1
GATE IN 2015
MCQ (Single Correct Answer)
+1
-0.3
The double integral $$\,\,\int_0^a {\int_0^y {f\left( {x,y} \right)\,dx\,dy\,\,\,} } $$ is equivalent to
A
$$\int_0^x {\int_0^y {f\left( {x,y} \right)dx\,dy} } $$
B
$$\int_0^a {\int_x^y {f\left( {x,y} \right)dx\,dy} } $$
C
$$\int_0^a {\int_x^a {f\left( {x,y} \right)dx\,dy} } $$
D
$$\int_0^a {\int_0^a {f\left( {x,y} \right)dx\,dy} } $$
2
GATE IN 2015
MCQ (Single Correct Answer)
+1
-0.3
The magnitude of the directional derivative of the function $$f\left( {x,y} \right) = {x^2} + 3{y^2}$$ in a direction normal to the circle $$\,{x^2} + {y^2} = 2,$$ at the point $$(1,1),$$ is
A
$$4\sqrt 2 $$
B
$$5\sqrt 2 $$
C
$$7\sqrt 2 $$
D
$$9\sqrt 2 $$
3
GATE IN 2015
MCQ (Single Correct Answer)
+1
-0.3
The probability that a thermistor randomly picked up from a production unit is defective is $$0.1.$$ The probability that out of $$10$$ thermistors randomly picked up, $$3$$ are defective is
A
$$0.001$$
B
$$0.057$$
C
$$0.107$$
D
$$0.3$$
4
GATE IN 2015
Numerical
+2
-0
The probability density function of a random variable $$X$$ is $$\,{P_x}\left( x \right) = {e^{ - x}}\,\,$$ for $$\,\,x \ge 0\,\,$$ and $$0$$ otherwise. The expected value of the function $$\,{g_x}\left( x \right) = {e^{3x/4}}$$ is___________.
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