GATE EC 2021 Question Paper (07-Feb-2021) (Shift 2)

Consider the integral ${\oint }_C\frac{\sin (x)}{x^2(x^2+4)}dx$

Where C is a counter-clockwise oriented circle defined as |x - i| = 2. The value of the integral is

A box contains the following three coins.

I. A fair coin with head on one face and tail on the other face.

II. A coin with heads on both the faces.

III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

The switch in the circuit in the figure is in position P for long time and then moved to position Q at time t = 0.



The value of $\frac{dv\left(t\right)}{dt}$ at t = 0⁺ is

Consider the two-port network shown in the figure.



The admittance parameters, in siemens, are

For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity (∂V${}_T$ /∂|V${}_{BS}$ |) is found to be 50 mV/V at a substance voltage |V${}_{BS}$ | = 2 V, where V${}_T$ is the threshold voltage of the MOSFET. Assume that, |V${}_{BS}$ | >> 2ϕ${}_B$, where qϕ${}_B$ is the separation between the Fermi energy level E${}_F$ and the intrinsic level Eᵢ in the bulk. Parameters given are

Electron charge (q) = 1.6 × 10⁻¹⁹ C

Vacuum permittivity (ε₀) = 8.85 × 10⁻¹² F/m

Relative permittivity of silicon (ε${}_{Si}$) = 12

Relative permittivity of oxide (εₒₓ) = 4

The doping concentration of the substrate is