1
GATE CSE 2014 Set 3
+1
-0.3
Consider the following interm expression of $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15}$$
The minterms $$2, 7, 8$$ and $$13$$ are 'do not care' terms. The minimal sum-of-products form for $$F$$ is _______
A
$$Q\overline S + \overline Q S$$
B
$$\overline Q \overline S + QS$$
C
$$\overline Q \overline R \overline S + \overline Q R\overline S + Q\overline R S + QRS$$
D
$$\overline P \overline Q \overline S + \overline P QS + PQS + P\overline Q \overline S$$
2
GATE CSE 2014 Set 3
+2
-0.6

The above synchronous sequential circuit built using $$JK$$ flip-flops is initialized with $${Q_2}{Q_1}{Q_0} = 000.\,\,$$ The state sequence for this circuit for the next $$3$$ clock cycles is

A
$$001,010,011$$
B
$$111,110,101$$
C
$$100,110,111$$
D
$$100,011,001$$
3
GATE CSE 2014 Set 3
+1
-0.3
Consider the following statements:
P: Good mobile phones are not cheap
Q: Cheap mobile phones are not good
L: P implies Q
M: Q implies P
N: P is equivalent to Q

Which of the following about L, M, and N is Correct?

A
Only L is TRUE.
B
Only M is TRUE.
C
Only N is TRUE.
D
L, M and N are TRUE.
4
GATE CSE 2014 Set 3
Numerical
+2
-0
Let S be a sample space and two mutually exclusive events A and B be such that $$A\, \cup \,B = \,S$$. If P(.) denotes the probability of the event, the maximum value of P(A) P(B) is ________________.
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