# Joint Entrance Screening Test (JEST) Past Year Question Papers 2019 Part 2

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Q16. Which one of the following vectors lie along the line of intersection of the two planes

?

(a)

(b)

(c)

(d)

Q17. What is the value of the integral ?

(a)

(b)

(c)

(d) 0

Q18. Two joggers *A* and *B* are running at a steady pace around a circular track. *A* takes *A T* minutes whereas *B* takes minutes to complete one round. Assuming that they have started together, what will be time taken by *A* to overtake *B* for the first time?

(a)

(b)

(c)

(d)

Q19. The magnetic field (Gaussian units) in an empty space is described by

What is the *y* - component of the electric field?

(a)

(b)

(c)

(d) 0

Q20. Let *A* be a hermitian matrix, and *C* and *D* be the unitary matrices. Which one of the following matrices is unitary?

(a)

(b)

(c)

(d)

Q21. The wave function (for real constants *A* and *b)* is a normalized Eigen function of the Schrodinger equation for a particle of mass *m* and energy *E* in a one-dimensional potential such that . Which of the following is correct?

(a)

(b)

(c)

(d)

Q22. A quantum particle of mass *m* is in a one-dimensional potential of the form

where is a constant. Which one of the following represents the possible ground state wave function of the particle?

(a)

(b)

(c)

(d)

Q23. Consider a matrix what is ?

(a)

(b)

(c)

(d)

Q24. Consider a grand ensemble of a system of one-dimensional non-interacting classical harmonic oscillators (each of frequency ) . Which one of the following equations is correct? Here the angular bracket indicate the ensemble average. *N*, *E*, and *T* represent the number of particles, energy, and temperature, respectively. *B k* is the Boltzmann constant.

(a)

*(b)*

(c)

(d)

Q25. A bullet with initial speed is fired at a log of wood. The resistive force by wood on the bullet is given by , where . What is the time taken to stop the bullet inside the wood log?

(a)

(b)

(c)

(d)