1
GATE CSE 2016 Set 1
Numerical
+2
-0
Consider the following experiment.
Step1: Flip a fair coin twice.
Step2: If the outcomes are (TAILS, HEADS) then output $$Y$$ and stop.
Step3: If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $$N$$ and stop.
Step4: If the outcomes are (TAILS, TAILS), then go to Step 1.

The probability that the output of the experiment is $$Y$$ is (up to two decimal places) _____________.

2
GATE CSE 2016 Set 1
Numerical
+1
-0
A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interval the value of the function is zero. The value of $$a$$ is _________.
3
GATE CSE 2016 Set 1
Numerical
+1
-0
Let $$p,q,r,s$$ represent the following propositions.

$$p:\,\,\,x \in \left\{ {8,9,10,11,12} \right\}$$
$$q:\,\,\,x$$ is a composite number
$$r:\,\,\,x$$ is a perfect square
$$s:\,\,\,x$$ is a prime number

The integer $$x \ge 2$$ which satisfies $$\neg \left( {\left( {p \Rightarrow q} \right) \wedge \left( {\neg r \vee \neg s} \right)} \right)$$ is ______________.

4
GATE CSE 2016 Set 1
+1
-0.3
Let $${a_n}$$ be the number of $$n$$-bit strings that do NOT contain two consecutive $$1s.$$ Which one of the following is the recurrence relation for $${a_n}$$?
A
$${a_n} = {a_{n - 1}} + 2{a_{n - 2}}$$
B
$${a_n} = {a_{n - 1}} + {a_{n - 2}}$$
C
$${a_n} = 2{a_{n - 1}} + {a_{n - 2}}$$
D
$${a_n} = 2{a_{n - 1}} + 2{a_{n - 2}}$$
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