1
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 ______.
2
GATE CSE 2014 Set 2
+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
3
GATE CSE 2012
+2
-0.6
How many onto (or subjective) functions are there form an n-element $$(n\, \ge \,2)$$ set to a 2-element set ?
A
$${2^n}$$
B
$${2^n}\, - 1$$
C
$${2^n}\, - 2$$
D
$$2\,({2^n}\, - 2)$$
4
GATE CSE 2009
+2
-0.6
For the compositive table of a cyclic group shown below

Which one of the following choices is correct?

A
a, b are generators
B
b, c are generators
C
c, d are generators
D
d, a are generators
GATE CSE Subjects
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