List of top Questions asked in GATE AG- 2023

Evaluate the limit \[ \lim_{x\to 0}\frac{\sqrt{\,1+x\,}-1}{x}. \]
The value of \[ I=\int_0^{\pi/2}\frac{(\sin x+\cos x)^2}{\sqrt{1+\sin 2x}}\,dx \] is:
\(y=ae^{mx}+be^{-mx}\) is the solution of the differential equation:
In rotary tiller, the total energy requirement for carrying out tillage will decrease if
The effectiveness of the turbocharger of a diesel engine increases when
A line of symmetry is a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of \(16\) unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both \(PQ\) and \(MN\) form lines of symmetry? (The figure is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}
Human beings are one among many creatures that inhabit an imagined world. In this world, some creatures are cruel. If it is given that the statement "Some human beings are not cruel creatures" is FALSE, then which of the following statements can be logically inferred with certainty? (i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.
To construct a wall, sand and cement are mixed in the ratio \(3:1\). The costs per unit of sand and cement are in the ratio \(1:2\). If the total cost of sand and cement is ₹~1000, what is the cost (in rupees) of cement used?
The World Bank has declared that it will not offer new financing to Sri Lanka until the country has an adequate macroeconomic policy framework. It adds that Sri Lanka needs structural reforms for stabilisation and to tackle root causes of the crisis. The crisis has starved the country of foreign exchange and led to shortages of essentials. The Bank is repurposing existing loans to ease shortages. Based only on this passage, which statement can be inferred with certainty?
The coefficient of \(x^4\) in \((x-1)^3(x-2)^3\) is equal to \underline{\hspace{1cm}}.
Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and not allowed to overlap.
References : ................ :: Guidelines : Implement (By word meaning)
In the given figure, \(PQRS\) is a parallelogram with \(PS = 7\) cm, \(PT = 4\) cm and \(PV = 5\) cm. What is the length of \(RS\) in cm? (The diagram is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}
In 2022, June Huh was awarded the Fields medal. He was also a poet, did not win any medals in the International Mathematics Olympiads, and dropped out of college. Based only on this information, which statement can be inferred with certainty?
"You are delaying the completion of the task. Send ................ contributions at the earliest."