Since the number of boys and girls in a class are always finite.
Therefore, set G and H are finite sets.

C is an infinite set as there are many numbers less than $ - 3 $

Since the numbers of animals on the earth are countable(limited).
Therefore, set of all the animals on the earth is "finite" set.
Option A is correct.

A non empty set has atleast one element.

From the given options we see that the SET C has one element which is $ 2 $

(2), (3), and (4) are finite sets.

The set of positive integers is never ending. There is no such defined largest integer. Hence the set is infinite

In the problem statement we are taking union of $B$ and $C$ and then taking its intersection with $A$.

Definition: A finite set is a set which has fixed or finite number of elements.
$A=$ Set of animals on the earth is a finite set because number of animals on the earth is large in number, but it is finite/fixed.

$(i)(x-1)(x-2)=0$

The set ${ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in R} $ consists of all the points in the first quadrant which lie inside the circle ${ x }^{ 2 }+{ y }^{ 2 }=1$ and above the line $x+y=1$ .So, it is not a finite set.
Option $A$ is correct.

The intersection of an infinite set may be finite.
Example:
$A={x:x\in N; x>2}$
$B={x:x\in I; x<5}$
Here, Both $A$ and $B$ are infinite but its intersection are finite.

Definition: A set having infinite number of elements is known as infinite set.
 ${x:x\in R:1\le x\le 3}$ is a infinite set because since $x\in R$, there are infinte number of real numbers lie in between two numbers.

option C 

Given the set contains $n$ elements.

A will be an infinite set as we have many multiples of 3 such has 3, 6, 9, 12 and so on

Set D will be infinite as there will be infinite powers of 2 since n can be any natural number from 1 to infinity.

B is a finite set as 13 has only two factors which are 1, and 13.

We can have many fractions between the numbers 3 and 4.
Hence, this set is an infinite set

We have to identify the type of set.

Given $A={x|x\in N, 2 \leq x \leq 3 }$

               $={2,3}$ which is a finite set.

Therefore $A$ is a finite set.

$S$ is given by $S={x:x\in N: x\le15}$
$S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}$
$\therefore n(S)=15$
The power set is set of all the possible subsets of $S.$
Number of elements in power set $=$ Total number of subsets
So, cardinality of power set $S=2^{15}=32768$

Countably Infinite: Set of natural numbers are countably infinite because one can count natural number one after other easily.
Uncountably infinite: Set of real numbers are uncountably infinite because real numbers cannot be counted.

$(i)A={x:x\in Z: x^2 $ is even $}$
$A={...,-6,-4,-2,0,2,4,6,...}$ which is an infinite set.
$(ii)B={x:x\in R:-4<x<-2}$
There will be infinite real numbers any two numbers so, it is an infinite set.

$(i)$The set of lines which are parallel to x-axis is an infinite set because line parallel to x-axis are infinite in number.
$(ii)$The set of animals living on the earth is a finite set because the number of animals living on the earth is finite (although it is quite a big number)
$(iii)$ The set of numbers which are multiple of $5$ is an infinite numbers multiples of $5$ are infinite in number.
$(iv)$ The set of the circles passing through the origin $(0,0)$ is an infinite set because infinite number of circles can pass through the origin.

$(i)$ The sets of months in a year is a finite set because it has $12$ elements.
$(ii){1,2,3,....}$ is an infinite set as it has infinite number of elements.
$(iii){1,2,3,...,99,100}$ is a finite set as it has number from $1$ to $100$ which is finite in number.
$(iv)$ The set of positive integers greater than $100$ is an infinite set because positive integers greater than $100$ are infinite in number. 

Given that:
$A={a,{b}},$
 $P(A)={\phi,a,{b},{a,{b}}}$

$(i)A={x:x\in Z: x^2 $ is even $}$
$A={...,-3,-1-1,3,...}$ which is an infinite set.
$(ii)B={x:x\in R:-2<x<-4}$
$B={...,-14,-13,-12,-11}$ so it is an infinite set.