1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3,..., 20. What is the promutations that 2 appears at an earlier position than any other even number in the selected permutation?
A
$${{1 \over 2}}$$
B
$${{1 \over 10}}$$
C
$${{9! \over 20!}}$$
D
None of the above.
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
When a coin is tossed, the probability of getting a Head is p, 0 < p < 1. Let N be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are indepandent, the expected value of N is
A
1/p
B
1/ (1 - p)
C
$$1/{p^2}$$
D
$$1/{(1 - p)^2}$$
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:
A
$$1/{2^n}$$
B
1 - 1/n
C
1/n!
D
$$1 - \,\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {{2^n}}$}}$$
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the tails are independent, the expected number of tosses are
A
3
B
4
C
5
D
6
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