1
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the following Boolean expression for $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overline P Q\overline R S.$$
The minimal sum-of-products form of $$F$$ is
A
$${PQ} + QR + QS$$
B
$$P + Q + R + S$$
C
$$\overline P + \overline Q + \overline R + \overline S $$
D
$$\overline P R + \overline P \overline R S + P$$
2
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the $$4$$-to-$$1$$ multiplexer with two select lines $${S_1}$$ and $${S_0}$$ given below GATE CSE 2014 Set 1 Digital Logic - Combinational Circuits Question 5 English

The minimal sum-of-products form of the Boolean expression for the output $$F$$ of the multiplexer is

A
$$\overline P Q + Q\overline R + P\overline Q R$$
B
$$\overline P Q + \overline P Q\overline R + PQ\overline R + P\overline Q R$$
C
$$\overline P QR + \overline P Q\overline R + Q\overline R + P\overline Q R$$
D
$$PQ\overline R $$
3
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the statement
"Not all that glitters is gold"
Predicate glitters$$(x)$$ is true if $$x$$ glitters and
predicate gold$$(x)$$ is true if $$x$$ is gold.

Which one of the following logical formulae represents the above statement?

A
$$\forall x:\,glitters\,\left( x \right) \Rightarrow \neg gold\left( x \right)$$
B
$$\forall x:\,gold\left( x \right) \Rightarrow glitters\left( x \right)$$ v
C
$$\exists x:\,gold\left( x \right) \wedge \neg glitters\left( x \right)$$
D
$$\exists x:\,glitters\,\left( x \right) \wedge \neg gold\left( x \right)$$
4
GATE CSE 2014 Set 1
Numerical
+1
-0
Suppose you break a stick of unit length at a point chosen uniformaly at random. Then the expected length of the shorter stick is __________________.
Your input ____
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