1
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 ____
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
MCQ (Single Correct Answer)
+2
-0.6
Let $$g\left( x \right) = \left\{ {\matrix{ { - x} & {x \le 1} \cr {x + 1} & {x \ge 1} \cr } } \right.$$ and
$$f\left( x \right) = \left\{ {\matrix{ {1 - x,} & {x \le 0} \cr {{x^{2,}}} & {x > 0} \cr } } \right..$$
Consider the composition of $$f$$ and $$g,$$ i.e., $$\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right).$$ The number of discontinuities in $$\left( {f \circ g} \right)\left( x \right)$$ present in the interval $$\left( { - \infty ,0} \right)$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$4$$
4
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
An urn contains $$5$$ red balls and $$5$$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
A
$${1 \over 2}$$
B
$${4 \over 9}$$
C
$${5 \over 9}$$
D
$${6 \over 9}$$
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