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

The vector function F(r) = -x î + yĵ is defined over a circular are C shown in the figure.



The line integral of ∫${}_C$ F(r) ⋅ dr is

Consider the differential equation given below:

$\frac{dy}{dx}+\frac{x}{1-x^2}y=x\sqrt{y}$

The integrating factor of the differential equation is:

Two continuous random variables X and Y are related as

Y = 2X + 3

Let ${\sigma }_X^2$ and ${\sigma }_Y^2$ denote the variances of X and Y, respectively. The variances are related as

Consider a real-value based-band signal x(t), band limited to 10 kHz. The Nyquist rate for the signal y(t) = x(t) $x(1+\frac{t}{2})$ is

Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of x[n] and h[n]. The value(s) of k for which z[k] = y[k] is/are