Joint Entrance Examination

Graduate Aptitude Test in Engineering

1

Numerical

The K_{$$\alpha$$} X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy of this atom when an L electron is knocked out will be __________ keV. (Round off to the nearest integer)

[h = 4.14 $$\times$$ 10^{$$-$$15} eVs, c = 3 $$\times$$ 10^{8} ms^{$$-$$1}]

[h = 4.14 $$\times$$ 10

Your Input ________

Correct Answer is **10**

$${E_{{k_\alpha }}} = {E_k} - {E_L}$$

$${{hc} \over {{\lambda _{{k_\alpha }}}}} = {E_k} - {E_L}$$

$${E_L} = {E_k} - {{hc} \over {{\lambda _{{k_\alpha }}}}}$$

= 27.5 KeV $$ - {{12.42 \times {{10}^{ - 7}}eVm} \over {0.071 \times {{10}^{ - 9}}m}}$$

E_{L} = (27.5 $$-$$ 17.5) keV

= 10 keV

$${{hc} \over {{\lambda _{{k_\alpha }}}}} = {E_k} - {E_L}$$

$${E_L} = {E_k} - {{hc} \over {{\lambda _{{k_\alpha }}}}}$$

= 27.5 KeV $$ - {{12.42 \times {{10}^{ - 7}}eVm} \over {0.071 \times {{10}^{ - 9}}m}}$$

E

= 10 keV

2

Numerical

A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V and the voltage drop across a resistor of 1000 $$\Omega$$ in the collector circuit is 0.6 V. If the current gain factor ($$\beta$$) is 24, then the base current is _____________ $$\mu$$A. (Round off to the Nearest Integer)

Your Input ________

Correct Answer is **25**

$$\beta = {{{I_C}} \over {{I_B}}} = 24;$$

R_{C} = 1000

$$\Delta$$V = 0.6

$${I_C} = {{0.6} \over {1000}}$$

I_{C} = 6 $$\times$$ 10^{$$-$$4}

$${I_B} = {{{I_C}} \over \beta } = {{6 \times {{10}^{ - 4}}} \over {24}} = 25\mu A$$

R

$$\Delta$$V = 0.6

$${I_C} = {{0.6} \over {1000}}$$

I

$${I_B} = {{{I_C}} \over \beta } = {{6 \times {{10}^{ - 4}}} \over {24}} = 25\mu A$$

3

Numerical

A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $$\mu$$F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _____________ $$\Omega$$.

Your Input ________

Correct Answer is **150**

T_{m} =30 ms

C = 200 $$\mu$$F

$${q \over N} = {{{Q_0}{e^{ - t/RC}}} \over {{N_0}{e^{ - \lambda t}}}} = {{{Q_0}} \over {{N_0}}}{e^{t\left( {\lambda - {1 \over {RC}}} \right)}}$$

Since q/N is constant hence

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

$$R = {1 \over {\lambda C}} = {{{T_m}} \over C} = {{30 \times {{10}^{ - 3}}} \over {200 \times {{10}^{ - 6}}}} = 150\Omega $$

C = 200 $$\mu$$F

$${q \over N} = {{{Q_0}{e^{ - t/RC}}} \over {{N_0}{e^{ - \lambda t}}}} = {{{Q_0}} \over {{N_0}}}{e^{t\left( {\lambda - {1 \over {RC}}} \right)}}$$

Since q/N is constant hence

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

$$R = {1 \over {\lambda C}} = {{{T_m}} \over C} = {{30 \times {{10}^{ - 3}}} \over {200 \times {{10}^{ - 6}}}} = 150\Omega $$

4

Numerical

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular are of radius 30 cm. The value of B is ___________ $$\times$$ 10^{$$-$$7} T.

Given hc = 20 $$\times$$ 10^{$$-$$26} J-m, mass of electron = 9 $$\times$$ 10^{$$-$$31} kg

Given hc = 20 $$\times$$ 10

Your Input ________

Correct Answer is **125**

By photoelectric equation

$${{hc} \over \lambda } - \phi = {k_{\max }}$$

$${k_{\max }} = {{1240} \over {500}} - 1.25 \approx 1.25$$

$$r = {{\sqrt {2mk} } \over {eB}}$$

$$B = {{\sqrt {2mk} } \over {er}}$$

$$ = 125 \times {10^{ - 7}}T$$

$${{hc} \over \lambda } - \phi = {k_{\max }}$$

$${k_{\max }} = {{1240} \over {500}} - 1.25 \approx 1.25$$

$$r = {{\sqrt {2mk} } \over {eB}}$$

$$B = {{\sqrt {2mk} } \over {er}}$$

$$ = 125 \times {10^{ - 7}}T$$

On those following papers in Numerical

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2021 (Online) 27th July Evening Shift (1)

JEE Main 2021 (Online) 27th July Morning Shift (2)

JEE Main 2021 (Online) 25th July Evening Shift (1)

JEE Main 2021 (Online) 20th July Evening Shift (1)

JEE Main 2021 (Online) 17th March Morning Shift (1)

JEE Main 2021 (Online) 26th February Evening Shift (1)

JEE Main 2020 (Online) 5th September Evening Slot (1)

JEE Main 2020 (Online) 7th January Morning Slot (1)

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