1
GATE ECE 2015 Set 2
Numerical
+1
-0
Let the random variable $$X$$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $$X$$ is ________.
Your input ____
2
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let $$\,\,X \in \left\{ {0,1} \right\}\,\,$$ and $$\,\,Y \in \left\{ {0,1} \right\}\,\,$$ be two independent binary random variables. If $$\,\,P\left( {X\,\, = 0} \right) = p\,\,$$ and $$\,\,P\left( {Y\,\, = 0} \right) = q\,\,$$, then $$P\left( {X + Y \ge 1} \right)$$ is equal to
A
$$pq+(1-p)(1-q)$$
B
$$pq$$
C
$$p(1-q)$$
D
$$1-pq$$
3
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $$1/6$$ and that of Ramesh is $$1/8$$. What is the probability that only one of them will be selected?
A
$$47/48$$
B
$$1/4$$
C
$$13/48$$
D
$$35/48$$
4
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ is
A
$$\,\,\tan \,y - \cot \,x = C\,\,$$
B
$$\tan \,x - \cot \,y = C\,$$
C
$$\,\,\tan \,y + \cot \,x = C\,\,$$
D
$$\tan \,x + \cot \,y = C\,$$
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