1
GATE PI 2014
+1
-0.3
Directional derivative of $$\phi = 2xz - {y^2}$$ at the point $$(1, 3, 2)$$ becomes maximum in the direction of
A
$$4i+2j-3k$$
B
$$4i-6j+2k$$
C
$$2i-6j+2k$$
D
$$4i-6j-2k$$
2
GATE PI 2014
+2
-0.6
If $$\,\phi = 2{x^3}{y^2}{z^4}$$ then $${\nabla ^2}\phi$$ is
A
$$12x{y^2}{z^4} + 4{x^2}{z^4} + 20{x^3}{y^2}{z^3}$$
B
$$2{x^2}{y^2}z + 4{x^3}{z^4} + 24{x^3}{y^2}{z^2}$$
C
$$12x{y^2}{z^4} + 4{x^2}{z^4} + 24{x^3}{y^2}{z^2}$$
D
$$4x{y^2}z + 4{x^2}{z^4} + 24{x^3}{y^2}{z^2}$$
3
GATE PI 2014
+1
-0.3
In a given day in the rainy season, it may rain$$70$$% of the time . If it rains, chance that a village fair will make a loss on that day is $$80$$%. However, if it does not rain, chance that the fair will make a loss on that day is only $$10$$%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day?
A
$$3/10$$
B
$$9/11$$
C
$$14/17$$
D
$$27/41$$
4
GATE PI 2014
Numerical
+2
-0
A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard deviation were determined to be $$80$$ and $$12,$$ respectively. The standard error of mean is ______.
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