GATE IN 2011 Question Paper (13-Feb-2011) (Shift-2)

The integral

$\frac{1}{\sqrt{2\pi }}{\int }_{-\infty }^{\infty }{t}^2{e}^{-t^2/2}\delta (1-2t)dt$ is equal to

Shown below is the pole-zero plot of a digital filter



Which one of the following statements is TRUE?

The continuous time signal $x(t)=\cos (100\pi t)+\sin (300\pi t)$ is sampled at the rate 100 Hz to get the signal

$x_s(t)={\sum }_{n=-\infty }^{\infty }x(n{T}_s)\delta (t-n{T}_s)$, $T_s=\text{sampling period}$

The signal $x_s(t)$ is passed through an ideal low pass filter with cutoff frequency 100 Hz. The output of the filter is proportional to

Consider a system with input $x(t)$ and output $y(t)$ related as follows

$y(t)=\frac{d}{dt}\{e^{t}x(t)\}$

Which one of the following statements is TRUE?

The first two rows of Routh's table of a third-order characteristic equation areIt can be inferred that the system has