1
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
$${f^{ - 1}}\,(x,\,y)\, = \,(2\,(x\, - \,y),\,2\,(x\, + y))$$
2
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
Let $$A$$ and $$B$$ be sets and let $${A^c}$$ and $${B^c}$$ denote the complements of the sets $$A$$ and $$B$$. The set $$\left( {A - B} \right) \cup \left( {B - A} \right) \cup \left( {A \cap B} \right)$$ is equal to
A
$${A \cup B}$$
B
$${{A^c} \cup {B^c}}$$
C
$${A \cap B}$$
D
$${{A^c} \cap {B^c}}$$
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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