GATE 2025 MT – Question 48
For the two-dimensional field $T(x,y)=\tfrac13xy(x+y)$, the magnitude of its gradient at $(1,1)$ is ______ (rounded to two decimal places).
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Correct answer: 1.40 to 1.42
Explanation
Differentiate: $T_x=(2xy+y^2)/3$ and $T_y=(x^2+2xy)/3$.
At $(1,1)$ both derivatives equal 1. Hence $|\nabla T|=\sqrt{1^2+1^2}=\sqrt2=1.4142\ldots$. The answer is **1.41**.