = $$ \propto $$ to n = 1, for Lyman Series.

In series limit for Lyman series,

$${1 \over {{\lambda _L}}}$$ = RZ

$$ \Rightarrow $$$$\,\,\,$$ $${1 \over {{\lambda _L}}}$$ = RZ

We know,

E = $${{hc} \over \lambda }$$ = h$$\gamma $$

$$ \Rightarrow $$$$\,\,\,$$ $$\gamma $$ = $${c \over \lambda }$$

So, frequency in Lyman Series,

$$\gamma $$

In Pfund series,

n

$$\therefore\,\,\,$$ $${1 \over {{\lambda _P}}}$$ = RZ

$$ \Rightarrow $$$$\,\,\,$$ $${1 \over {{\lambda _P}}}$$ = $${{R{Z^2}} \over {25}}$$

$$\therefore\,\,\,$$ $${\gamma _P}$$ = $${c \over {{\lambda _P}}}$$ = c $$ \times $$ $${{R{Z^2}} \over {25}}$$

$$\therefore\,\,\,$$ $$\gamma $$

Number in Brackets after Paper Name Indicates No of Questions

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Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

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Dual Nature of Radiation *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*

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Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*