GATE EC 2022 Question Paper (06-Feb-2022) (Shift 1)

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.

The parameter α lies in the interval [0.25, 1]. The value of α for which the capacity of this channel is maximized, is ________ (rounded off to two decimal places).

A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{out}}{\partial V_{in}}$ is _______(rounded off to two decimal places).

Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?

Consider the following wave equation,

$\frac{{\partial }^{2}f(x,t)}{\partial t^2}=10000\frac{{\partial }^{2}f(x,t)}{\partial x^2}$

Which of the given options is/are solution(s) to the given wave equation?

The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler has taken 5 wickets each. The median number of wickets taken by the bowler in a match is __________ (rounded off to one decimal place).