# 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 0.8c and 0.6c 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 = 0s. The time of collision (in seconds) of the two rockets as measured in rocket As 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 = 15kg 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 = 20cm

m = 15kg

z

g = 10ms − 2

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