1
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},\,{x_3},\,{x_4}$$ are Boolean Variables, and $$ \oplus $$ is the $$XOR$$ operator.

Which one of the following must always be TRUE?

A
$${x_1}{x_2}{x_3}{x_4} = 0$$
B
$${x_1}{x_3} + {x_2} = 0$$
C
$${\overline x _1} \oplus {\overline x _3} = {\overline x _2} \oplus {\overline x _4}$$
D
$${x_1} + {x_2} + {x_3} + {x_4} = 0$$
2
GATE CSE 2016 Set 2
Numerical
+1
-0
Let $$X$$ be the number of distinct $$16$$-bit integers in $$2’s$$ complement representation. Let $$Y$$ be the number of distinct $$16$$-bit integers in sign magnitude representation.
Then $$X −Y$$ is ____________.
Your input ____
3
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A binary relation $$R$$ on $$N \times N$$ is defined as follows: $$(a,b)R(c,d)$$ if $$a \le c$$ or $$b \le d.$$ Consider the following propositions:

$$P:$$ $$R$$ is reflexive
$$Q:$$ $$R$$ is transitive

Which one of the following statements is TRUE?

A
Both $$P$$ and $$Q$$ are true
B
$$P$$ is true and $$Q$$ is false
C
$$P$$ is false and $$Q$$ is true
D
Both $$P$$ and $$Q$$ are false
4
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider a set $$U$$ of $$23$$ different compounds in a Chemistry lab. There is a subset $$S$$ of $$U$$ of $$9$$ compounds, each of which reacts with exactly $$3$$ compounds of $$U.$$ Consider the following statements:

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ Each compound in $$U \ S$$ reacts with an odd number of compounds.
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ At least one compound in $$U \ S$$ reacts with an odd number of compounds.
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,$$ Each compound in $$U \ S$$ reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

A
Only $${\rm I}$$
B
Only $${\rm II}$$
C
Only $${\rm III}$$
D
None
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