GATE EC 2026 Question Paper (15-Feb-2026) (Shift 1)

The state and output equations for a control system are:

$$\dot{x}=\left[\begin{array}{cc}-4& -1.5\\ 4& 0\end{array}\right]x+\left[\begin{array}{c}2\\ 0\end{array}\right]u$$

$$y=\left[\begin{array}{cc}1.5& 0.625\end{array}\right]x$$
Which of the following expressions correctly represents the transfer function $\frac{Y(s)}{U(s)}$ of the system with zero initial conditions?

The address of the first location of a 256 kilo byte (KB) memory is (2500)${}_{\text{H}}$.
Choose the correct address of the last location of the memory.

Consider a real signal $x(t)$, $-\infty <t<\infty$, such that

$x(t)=0$ for $t<0$, $x(t)=2$ for $0\le t<1$ and $x(t)=0$ for $t\ge 1$.

Let $E[x(t)]={\int }_{-\infty }^{\infty }[x(t){]}^{2}dt$.

Which of the following options correctly represents the ratio,

$E[x(t)]/E[3x(-3t+5)]$?

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_b/N_o=8.4\text{ dB}$ at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator.
Assume the complimentary error function

$$\text{erfc}(u)\cong \left[1/(u\sqrt{\pi )}\right]\exp (-u^2).$$
Which is the nearest bit error rate (BER) at the output of the demodulator?

What is the $10^{\prime }$ s complement of $(47{)}_{10}$?