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

For the given digital circuit, $A=B=1$. Assume that AND, OR, and NOT gates have propagation delays of 10 ns, 10 ns, and 5 ns respectively. All lines have zero propagation delay. Given that $C=1$ when the circuit is turned on, the frequency of steady-state oscillation of the output $Y$ is ________.

In the circuit shown, the initial binary content of shift register A is 1101 and that of shift register B is 1010. The shift registers are positive-edge triggered, and the gates have no delay.
When the shift control is high, what will be the binary content of the shift registers A and B after four clock pulses?

The magnitude and phase plots shown in the figure match with the transfer-function ________.

A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0,\forall t<0$. From the list given below, select ALL the signals whose continuous-time Fourier transform is purely imaginary.

A silica-glass fiber has a core refractive index of 1.47 and a cladding refractive index of 1.44. If the cladding is completely stripped out and the core is dipped in water having a refractive index of 1.33, the numerical aperture of the modified fiber is ________ (rounded off to three decimal places).