1
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the set $S$ of points $(x, y) \in R^2$ which minimize the real valued function

$$ f(x, y)=(x+y-1)^2+(x+y)^2 $$

Which of the following statements is true about the set $S$ ?

A
The number of elements in the set $S$ is finite and more than one.
B
The numebr of elements in the set $S$ is infinite.
C
The set $S$ is empty.
D
The number of elements in the set $S$ is exactly one.
2
GATE EE 2017 Set 2
Numerical
+1
-0
Let $$x$$ and $$y$$ be integers satisfying the following equations $$$2{x^2} + {y^2} = 34$$$ $$$x + 2y = 11$$$
The value of $$(x+y)$$ is _________.
Your input ____
3
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 _______.
Your input ____
4
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)
Your input ____
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