1
GATE CSE 2011
+2
-0.6
Consider the following circuit involving three Dtypes flip-flops used in a certain type of Counter configuration.

If at some instance prior to the occurrence of the clock edge, $$P, Q$$ and $$R$$ have a value $$0,1$$ and $$0$$ respectively, what shall be the value of $$PQR$$ after the clock edge?

A
$$000$$
B
$$001$$
C
$$010$$
D
$$011$$
2
GATE CSE 2011
+1
-0.3
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?
A
1/3
B
$${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}$$
C
$${\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$
D
2/3
3
GATE CSE 2011
+1
-0.3
If the difference between the expectation of the square of a random variable $$\left( {E\left[ {{X^2}} \right]} \right)$$ and the square of the expectation of the random variable $${\left( {E\left[ X \right]} \right)^2}$$ is denoted by R then
A
R = 0
B
R < 0
C
$$R\, \ge \,0$$
D
R > 0
4
GATE CSE 2011
+2
-0.6
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is probability that the two cards are selected with the number on the first card is one higher than the number on the second card.
A
$${{1 \over 5}}$$
B
$${{4 \over 25}}$$
C
$${{1 \over 4}}$$
D
$${{2 \over 5}}$$
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