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 ...

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. ...

Q. The frequencies of the primary magnetic field generated by worldwide thunderstorm activity vary in the range (A) 10-6 Hz -10-3 Hz (B) 10-3 Hz -1 Hz (C) 1 Hz -103 ...

Q. The effect of small scale near surface inhomogeneities can be removed from magnetic data by A. upward continuation. B. downward continuation. C. second vertical derivative. D. reduction to pole. Ans: upward continuation.