1
GATE ME 2012
MCQ (Single Correct Answer)
+1
-0.3
At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has
A
a maximum value
B
a minimum value
C
a singularity
D
a point of inflection
2
GATE ME 2012
MCQ (Single Correct Answer)
+2
-0.6
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}$$ where $$y$$ is the height of the arch in meters. The maximum possible height of the arch is
A
$$8$$ meters
B
$$10$$ meters
C
$$12$$ meters
D
$$14$$ meters
3
GATE ME 2012
MCQ (Single Correct Answer)
+1
-0.3
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by
A
$${{1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat j}$$
B
$${{1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat j}$$
C
$${\widehat k}$$
D
$${{1 \over {\sqrt 3 }}\widehat i + {1 \over {\sqrt 3 }}\widehat j + {1 \over {\sqrt 3 }}\widehat k}$$
4
GATE ME 2012
MCQ (Single Correct Answer)
+2
-0.6
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $$X'$$ s shock absorbers, $$96$$% are reliable. Of $$Y'$$ s shock absorbers, $$72$$% are reliable. The probability that a randomly choosen shock absorber, which is found to reliable, is made by $$Y$$ is
A
$$0.288$$
B
$$0.334$$
C
$$0.667$$
D
$$0.720$$
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