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

Consider a real baseband signal $x(t)=e^{-2t}$, for $t$ (in seconds) $\ge 0$.
If 99% of energy of $x(t)$ lies within $B\text{ Hz}$, then which of the following options is TRUE for the value of $B$?

Consider the discrete time system (S) with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_1[n]$ and $h_2[n]$ are linear and time invariant.
Which of the following statements is necessarily TRUE?

A Boolean function, $f(x,y,z)$ with $x$ as MSB and $z$ as LSB is realized by 4:1 multiplexer (MUX) with select lines, $S_1$ and $S_0$ ( $S_1$ is MSB, $S_0$ is LSB) and inputs, $I_0$, $I_1$, $I_2$, $I_3$ as shown in the Figure.
Which of the following options is the correct expression of $f(x,y,z)$?

A shift-left Shift Register (SR) and a D flip-flop are connected to a synchronized clock as shown in the Figure. Assume that the SR and D flip-flops are initially cleared and the XOR gate has no propagation delay.
Which of the following options gives the correct binary representation ($b_7{b}_6{b}_5{b}_4{b}_3{b}_2{b}_1{b}_0$) of the content of the shift register immediately after the 5${}^{\text{th}}$ clock transition (positive edge)?

A small signal source, $V_i(t)=A\cos (10^{5}t)+B\sin (10^{7}t)$ is applied to a BJT circuit as shown in the Figure.
Assume zero source resistance, $V_{BE}=0.7\text{ V}$, ${\beta }_{dc}=99$, Early voltage $=100\text{ V}$ and Thermal voltage $=25\text{ mV}$. Effect of internal parasitic capacitances of the BJT may be neglected.
Which expression is the best approximation of the output voltage $V_o(t)$?