1
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider the following relation on subsets of the set S integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two setss is in U.

Consider the following two statements:
S1 There is a subset of S that is larger than every other subset. S2: There is a subset of S that is smaller than every other subset.
Which one of the following is CORRECT?

A
Both S1 and S2 are true
B
S1 is true and S2 is false
C
S2 is true and S1 is false
D
Neither S1 nor S2 is true
2
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for all $$0 \le i \le 2014.$$ Consider the following statements:
$$P$$. For each such function it must be the case that for every $$i$$, $$f\left( i \right) = i$$
$$Q$$. For each such function it must be the case that for some $$i$$, $$f\left( i \right) = 1$$
$$R$$. Each such function must be onto.

Which one of the following id CORRECT?

A
$$P, Q$$ and $$R$$ are true
B
Only $$Q$$ and $$R$$ are true
C
Only $$P$$ and $$Q$$ are true
D
Only $$R$$ is true
3
GATE CSE 2014 Set 3
Numerical
+2
-0
There are two elements $$x, y$$ in a group $$\left( {G,\, * } \right)$$ such that every elements in the group can be written as a product of some number of $$x's$$ and $$y's$$ in some order. It is known that
$$x * x = y * y = x * y * x * y = y * x * y * x = e$$
where $$e$$ is the identity element. The maximum number of elements in such a group is ______.
Your input ____
4
GATE CSE 2014 Set 1
Numerical
+2
-0
Let S denote the set of all functions $$f:\,{\{ 0,\,1\} ^4}\, \to \,\{ 0,\,1\} $$. Denote by N the number of functions from S to the set {0, 1}. The value of $${\log _2}$$ $${\log _2}$$ N is___________________
Your input ____
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