Let's go through each part of the question step-by-step.
### Question 1:
Choose the correct answer:
a) 3
b) [tex]\(2x\)[/tex]
c) -1
d) [tex]\(d^2\)[/tex]
Solution: The correct answer from the choices given is a) 3.
### Question 2:
A rational number between [tex]\(0.2323323332 \ldots\)[/tex] and [tex]\(0.2121121112\)[/tex] is:
a) 0.233
b) 0.571
c) 0.232
d) none of these
Solution: A rational number between [tex]\(0.2323323332 \ldots\)[/tex] and [tex]\(0.2121121112\)[/tex] is a) 0.233.
### Question 3:
Two irrational numbers whose difference is irrational:
a) [tex]\(\sqrt{2}, (\sqrt{3} + \sqrt{2})\)[/tex]
b) [tex]\(\sqrt{3}, (\sqrt{3} + 2)\)[/tex]
c) [tex]\(5, (5 + \sqrt{3})\)[/tex]
d) none of these
Solution: The set of two irrational numbers whose difference is irrational is a) [tex]\(\sqrt{2}, (\sqrt{3} + \sqrt{2})\)[/tex].
### Question 4:
If [tex]\(P, Q\)[/tex], and [tex]\(R\)[/tex] are three points on a line and [tex]\(Q\)[/tex] lies between [tex]\(P\)[/tex] and [tex]\(R\)[/tex], then:
a) [tex]\(PR + QR = PR\)[/tex]
b) [tex]\(PQ + PR = PR\)[/tex]
c) [tex]\(PQ + PR = QR\)[/tex]
d) [tex]\(PQ + QR = PR\)[/tex]
Solution: If [tex]\(Q\)[/tex] lies between [tex]\(P\)[/tex] and [tex]\(R\)[/tex], then the correct relationship is d) [tex]\(PQ + QR = PR\)[/tex].
### Question 5:
What does geometry mean?
Solution: Geometry is a branch of mathematics that deals with shapes, sizes, and the properties of space.
By analyzing the context and detail in the question, we have completed all the steps required to solve the given problem correctly.
