October 2023

Q. The Thevenin equivalent circuit representation across terminals p-q of the circuit shown in the figure is a (A) 1 V source in series with 150 kΩ            (B) 1 V source in parallel with 100 kΩ (C) 2 V source in series with 150 kΩ            (D) 2 V source in parallel with 200 kΩ Ans: […]

Q. A series R-C circuit is excited by a 1Ð0 V sinusoidal ac voltage source. The locus diagram of the phasor current 𝐼= (x + jy) A, when C is varied, while keeping R fixed, is Ans: Option 1

Q. Consider two functions 𝑓(𝑥) = (𝑥 − 2)2 and 𝑔(𝑥) = 2𝑥 − 1, where 𝑥 is real. The smallest value of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥) 𝑖𝑠 __________. Ans: 1

Q. 𝑋 and 𝑌 are two independent random variables with variances 1 and 2, respectively. Let 𝑍 = 𝑋 − 𝑌. The variance of 𝑍 is (A) 0                           (B) 1                           (C) 2                          (D) 3 Ans: 3

Q. Let  𝑓1(𝑧) = 𝑧2    and  𝑓2(𝑧) = 𝑧̅ be two complex variable functions. Here 𝑧̅   is the complex conjugate of z. Choose the correct answer. A. Both 𝑓1(𝑧) and 𝑓2(𝑧) are analytic B. Only 𝑓1(𝑧) is analytic C. Only 𝑓2(𝑧) is analytic D. Both 𝑓1(𝑧) and 𝑓2(𝑧) are not analytic Ans: Only 𝑓1(𝑧) is

Q. Let 𝑁 be a 3 by 3 matrix with real number entries. The matrix 𝑁 is such that 𝑁2 = 0. The eigen values of N are (A) 0, 0, 0                   (B) 0,0,1                     (C) 0,1,1                    (D) 1,1,1 Ans: 0, 0, 0  

Q. Using the Gutenberg-Richter recurrence relationship, the mean annual rate of exceedance of earthquake occurrence in a seismic belt is 0.3 per year for an earthquake of magnitude 6.0. The return period for an earthquake of magnitude 6.0 in this belt is_____years. Ans: 3.0-3.5

Q. The angle of inclination of the remanent magnetization measured on a basalt flow at a location P (28°N 85°E) is 40°. The palaeomagnetic latitude of the basalt flow is________________°N. Ans: 22.5-23.0

Q. Which one of the following well log responses characterizes an overpressured zone in the subsurface? A. High velocity and high resistivity. B. Low velocity and low density. C. High velocity and low resistivity. D. Low velocity and high density. Ans: Low velocity and low density.

Q. Assertion (a): The Static Self-Potential for a thick, clean freshwater bearing sandstone formation is positive. Reason(r): Resistivity of the formation water is less than the resistivity of salt water mud- filtrate. A. Both (a) and (r) are true and (r) is the correct reason for (a). B. Both (a) and (r) are true and