GATE CSE 1996 | GATE CSE Year Wise Previous Years Questions

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GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

The probability that the top and bottom cards of a randomly shuffled deck are both access is

$${4 \over {52}}\, \times \,{4 \over {52}}\,$$

$${4 \over {52}}\, \times \,{3 \over {52}}\,$$

$${4 \over {52}}\, \times \,{3 \over {51}}\,$$

$${4 \over {52}}\, \times \,{4 \over {51}}\,$$

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

Which one of the following is false? Read $$ \wedge $$ as AND, $$ \vee $$ as OR, $$ \sim $$ as NOT, $$ \to $$ as one way implication and $$ \leftrightarrow $$ two way implication.

$$\left( {\left( {x \to y} \right) \wedge x} \right) \to y$$

$$\left( {\left( { \sim x \to y} \right) \wedge \left( { \sim x \to \sim y} \right)} \right) \to x$$

$$\left( {x \to \left( {x \vee y} \right)} \right)$$

$$\left( {\left( {x \vee y} \right) \leftrightarrow \left( { \sim x \to \sim y} \right)} \right)$$

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)

-0.3

Which of the following statements is false?

The set of rational numbers is an abelian group under addition.

The set of integers is an abelian group under addition.

The set of rational numbers from an abelian group under multiplication.

The set of real numbers excluding zero is an abelian group under multiplication.

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