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

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $$\lambda $$. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

A

$${{25} \over {16}}$$ $$\lambda $$

B

$${{27} \over {20}}$$ $$\lambda $$

C

$${{16} \over {25}}$$ $$\lambda $$

D

$${{20} \over {27}}$$ $$\lambda $$

For M $$ \to $$ L steel

$${1 \over \lambda }$$ = K $$\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right) = {{K \times 5} \over {36}}$$

for N $$ \to $$ L

$${1 \over {\lambda '}}$$ = K$$\left( {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right) = {{K \times 3} \over {16}}$$

$$\lambda ' = {{20} \over {27}}\lambda $$

$${1 \over \lambda }$$ = K $$\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right) = {{K \times 5} \over {36}}$$

for N $$ \to $$ L

$${1 \over {\lambda '}}$$ = K$$\left( {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right) = {{K \times 3} \over {16}}$$

$$\lambda ' = {{20} \over {27}}\lambda $$

2

A particle of mass m moves in a circular orbit in a central potential field U(r) = $${1 \over 2}$$ kr^{2}. If Bohr 's
quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :

A

r_{n} $$ \propto $$ $$\sqrt n $$, E_{n} $$ \propto $$ n

B

r_{n} $$ \propto $$ $$\sqrt n $$, E_{n} $$ \propto $$ $${1 \over n}$$

C

r_{n} $$ \propto $$ n, E_{n} $$ \propto $$ n

D

r_{n} $$ \propto $$ n^{2}, E_{n} $$ \propto $$ $${1 \over {{n^2}}}$$

Force due to this field, F = $$ - {{\partial U} \over {\partial r}}$$

F = $$ - {\partial \over {\partial r}}\left( {{1 \over 2}k{r^2}} \right)$$ = -kr

For circular orbit, $${{m{v^2}} \over r}$$ = -kr

$$ \Rightarrow $$ v $$ \propto $$ r ..... (1)

Fron Bohrâ€™s quantization condition

mvr = $${{nh} \over {2\pi }}$$ .....(2)

From (1) and (2),

$${r_n}$$ $$ \propto $$ $${n^{{1 \over 2}}}$$

Given, U(r) = $${1 \over 2}$$kr^{2}

$$ \Rightarrow $$ E_{n} = $$ - {1 \over 2}U\left( r \right)$$ = $$ - {1 \over 4}k{r^2}$$

$$ \Rightarrow $$ E_{n} $$ \propto $$ n

F = $$ - {\partial \over {\partial r}}\left( {{1 \over 2}k{r^2}} \right)$$ = -kr

For circular orbit, $${{m{v^2}} \over r}$$ = -kr

$$ \Rightarrow $$ v $$ \propto $$ r ..... (1)

Fron Bohrâ€™s quantization condition

mvr = $${{nh} \over {2\pi }}$$ .....(2)

From (1) and (2),

$${r_n}$$ $$ \propto $$ $${n^{{1 \over 2}}}$$

Given, U(r) = $${1 \over 2}$$kr

$$ \Rightarrow $$ E

$$ \Rightarrow $$ E

3

In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha $$-particles and 4 $$\beta $$-particles which are emitted. If the end nucleus is $${}_Z^A$$X, A and Z are given by :

A

A = 208; Z = 80

B

A = 208; Z = 82

C

A = 200; Z = 81

D

A = 202; Z = 80

$${}_{90}^{232}$$Th $$\buildrel \, \over
\longrightarrow $$ $${}_{78}^{208}$$Y + $${}_2^4$$He

$${}_{78}^{208}$$Y $$\buildrel \, \over \longrightarrow $$ $${}_{82}^{208}$$ X + 4$$\beta $$

$${}_{78}^{208}$$Y $$\buildrel \, \over \longrightarrow $$ $${}_{82}^{208}$$ X + 4$$\beta $$

4

Radiation coming from transitions
n = 2 to n = 1 of hydrogen atoms fall on He^{+}
ions in n = 1 and n = 2 states. The possible
transition of helium ions as they absorb energy
from the radiation is :

A

n = 1 $$ \to $$ n = 4

B

n = 2 $$ \to $$ n = 5

C

n = 2 $$ \to $$ n = 4

D

n = 2 $$ \to $$ n = 3

Energy released for tension n = 2 to n = 1 of hydrogen atom

$$E = 13.6{Z^2}\left( {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right)$$

Z = 1, n_{1} = 1, n_{2} = 2

$$E = 13.6 \times 1 \times \left( {{1 \over {{1^2}}} - {1 \over {{2^2}}}} \right)$$

$$E = 13.6 \times {3 \over 4}eV$$ = 10.2 eV

For He^{+} ion z = 2

(A) n = 1 to n = 4

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{1^2}}} - {1 \over {{4^2}}}} \right) = 13.6 \times {{15} \over 4}eV$$

(B) n = 2 to n = 4

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right) = 13.6 \times {{3} \over 4}eV$$

(C) n = 2 to n = 5

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right) = 13.6 \times {{21} \over 25}eV$$

(D) n = 2 to n = 3

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right) = 13.6 \times {{5} \over 9}eV$$

So, possible transition is n = 2 $$\to$$ n = 4

$$E = 13.6{Z^2}\left( {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right)$$

Z = 1, n

$$E = 13.6 \times 1 \times \left( {{1 \over {{1^2}}} - {1 \over {{2^2}}}} \right)$$

$$E = 13.6 \times {3 \over 4}eV$$ = 10.2 eV

For He

(A) n = 1 to n = 4

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{1^2}}} - {1 \over {{4^2}}}} \right) = 13.6 \times {{15} \over 4}eV$$

(B) n = 2 to n = 4

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right) = 13.6 \times {{3} \over 4}eV$$

(C) n = 2 to n = 5

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right) = 13.6 \times {{21} \over 25}eV$$

(D) n = 2 to n = 3

$$E = 13.6 \times {2^2} \times \left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right) = 13.6 \times {{5} \over 9}eV$$

So, possible transition is n = 2 $$\to$$ n = 4

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (3) *keyboard_arrow_right*

AIEEE 2003 (9) *keyboard_arrow_right*

AIEEE 2004 (3) *keyboard_arrow_right*

AIEEE 2005 (5) *keyboard_arrow_right*

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JEE Main 2013 (Offline) (1) *keyboard_arrow_right*

JEE Main 2014 (Offline) (2) *keyboard_arrow_right*

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Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

Practical Physics *keyboard_arrow_right*

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*

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*