# Joint Entrance Screening Test (JEST) Past Year Question Papers 2019 Part 1

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## Part-A: 1-Mark Questions

Q1. Let be the position vector of a point on a closed contour *C*. What is the value of the line integral ?

(a) 0

(b)

(c) 1

(d)

Q2. A dc voltage of 80 Volt is switched on across a circuit containing a resistance of in series with an inductance of 20*H*. What is the rate of change of current at the instant when the current is 12 *A*?

(a) 0 *A*/ *s*

(b) 1 *A*/ *s*

(c) 5 *A*/ *s*

(d) 80 *A*/ *s*

Q3. Consider the function . In which domain of the complex plane is this function analytic?

(a) First and second quadrants

(b) Second and third quadrants

(c) Second and fourth quadrants

(d) Nowhere

Q4. Consider the following transformation of the phase space coordinates

For what values of *a* and *b* will the transformation be canonical?

(a) 1,1

(b)

(c)

(d)

Q5. What is the binding energy of an electron in the ground state of a ion?

(a) 6.8*eV*

(b) 13.6*eV*

(c) 27.2*eV*

(d) 54.4*eV*

Q6. A collimated white light source illuminates the slits of a double slit interference setup and forms the interference pattern on a screen. If one slit is covered with a blue filter, which one of the following statements is correct?

(a) No interference pattern is observed after the slit is covered with the blue filter

(b) Interference pattern remains unchanged with and without the blue filter

(c) A blue interference pattern is observed

(d) The central maximum is blue with coloured higher order maxima

Q7. Consider a system of *N* distinguishable particles with two energy levels for each particle, a ground state with energy zero and an excited state with energy . What is the average energy per particle as the system temperature ?

(a) 0

(b)

(c)

(d)

Q8. Consider a diatomic molecule with an infinite number of equally spaced non-degenerate energy levels. The spacing between any two adjacent levels is and the ground state energy is zero.

What is the single particle partition function *Z?*

(a)

(b)

(c)

(d)

Q9. A very long solenoid (axis along *z* direction) of *n* turns per unit length carries a current which increases linearly with time, . What is the magnetic field inside the solenoid at a given time *t?*

(a)

(b)

(c)

(d)

Q10. Suppose is a conservative vector, is a non-conservative vector and is non-zero scalar everywhere. Which one of the following is true?

(a)

(b)

(c)

(d)

Q11. Consider two matrices, *A* and *B* such that is invertible. Define two matrices, and . Which of the following relations always hold true?

(a)

(b)

(c)

(d)

Q12. The refractive index (*n*) of the entire environment around a double slit interference setup is changed from to . Which one of the following statements is correct about the change in the interference pattern?

(a) The fringe pattern disappears

(b) The central bright maximum turns dark, i.e.. becomes a minimum

(c) Fringe width of the pattern increases by a factor 2

(d) Fringe width of the pattern decreases by a factor 2

Q13. A cyclotron can accelerate deuteron to 16*MeV*. If the cyclotron is used to accelerate - particles, what will be their energy? Take the mass of deuteron to be twice the mass of proton and mass of alpha particles to be four times the mass of protons.

(a) 8*MeV*

(b) 16*MeV*

(c) 32*MeV*

(d) 64*MeV*

Q14. Consider a hypothetical world in which the electron has spin instead of . What will be the electronic configuration for an element with atomic number ?

(a)

(b)

(c)

(d)

Q15. Two objects of unit mass are thrown up vertically with a velocity of at latitudes and *S*, respectively. The angular velocity of the rotation of Earth is given to be .

In which direction will the objects deflect when they reach their highest point (due to Coriolis force) ? Assume zero air resistance.

(a) To the east in Northern hemisphere and west in Southern Hemisphere

(b) To the west in Northern hemisphere and east in Southern Hemisphere

(c) To the east in both hemispheres

(d) To the west in both hemispheres