# Joint Entrance Screening Test (JEST) Past Year Question Papers 2018 Part 3

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## PART B (THREE MARKS QUESTIONS)

Q1. An electronic circuit with 10000 components performs its intended function success fully with a probability 0.99 if there are no faulty components in the circuit. The probability that there are faulty components is 0.05. If there are faulty components, the circuit performs successfully with a probability 0.3. The probability that the circuit performs successfully is . What is *x?*

Q2. If an Aeolian group is constructed with two distinct elements *a* and *b* such that where *I* is the group identity. What is the order of the smallest Aeolian group containing *a*, *b* and *I?*

Q3. In the circuit shown below, the capacitor is initially unchanged. Immediately after the key *K* is closed; the reading in the ammeter is 27 *mA*.

What will the reading (in *mA*) be a long time later?

Q4. The normalized Eigen functions and eigenvalues of the Hamiltonian of a Particle confined to move between in one dimension are respectively. Here 1,2, 3 … Suppose the state of the particle is

where *A* is the normalization constant. If the energy of the particle is measured, the probability to get the result as is . What is the value of *x?*

Q5. Consider the transistor circuit shown in the figure. Assume and the leakage current is negligible.

What is the required value of in kilo-ohms if the base current is to be ?

Q6. A harmonic oscillator has the following Hamiltonian

It is perturbed with a potential some of the matrix elements of in terms of its expectation value in the ground state are given as follows:

where is the normalized Eigen state of corresponding to thee eigenvalue . Suppose and denote the energy correction of to thee ground state and the first excited state, respectively. What is the fraction ?

Q7. A person on Earth observes two rockets *A* and *B* directly approaching each other with speeds 0.8*c* and 0.6*c* respectively. At a time when the distance between the rockets is observed to be , the clocks of the rockets and the Earth are synchronized to *t* = 0*s*. The time of collision (in seconds) of the two rockets as measured in rocket *A* ′ *s* frame is . What is *x?*

Q8. Two parallel rails of a railroad track are insulated from each other and from the ground.

The distance between the rails is 1 meter. A voltmeter is electrically connected between the rails. Assume the vertical component of the earth՚s magnetic field to the 0.2 gauss.

What is the voltage developed between the rails when a train travels at a speed of 180 *km*/ *h* along the track? Give the answer in milli-volts.

Q9. Consider a simple pendulum in three-dimensional space. It consists of a string length *cm* and bob mass *m =* 15*kg* attached to it as shown in the figure below The acceleration due to gravity is downwards as shown in the figure with a magnitude .

The pendulum is pulled in the *x-z* plane to a position where the string makes an angle with the *z* -axis. It is then released an angular velocity radians per second about the z-axis. What should be the value of in radians per second so that the angle lie siring makes with the *z* -axis does not change with time?

Q10. Two conductors are embedded in a material of conductivity and dielectric constant the resistance between the two conductors is ohm. What is the capacitance (in *pF)* between the two conductors? Ignore the decimal part of the answer.

*y*

*x*

*l* = 20*cm*

*m* = 15*kg*

*z*

*g* = 10*ms* − 2