GATE IN 2015 Question Paper (01-Feb-2015) (Shift 2)

The probability that a thermistor randomly picked up from a production unit is defective is 0.1. The probability that out of 10 thermistors randomly picked up, 3 are defective is

The probability density function of a random variable X is p${}_X$ (x) = e${}^{-x}$ for x ≥ 0 and 0 otherwise. The expected value of the function g${}_X$ (x) = e${}^{3x/4}$ is ___________.

The z-transform of x[n] = a${}^{|n|}$, 0 < |a|< 1, is X(z). The region of convergence of X(z) is

The current in amperes through the resistor R in the circuit shown in the figure is __________ A.

The linear I-V characteristics of 2-terminal non-ideal dc sources X and Y are shown in the figure. If the sources are connected to a 1 Ω resistor as shown, the current through the resistor in amperes is __________ A.