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

Consider an even polynomial p(s) given by

p(s) = s⁴ + 5s² + 4 + K

where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the imaginary axis is ________.

In a non-degenerate bulk semiconductor with electron density n = 10¹⁶ cm⁻³ , the value of E${}_C$ - E${}_{Fn}$ = 200 meV, where E${}_C$ and E${}_{Fn}$ denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 10¹⁰ cm⁻³ . For n = 0.5 × 10¹⁶ cm⁻³ , the closest approximation of the value of (E${}_C$ − E${}_{Fn}$), among the given options, is __________.

Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width (W) to gate length (L) ratios $\left(\frac{W}{L}\right)$ of the transistors are as shown. Both the transistors have the same gate oxide capacitance per unit area. For the pMOSFET, the threshold voltage is -1 V and the mobility of holes is 40 $\frac{\mathrm{c}{\mathrm{m}}^2}{V.s}$. For the nMOSFET, the threshold voltage is 1 V and the mobility of electrons is 300 $\frac{\mathrm{c}{\mathrm{m}}^2}{V.s}$ The steady state output voltage V₀ is _________.

Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A₀, A₁, A₂, and A₃ are ________.

The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and -1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady-state voltages are ___________.