Trivial Relation

Q. The number of bijective funcitons $f:\{1,3,5,7,...,99\}\to \{2,4,6,8,...,100\}$ such that $f\left(3\right)\ge f\left(9\right)\ge f\left(15\right)\ge f\left(21\right)\ge ...\ge \left(99\right)$, is ____

1. $33!\times 17!$
2. ${}^{50}{P}_{33}$
3. ${}^{50}{P}_{17}$
4. $\frac{50!}{2}$

Q.

How many trivial relations can be formed on a set which has 64 elements?

__

Q. Let $A$ be the set of first $10$ natural numbers. If a relation $R$ is defined on $A$, then the correct options(s) is/are

1. $R=\left\{\right(a,b):a+b>20,a,b\in A\}$ is a void relation
2. $R=\left\{\right(a,b):\frac{a}{b}\text{is a real number},a,b\in A\}$ is a universal relation.
3. $R=\left\{\right(a,b):ab=1,a,b\in A\}$ is an identity relation.
4. If $B=\{2,5,10\}$, then the number of common elements between $A\times B$ and $B\times A$ is $9$

Q.

A trivial relation on a set A has the least number of elements.

1. True

2. False

Q.

How many trivial relations can be formed on a set which has 64 elements?

__

Q.

Sir I am not able to understand the topic 'singleton/unit set'. Please help me to understand this topic.

Q. If set $A$ has $4$ elements, set $B$ has $2$ elements and $A,B$ have one element in common, then the number of non trivial relations from $A$ to $B$ is

Q.

A trivial relation on a set A has the least number of elements.

1. True

2. False

Q.

How many trivial relations can be formed on a set which has 64 elements?

__

Q.

A trivial relation on a set A has the least number of elements.

1. True

2. False

Q. If set $A$ has $4$ elements, set $B$ has $2$ elements and $A,B$ have one element in common, then the number of non trivial relations from $A$ to $B$ is

Q.

How many trivial relations can be formed on a set which has 64 elements?

__

Q.

A trivial relation on a set A has the least number of elements.

1. True

2. False

Q. Let $A$ be the set of first $10$ natural numbers. If a relation $R$ is defined on $A$, then the correct options(s) is/are

1. $R=\left\{\right(a,b):a+b>20,a,b\in A\}$ is a void relation
2. $R=\left\{\right(a,b):\frac{a}{b}\text{is a real number},a,b\in A\}$ is a universal relation.
3. $R=\left\{\right(a,b):ab=1,a,b\in A\}$ is an identity relation.
4. If $B=\{2,5,10\}$, then the number of common elements between $A\times B$ and $B\times A$ is $9$

Q.

A trivial relation on a set A has the least number of elements.

1. True

2. False