List of top Questions asked in GATE ES

Given are two ordinary differential equations
P: $\dfrac{dy}{dx} + x = x \sin y$
Q: $\dfrac{dy}{dx} + x y = e^{x} y$
The correct choice is:
P and Q are square matrices. Consider the following:
X: $(P^{-1})^{-1} = P$
Y: Symmetric if $Q = -Q^T$
The correct choice is:
Given are two infinite series
P: $\displaystyle \sum \frac{n^2 + 1}{n^2}$
Q: $\displaystyle \sum \left(1 + \frac{1}{n}\right)^{-n}$
The correct choice is:
For testing alkalinity for a water sample, first phenolphthalein indicator is added. The water remains colorless. However, when a few drops of methyl orange are added to the sample, the color turns yellow. As per these observations, the correct choice is:
Permit : __________ :: Enforce : Relax (By word meaning)
Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?
A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco. Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?
How many triangles are present in the given figure?
Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that surprisingly none of the students from the Department of Human Sciences had completed the registration process.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.
(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.
(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.
Which one of the following options represents the given graph?