GATE EC 2020 Question Paper (02-Feb-2020) (Shift 2)

Consider the following system of linear equations,

x₁ + 2x₂ = b₁

2x1 + 4x2 = b2

3x1 + 7x2 = b3

3x1 + 9x2 = b4

Which one of the following conditions ensures that a solution exists for the above system?

Which one of the following options contains two solutions of the differential equation $\frac{dy}{dx}=\left(y-1\right)x?$

The current I in the given network is

A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos (200πt) at sampling instants t = n/400, n = 0, 1, …, 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as:

$X\left[k\right]=\sum _{n=0}^{7}x\left[n\right]e^{-j\frac{\pi kn}{4}},k=0,1,\dots ,7.$

Which one of the following statements is TRUE?

For the given circuit, which one of the following is the correct state equation?