1
GATE CSE 2024 Set 1
Numerical
+1
-0

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$. The number of possible values of $|A|$ is _______

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2
GATE CSE 2021 Set 2
MCQ (More than One Correct Answer)
+1
-0

Consider the following sets, where n > 2:
S1: Set of all n x n matrices with entries from the set {a, b, c}

S2: Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0, 1, 2}

Which of the following choice(s) is/are correct?

A
There does not exist an injection from S1 to S2.
B
There exists a bijection from S1 to S2
C
There exists a surjection from S1 to S2.
D
There does not exist a bijection from S1 to S2
3
GATE CSE 2020
Numerical
+1
-0
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ______.
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4
GATE CSE 2020
Numerical
+1
-0
Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _____.
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