GATE CSE 2001 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2001

MCQ (Single Correct Answer)

-0.6

Consider the following statements:

S1: There exist infinite sets A, B, C such that
$$A\, \cap \left( {B\, \cup \,C} \right)$$ is finite.
S2: There exist two irrational numbers x and y such that (x + y) is rational.
Which of the following is true about S1 and S2?

Only S1 is correct

Only S2 is correct

Both S1 and S2 are correct

None of S1 and S2 is correct

GATE CSE 2001

MCQ (Single Correct Answer)

-0.3

Consider the following relations:
$${R_1}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is even over the set of integers
$${R_2}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is odd over the set of integers
$${R_3}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,a.b > 0$$ over the set of non-zero rational numbers
$${R_4}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left| {a - b} \right| \le 2$$ over the set of natural numbers

Which of the following statements is correct?

$${R_1}$$ and $${R_2}$$ are equivalence relations, $${R_3}$$ and $${R_4}$$ are not

$${R_1}$$ and $${R_3}$$ are equivalence relations, $${R_2}$$ and $${R_4}$$ are not

$${R_1}$$ and $${R_4}$$ are equivalence relations, $${R_2}$$ $${R_3}$$ are not

$${R_1}$$, $${R_2}$$, $${R_3}$$ and $${R_4}$$ are all equivalence relations

GATE CSE 2001

MCQ (Single Correct Answer)

-0.3

Consider the following statements:
S1: The sum of two singular n x n matrices may be non-singular
S2: The sum of two n x n non-singular matrices may be singular

Which of the following statements is correct?

S1 and S2 are both true

S1 is true, S2 is false

S1 is false, S2 is true

S1 and S2 are both false

GATE CSE 2001

MCQ (Single Correct Answer)

-0.6

How many 4 digit even numbers have all 4 digits distinct?

2240

2296

2620

4536

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