1
GATE EE 2022
+1
-0.33

Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R?

A
$$\int\!\!\!\int\limits_R {dxdy}$$
B
$$\oint\limits_C {xdy}$$
C
$$\oint\limits_C {ydx}$$
D
$${1 \over 2}\oint\limits_C {(xdy - ydx)}$$
2
GATE EE 2017 Set 1
Numerical
+1
-0
Let $${\rm I} = c\int {\int {_Rx{y^2}dxdy,\,\,} }$$ where $$R$$ is the region shown in the figure and $$c = 6 \times {10^{ - 4}}.\,\,$$ The value of $${\rm I}$$ equals ___________.
3
GATE EE 2017 Set 2
Numerical
+1
-0
Let $$\,{y^2} - 2y + 1 = x$$ and $$\,\sqrt x + y = 5.\,\,$$ The value of $$\,x + \sqrt y \,\,$$ equals ________. (Given the answer up to three decimal places)
4
GATE EE 2017 Set 2
Numerical
+1
-0
Consider a function $$f\left( {x,y,z} \right)$$ given by $$f\left( {x,y,z} \right) = \left( {{x^2} + {y^2} - 2{z^2}} \right)\left( {{y^2} + {z^2}} \right).$$ The partial derivative of this function with respect to $$x$$ at the point $$x=2, y=1$$ and $$z=3$$ is _______.