# Joint Entrance Screening Test (JEST) Past Year Question Papers 2017 Part 2

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Q12. Consider magnetic vector potential and scalar potential which define the magnetic field and electric field . If one adds to for a well-defined , then what should be added to so that remains unchanged up to an arbitrary function of time, *f* (*t)* ?

(a)

(b)

(c)

(d) -

Q13. In the following silicon diode circuit , determine the output voltage waveform *out V* for the given input wave.

1.

2.

3.

4.

Q14. and are respectively are orthonormal wave functions of the ground and first excited states of a one-dimensional simple harmonic oscillator. Consider the normalized wave function where and are real. For what values of and will be maximized?

(a)

(b)

(c)

(d)

Q15. Consider the following circuit in steady state condition. Calculate the amount of charge stored in and capacitors respectively.

(a) and

(b) and

(c) and

(d) and

Q16. If the mean square fluctuations in energy of a system in equilibrium at temperature *T* is proportional to , then the energy of the system is proportional to

(a)

(b)

(c)

(d)

Q17. Suppose the spin degrees of freedom of a 2 - particle system can be described by a 21- dimensional Hilbert subspace. Which among the following could be the spin of one of the particles?

(a)

(b)

(c)

(d)

Q18. Water is poured at a rate of / *hour* from the top into a cylindrical vessel of diameter *D*. The vessel has a small opening of area at the bottom. What should be the minimum height of the vessel so that water does not overflow?

(a)

(b)

(c)

(d)