1
GATE PI 2015
MCQ (Single Correct Answer)
+1
-0.3
The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined
A
at all real values of $$x$$
B
only at positive integer values of $$x$$
C
only at negative integer values of $$x$$
D
only at rational values of $$x$$
2
GATE PI 2015
MCQ (Single Correct Answer)
+2
-0.6
The value of $$\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} {{{x^2} - xy} \over {\sqrt x - \sqrt y }}$$ is
A
$$0$$
B
$${{1 \over 2}}$$
C
$$1$$
D
$$\infty $$
3
GATE PI 2015
MCQ (Single Correct Answer)
+2
-0.6
A product is an assemble of $$5$$ different components. The product can be sequentially assembled in two possible ways. If the $$5$$ components are placed in a box and these are drawn at random from the box, then the probability of getting a correct sequence is
A
$${2 \over {5!}}$$
B
$${2 \over {5}}$$
C
$${2 \over {\left( {5 - 2} \right)!}}$$
D
$${2 \over {\left( {5 - 3} \right)!}}$$
4
GATE PI 2015
MCQ (Single Correct Answer)
+2
-0.6
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
A
$$X$$ and $$Y$$ are not independent
B
$$Y$$ and $$Z$$ are dependent
C
$$Y$$ and $$Z$$ are independent
D
$$X$$ and $$Z$$ are independent
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