GATE CSE 1996 | GATE CSE Year Wise Previous Years Questions

GATE CSE 1996

MCQ (Single Correct Answer)

-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

$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{1 \over {x\, + \,y}},\,{1 \over {x\, - \,y}}} \right)$$

$${f^{ - 1}}\,(x,\,y)\, = \,\,(x\, - \,y,\,\,x\, + y)$$

$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{{x\, + \,y} \over 2},\,{{x\, - \,y} \over 2}} \right)$$

$${f^{ - 1}}\,(x,\,y)\, = \,(2\,(x\, - \,y),\,2\,(x\, + y))$$

GATE CSE 1996

MCQ (Single Correct Answer)

-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

$$\left| X \right| = 1,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$

$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 1$$

$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$

None of the above

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

The recurrence relation $$\,\,\,\,\,$$ $$T\left( 1 \right) = 2$$
$$T\left( n \right) = 3T\left( {{n \over 4}} \right) + n$$ has the solution $$T(n)$$ equal to

$$O(n)$$

$$O$$ (log n)

$$O\left( {{n^{3/4}}} \right)$$

None of the above

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

Which one of the following is false?

The set of all bijective functions on a finite set forms a group under function composition.

The set {1, 2, ..., p - 1} forms a group under multiplication mod p where p is a prime number.

The set of all strings over a finite alphabet $$\sum $$ forms a group under concatenation.

A subset $$s\, \ne \,\phi $$ of G is a subgroup of the group if and only if for any pair of elements $$a,\,\,b\,\, \in \,\,s,\,\,a\,\,*\,\,{b^{ - 1}}\,\, \in \,s$$.

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