List of top Questions asked in GATE ES- 2021

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?
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?
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 the context of noise pollution, SPL is the sound pressure level in decibels (dB). The relationship between SPL, the root mean square (rms) sound pressure \( p \), and the reference (hearing threshold) pressure \( p_0 \) is expressed as _______.
Which of the following causes ‘Type-I’ settling in a sedimentation tank?
Which of the following is the terminal electron acceptor in the electron transport chain of aerobic respiration?
What is the order of preference of the various elements in integrated waste management hierarchy (highest preference to lowest preference)?
In fluid statics, the line of action of the buoyant force always acts through the
A sample of air is collected in the morning at an ambient temperature of 25°C. The concentration of carbon monoxide (CO) in this sample is 30 ppmv (ppm by volume). The same sample is analysed later in the afternoon when the sample temperature is 35°C. The analysis results will show the CO concentration as _______.
Evaluate the limit:

\[ \lim_{x \to 0} \frac{x^2}{\sin x} \]

= _______.
If \( d \) is the depth of an aquifer through which water is flowing, then the relationship between permeability \( K \) and transmissibility (also known as transmissivity) \( T \) is given by _______.

In context of municipal solid waste treatment, match the equipment in List I with their function in List II. 

Which of the following international multilateral agreements (conventions, protocols) from Column I match with the entries in Column II?

Match the entries in Column I with the correct entries in Column II. 

The 2×2 matrices P and Q satisfy the following relations: 

The matrix Q is equal to _______.

The following block diagram highlights the typical phases of the life cycle of a product. In the figure, ‘P’, ‘Q’, and ‘R’ represent various possible scopes of analyses in life cycle assessment. Which of the following statements is true? 

The table below shows the carbon content of four samples of powdered coal. If these four samples are mixed completely, what would be the resultant carbon percentage of the mixture by weight? 

A mechanized stationary container system is proposed for waste collection from a commercial area. The container unloading time is 0.1 hours per container. There are two containers at each location and the drive time between the two locations is 0.2 hours. The maximum waste ‘pick-up time’ is 2.4 hours per trip. The ‘pick-up time’ starts at the instant the truck arrives at the first pick-up location and ends when the last container on the route is emptied. The maximum number of locations which can be covered in a trip by the collection vehicle are _______ (answer in integer).