List of top Questions asked in GATE EE- 2023

The following columns present various modes of induction machine operation and the ranges of slip: \[ \begin{array}{c|c} A: Mode of operation & B: Range of Slip
\hline a.\; \text{Running in generator mode} & p) 0.0 \; \text{to} \; 1.0
b.\; \text{Running in motor mode} & q) 1.0 \; \text{to} \; 2.0
c.\; \text{Plugging in motor mode} & r) -1.0 \; \text{to} \; 0.0
\end{array} \] Find the correct matching.

A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is:

A square with sides of length \(6 \, \text{cm}\) is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is \underline{\hspace{1cm}} cm\(^2\). \begin{center} \includegraphics[width=0.5\textwidth]{03.jpeg} \end{center}

For a given vector \( \mathbf{w} = [1 \; 2 \; 3]^T \), the vector normal to the plane defined by \( \mathbf{w}^T \mathbf{x} = 1 \) is:

For the block diagram shown in the figure, the transfer function \(\dfrac{Y(s)}{R(s)}\) is: \begin{center} \includegraphics[width=0.5\textwidth]{04.jpeg} \end{center}

In the Nyquist plot of the open-loop transfer function \[ G(s)H(s) = \frac{3s+5}{s-1} \] corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in the \(s\)-plane is mapped into a point at: \begin{center} \includegraphics[width=0.5\textwidth]{05.jpeg} \end{center}

Which one of the following options represents the given graph? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}

Which one of the options does NOT describe the passage below or follow from it? We tend to think of cancer as a 'modern' illness because its metaphors are so modern. It is a disease of overproduction, of sudden growth, a growth that is unstoppable, tipped into the abyss of no control. Modern cell biology encourages us to imagine the cell as a molecular machine. Cancer is that machine unable to quench its initial command (to grow) and thus transform into an indestructible, self-propelled automaton.

The digit in the unit's place of \(3^{999}\times 7^{1000}\) is \underline{\hspace{1.5cm}.}

Students of all departments who have successfully completed registration are eligible to vote. By the due date, noneof the students from the Department of Human Sciences (HS) had completed registration. Which set(s) of statements can be inferred with certainty? \[ \begin{array}{l} \text{(i) All ineligible students would certainly belong to HS.}
\text{(ii) None from non-HS departments failed to complete registration on time.}
\text{(iii) All eligible voters would certainly be students not from HS.} \end{array} \]