List of top Questions asked in GATE Aerospace Engineering

The direction in which a scalar field \(\phi(x,y,z)\) has the largest rate of change is along:

If a monotonic and continuous function \(y=f(x)\) has exactly one root in the interval \(x_1<x<x_2\), then:

Consider the one–dimensional wave (advection) equation \[ \frac{\partial u}{\partial t}+\frac{\partial u}{\partial x}=0, -\infty<x<\infty,\ t\ge 0. \] For the initial condition \(u(x,0)=e^{-x^{2}}\), the solution at \(t=1\) is:

The World Bank has declared it will not offer new financing to Sri Lanka until an adequate macroeconomic policy framework is in place. It says Sri Lanka needs structural reforms focusing on economic stabilisation and tackling the root causes of its crisis. The crisis has starved the country of foreign exchange and led to shortages of food, fuel, and medicines. The Bank is repurposing existing loans to help with essentials. Based only on this passage, which statement can be inferred with certainty?

Find the coefficient of \(x^4\) in \((x-1)^3(x-2)^3\).

References : ............. : : Guidelines : Implement (By word meaning)

In the given figure, \(PQRS\) is a parallelogram with \(PS = 7\text{ cm}\), \(PT = 4\text{ cm}\) and \(PV = 5\text{ cm}\). 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 (the highest prize in Mathematics). When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. \medskip Based only on the above information, which of the following statements can be logically inferred with certainty?

A line of symmetry divides a figure into two parts that are mirror images. The given figure consists of 16 unit squares. Three are already black. What is the minimum number of additional squares that must be coloured black so that both \(PQ\) (vertical midline) and \(MN\) (diagonal) are lines of symmetry? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}

In an imagined world: - Some creatures are cruel. - Humans are one kind of creature. - It is given that the statement "Some human beings are not cruel creatures" is FALSE. Which 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.

Sand and cement are mixed in the ratio \(3:1\). Cost ratio of sand to cement is \(1:2\). Total cost of sand and cement is \(\,1000\) rupees. Find the cost of cement used.

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