GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

The opamp in the circuit shown is ideal, except that it has an input bias current of 1 nA and an input offset voltage of 10 µV. The resulting worst-case output voltage will be $\pm$ ______ µV (rounded off to the nearest integer).

The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them is 10 µN/m. When the gap is doubled, the force per unit length will be ______ µN/m (rounded off to one decimal place).

Consider the discrete-time signal $x[n]=u[-n+5]-u[n+3]$,
where $u[n]=\{\begin{array}{ll}1;& n\ge 0\\ 0;& n<0\end{array}$
The smallest n for which $x[n]=0$ is ______.

Let $y(t)=x(4t)$, where $x(t)$ is a continuous-time periodic signal with fundamental period of 100 s. The fundamental period of $y(t)$ is ______ s (rounded off to the nearest integer).

When the bridge given below is balanced, the current through the resistor $R_a$ is ______ mA (rounded off to two decimal places).