Q. In the circuit shown below, the input voltage 𝑉𝑖𝑛 is positive. The current (𝐼) – voltage (𝑉) characteristics of the diode can be assumed to be 𝐼 = 𝐼0𝑒𝑉/𝑉𝑇 under the forward bias condition, where 𝑉𝑇 is the thermal voltage and 𝐼0 is the reverse saturation current. Assuming an ideal op-amp, the output voltage […]

Q. If each of the values of inductance, capacitance and resistance of a series LCR circuit are doubled, the Q-factor of the circuit would (A) reduce by a factor √2 (B) reduce by a factor 2 (C) increase by a factor √2 (D) increase by a factor 2 Ans: reduce by a factor 2 Sol:

Q. In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant T1 . Similarly, the closed loop transfer function of the outer loop may be assumed to have a single time-constant T2. The desired relationship between T1 and T2 in a well-designed control

Q. The input 𝑥[𝑛] and output 𝑦[𝑛] of a discrete-time system are related as 𝑦[𝑛] = 𝛼𝑦[𝑛 − 1] + 𝑥[𝑛]. The condition on 𝛼 for which the system is Bounded-Input Bounded-Output (BIBO) stable is (A) |𝛼| < 1 (B) |𝛼| = 1 (C) |𝛼| > 1 (D) |𝛼| < 3/2 Ans: |𝛼| < 1

Q. In the Figures (a) and (b) shown below, the transformers are identical and ideal, except that the transformer in Figure (b) is centre-tapped. Assuming ideal diodes, the ratio of the root- mean-square (RMS) voltage across the resistor 𝑅 in Figure (a) to that in Figure (b) is (A) √2:1 (B) 2:1 (C) 2√2:1 (D)

Q. A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is Sol: A box has 8 red balls and 8 green balls. Two balls are drawn

Q. In an electromagnetic scale modeling experiment in the lab, the relation between the field and lab geometrical scaling factor (n) with the field and lab resistivity (𝜌𝑓 & 𝜌𝑚) as well as frequencies (𝑓𝑓 & 𝑓𝑚) will be Ans: Option A

Q. The phase difference between the input and output signals for a ‘Compensator device’ used in electromagnetic prospecting to nullify the effect of primary field at the receiver coil is (A) 0° (B) 45° (C) 90° (D) 180° Ans: 180°

Q. Which one of the following statements is INCORRECT with regard to Nuclear Magnetic Resonance (NMR) logging? (ΦNMR – NMR derived total porosity, ΦD – Density porosity) (A)The relaxation time (T2) decreases with decrease in pore size. (B)The ΦNMR is greater than ΦD in a water saturated sandstone formation. (C)The NMR logs provide lithology independent

Q. Which one of the following is CORRECT for the density porosity (fD) and neutron porosity (fN) estimated for a finely interbedded organic-rich, shaly sandstone formation relative to those for a shale-free sandstone formation at shallow depths? (A) ΦN decreases and ΦD increases. (B) ΦN increases and ΦD decreases. (C) Both ΦN and ΦD decrease.