1
GATE EE 2017 Set 2
+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
$$4$$
2
GATE EE 2017 Set 2
+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
$${6 \over 9}$$
3
GATE EE 2017 Set 2
Numerical
+1
-0
Assume that in a traffic junction, the cycle of the traffic signal lights is $$2$$ minutes of green (vehicle does not stop) and $$3$$ minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over $$5$$ minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is _________.
4
GATE EE 2017 Set 2
+2
-0.6
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $$3$$ tosses. Let the random variable $$Y$$ denotes the number of heads. The value of var $$\left\{ Y \right\},$$ where var $$\left\{ . \right\}$$ denotes the variance, equal
A
$${7 \over 8}$$
B
$${49 \over 64}$$
C
$${7 \over 64}$$
D
$${105 \over 64}$$
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