1
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following is false?
A
The set of all bijective functions on a finite set forms a group under function composition.
B
The set {1, 2, ..., p - 1} forms a group under multiplication mod p where p is a prime number.
C
The set of all strings over a finite alphabet $$\sum $$ forms a group under concatenation.
D
A subset $$s\, \ne \,\phi $$ of G is a subgroup of the group if and only if for any pair of elements $$a,\,\,b\,\, \in \,\,s,\,\,a\,\,*\,\,{b^{ - 1}}\,\, \in \,s$$.
2
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Let R denote the set of real numbers. Let f: $$R\,x\,R \to \,R\,x\,R\,$$ be a bijective function defined by f (x, y ) = (x + y, x - y). The inverse function of f is given by
A
$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{1 \over {x\, + \,y}},\,{1 \over {x\, - \,y}}} \right)$$
B
$${f^{ - 1}}\,(x,\,y)\, = \,\,(x\, - \,y,\,\,x\, + y)$$
C
$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{{x\, + \,y} \over 2},\,{{x\, - \,y} \over 2}} \right)$$
D
$${f^{ - 1}}\,(x,\,y)\, = \,(2\,(x\, - \,y),\,2\,(x\, + y))$$
3
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
Let $$X$$ $$X = \left\{ {2,3,6,12,24} \right\}$$. Let $$ \le $$ the partial order defined by $$x \le y$$ if $$x$$ divides $$y$$. The number of edges in the Hasse diagram of $$\left( {X, \le } \right)$$ is
A
$$3$$
B
$$4$$
C
$$9$$
D
None of the above
4
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. It is given that there are exactly 97 functions from $$X$$ to $$Y$$. From this one can conclude that
A
$$\left| X \right| = 1,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$
B
$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 1$$
C
$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$
D
None of the above
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