GATE IN 2024 Question Paper (04-Feb-2024) (Shift 2)

A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is ________ mA/°C (rounded off to two decimal places).

Consider a filter defined by the difference equation
$$y[n]-0.5y[n-2]=ax[n-4],$$
where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude response of the filter at $(\omega =\frac{\pi }{2})$ is $|H(\frac{\pi }{2})|=0.5,$ the value of a is ___________. (rounded off to two decimal places).

Consider the circuit shown in the figure.


The CMOS digital logic circuit has infinite input impedance. Assume the opamp is ideal. A 1.8 V Zener diode with a minimum Zener current of 2 mA is used. The corresponding maximum value of resistance $R_z$ is ________ k$\Omega$ (rounded off to one decimal place).

Figure shows an amplifier using an NMOS transistor. Assume that the transistor is in saturation with device parameters, ${\mu }_n{C}_{ox}=250\mu A/V^2$, threshold voltage $V_T=0.65\text{ V}$ and $W/L=4$. Ignore the channel length modulation effect. The drain current of the transistor at the operating point is ________ $\mu A$ (rounded off to nearest integer).

The number of complex multiplications required for computing a 16-point DFT using the decimation-in-time radix-2 FFT is ________ (in integer).