List of top Questions asked in GATE EC

Consider a system of linear equations $Ax = b$, where \[ A = \begin{bmatrix} 1 & -\sqrt{2} & 3 \\ -1 & \sqrt{2} & -3 \end{bmatrix}, \qquad b = \begin{bmatrix} 1 \\ 3 \end{bmatrix}. \] This system of equations admits ________________.

Consider the following inequalities.
\text{(i) } 2x - 1 $>$ 7
\text{(ii) } 2x - 9 $<$1
Which one of the following expressions below satisfies the above two inequalities?

In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below. Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies. Based on the information given above, the person who has copied in the exam is:

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360° view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery?

Four points $ P(0, 1), Q(0, -3), R(-2, -1), $ and $ S(2, -1) $ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets ₹1000 more than S, what is the share of Q (in ₹)?

A trapezium has vertices marked as P, Q, R, and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm, and SP = 3 cm. What is the shortest distance between PQ and SR (in cm)?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 $\times$ 4 grid using the unit squares as building blocks?

Mr. X speaks __________ Japanese __________ Chinese.

Given below are two statements and two conclusions.
Statement 1: All purple are green.
Statement 2: All black are green.
Conclusion I: Some black are purple.
Conclusion II: No black is purple.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.
The number of days in the given week in which one of the students spent a minimum of 10\% more than the other student, on a given day, is

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is _________

Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues. Which of the following can be deduced from the above passage?

Consider the following sentences:
(i) I woke up from sleep.
(ii) I wok up from sleep.
(iii) I was woken up from sleep.
(iv) I was wokened up from sleep.
Which of the above sentences are grammatically CORRECT?

Nostalgia is to anticipation as _________ is to _________. Which one of the following options maintains a similar logical relation in the above sentence?

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is

p and q are positive integers and \[ \frac{p}{q} + \frac{q}{p} = 3, \] then, \[ \frac{p^2}{q^2} + \frac{q^2}{p^2} = \]

The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is _________ bits.

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time $ t = 0 $. \[ \text{Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is A.} \]

A unity feedback system that uses proportional-integral (PI) control is shown in the figure.

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is 500 MHz.

A circuit with an ideal OPAMP is shown in the figure. A pulse $ V_{\text{IN}} $ of 20 ms duration is applied to the input. The capacitors are initially uncharged.

For the transistor M1 in the circuit shown in the figure, $ \mu_n C_{\text{ox}} = 100 \, \mu \text{A/V}^2 $ and $ \frac{W}{L} = 10 $, where $ \mu_n $ is the mobility of electrons, $ C_{\text{ox}} $ is the oxide capacitance per unit area, $ W $ is the width, and $ L $ is the length. The channel length modulation coefficient is ignored. If the gate-to-source voltage $ V_{GS} $ is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is _________ V.