List of top Calculus Questions on Partial derivatives asked in GATE MA

The surface area of the paraboloid \( z = x^2 + y^2 \) between the planes \( z = 0 \) and \( z = 1 \) is __________ (round off to ONE decimal place).

The work done by the force \( \mathbf{F} = (x + y) \hat{i} - (x^2 + y^2) \hat{j} \),
where \( \hat{i} \) and \( \hat{j} \) are unit vectors in \( \mathbf{O X} \) and \( \mathbf{O Y} \) directions, respectively, along the upper half of the circle \( x^2 + y^2 = 1 \) from \( (1, 0) \) to \( (-1, 0) \) in the \( xy \)-plane is

f(x,y)=\(\left\{\begin{matrix} 1-cos(\frac{x^2}{y^2}) \\  \sqrt{x^2+y^2} \end{matrix}\right.\) ;if y≠0 & n∈R, then