GATE 2022 EE question paper PDF and answer key

Given below are two statements and four conclusions drawn based on the statements.

Statement 1: Some bottles are cups.

Statement 2: All cups are knives.

Conclusion I: Some bottles are knives.

Conclusion II: Some knives are cups.

Conclusion III: All cups are bottles.

Conclusion IV: All knives are cups.

Which one of the following options can be logically inferred?

An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.

Which one of the following is a part of a possible trajectory of the ant during the movement?

For the circuit shown below with ideal diodes, the output will be

In the circuit shown below, the switch $S$ is closed at $t = 0$. The magnitude of the steady state voltage, in volts, across the $6\ \Omega$ resistor is _________. (round off to two decimal places).

The voltage at the input of an AC-DC rectifier is given by $v(t) = 230\sqrt{2}\sin\omega t$ where $\omega = 2\pi \times 50$ rad/s. The input current drawn by the rectifier is given by

$i(t) = 10\sin\left(\omega t - \frac{\pi}{3}\right) + 4\sin\left(3\omega t - \frac{\pi}{6}\right) + 3\sin\left(5\omega t - \frac{\pi}{3}\right).$

The input power factor, (rounded off to two decimal places), is, _________________ lag.