GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

The table shows the present state Q(t), next state Q(t+1), and the control input in a flip-flop. Identify the flip-flop.

Match the Exclusive-OR (XOR) operations (i) to (iv) with the results (p) to (s), where X is a Boolean input.

A light emitting diode (LED) emits light when it is ______ biased. A photodiode provides maximum sensitivity to light when it is ______ biased.

$F(z)=\frac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)={\sum }_{k=0}^{\infty }{a}_k(z-2{)}^k$, with the region of convergence (ROC) $|z-2|<1$. The coefficients $a_k,k\ge 0$, are given by the expression ______

The solution $x(t),t\ge 0$, to the differential equation
$\ddot{x}=-k\dot{x},k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is