# Joint Entrance Screening Test (JEST) Past Year Question Papers 2020 Part 1

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## PART a: 1 Mark Questions

Q1. The persons named *A*, *B*, *C*, *D*, *E*, *F*, *G*, *H*, *I*, *J* have come for an interview. They are being called one by one to the interview panel at random. What is the probability that *C* gives interview before *A* and *A* gives before *F?*

(a)

(b)

(c)

(d)

Q2. The ratio of maximum to minimum resistance that can be obtained with *N* number of resistors is (a) *N*

Q3. Consider three infinitely long, straight, and coplanar wires, which are placed parallel to each other. The distance between the adjacent wires is *d*. Each wire carries a current *I* in the same direction. Consider points on either side of the middle wire where the magnetic field vanishes. What is the distance of these points from the middle wire?

Q4. A rod consists of two equal sections of length *l* each with coefficient of thermal

, respectively. One end of the rod is kept at a fixed temperature and the other end at a temperature . If then the temperature at the interface is

(a)

(b)

(c)

(d)

Q5. If *f* (*t)* is a real and even function of *t*, which one of the following statements is true about its Fourier transform (here ⚹ indicates complex conjugation) ?

(a)

(b)

(c)

(d)

Q6. Consider an ideal gas whose entropy is given by

,

where *n* is the number of moles, is a constant, *R* is the universal gas constant, *U* is the internal energy and *V* is the volume of the gas. The specific heat at constant pressure is then given by

(a)

(b)

(c)

(d)

Q7. A 16 - bit analog to digital converter works in the range 0 - 1 Volt. The least count of the converter is

(a)

(b)

(c)

(d)

Q8. A particle in a spherically symmetric potential is known to be in an Eigen state of and with eigenvalues and , respectively. What is the value of ?

(a)

(b)

(c)

(d)

Q9. A particle of mass *m* carrying angular momentum *l* moves in a central potential

, where *k*, *a* are positive constants. If the particle undergoes circular motion, what is the equation determining its radius ?

(a)

(b)

(c)

(d)

Q10. Calculate the collector current and determine whether or not the transistor in figure shown below is in saturation. Assume

(a) 6.5*mA*, not in saturation

(b) 11.5*mA*, in saturation

(c) 11.5*mA*, not in saturation

(d) 6.5*mA*, in saturation

Q11. Charges are placed as follows: *q* at and and -*q* at and . At large distances, how does the electrostatic potential behave as a function of the distance *r* from the centre ?

(a)

(b)

Q12. An Hermitian matrix *A* is not a multiple of the identity matrix. Which one of the following statements is always true?

(a)

(b)

(c)

(d)

Q13. A ring of radius 0.5*m* has a gap of . If the ring carries a charge of + 1.0*C* distributed uniformly along it, then the electric field at the centre of the ring is

(a)

(b)

(c)

(d)