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

Consider the following series:

${\Sigma }_{n=1}^{\infty }\frac{n^d}{c^n}$

For which of the following combinations of c, d values does this series converge?

The outputs of four systems (S1, S2, S3, and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure.

Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?

Select the CORRECT statement(s) regarding semiconductor devices.

A state transition diagram with states A, B, and C, and transition probabilities p1, p2, … , p7 is shown in the figure (e.g., p1 denotes the probability of transition from state A to B). For this state diagram, select the statement(s) which is/are universally true.

Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B̅, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).