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

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

A

30.2 MeV

B

32.4 MeV

C

23.6 MeV

D

25.8 MeV

No. of proton in one dueteron = 2

$$\therefore\,\,\,$$ Total protons in two dueterons = 2 $$ \times $$ 2 = 4

$$\therefore\,\,\,$$ Binding energy of two dueteron

= 1.1 $$ \times $$ 4 = 4 : 4 MeV

In (

$$\therefore\,\,\,$$ Binding energy of (

Energy released in this process = 28 $$-$$ 4.4 = 23.6 MeV

2

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

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

3

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

4

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 = $${1 \over {{K^2}R{Z^2}}}$$

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

Number in Brackets after Paper Name Indicates No of Questions

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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*