Note: This is the Solution of review exercise 1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Review Exercise 1
Question # 01: Four option are given against each statement. Encircle the correct option.
\((i)\)\(\quad\)\(\sqrt{7}\) is:
\( a) \quad \) integer
\( b) \quad \) rational number
\(c) \quad \) irrational number
\( d) \quad \) natural number
\((ii)\)\(\quad\)\(\pi\) and \(e\) are:
\( a) \quad \) natural numbers
\( b) \quad \) integers
\(c) \quad \) rational numbers
\( d) \quad \) irrational numbers
\((iii)\) If \(n\) is not perfect square, then \(\sqrt{n}\) is:
\( a) \quad \) rational number
\( b) \quad \) natural number
\(c) \quad \) integer
\( d) \quad \) irrational numbers
\((iv)\)\(\quad\)\(\sqrt{3}+\sqrt{5}\) is:
\( a) \quad \) whole number
\( b) \quad \) integer
\(c) \quad \) rational number
\( d) \quad \) irrational number
\((v)\) For all \(x \in R\), \(x=x\) is called:
\( a) \quad \) reflexive property
\( b) \quad \) transitive property
\(c) \quad \) symmetric property
\( d) \quad \) trichotomy property
\((vi)\) Let \(a,b,c \in R \), then \(a>b\) and \(b>c\) \(\implies\) \(a>c\) is called _____
\( a) \quad \) trichotomy
\( b) \quad \) transitive
\(c) \quad \) additive
\( d) \quad \) multiplicative
\((vii)\)\(\quad\)\(2^x\times 8^x = 64\) then \(x=\):
\( a) \quad \) \(\frac{3}{2}\)
\( b) \quad \) \(\frac{3}{4}\)
\(c) \quad \) \(\frac{5}{6}\)
\( d) \quad \) \(\frac{2}{3}\)
\((viii)\)Let \(a,b\in R\), then \(a=b\) and \(b=a\) is called ________ property.
\( a) \quad \) reflexive
\( b) \quad \) symmetric
\(c) \quad \) transitive
\( d) \quad \) additive
\((ix)\)\(\quad\)\(\sqrt{75}+\sqrt{27}=\) :
\( a) \quad \) \(\sqrt{102}\)
\( b) \quad \) \(9\sqrt{3}\)
\(c) \quad \) \(5\sqrt{3}\)
\( d) \quad \) \(8\sqrt{3}\)
\((x)\) The product of \((3+\sqrt{5})\)\((3-\sqrt{5})\) is:
\( a) \quad \) prime number
\( b) \quad \) odd number
\(c) \quad \) irrational number
\( d) \quad \) rational number
Question 2: If \(a=\frac{3}{2}\), \(b=\frac{5}{3}\), \(c=\frac{7}{5}\) then verify that
\((i)\) \(\quad a(b+c)=ab+ac \)
\((ii)\) \(\quad (a+b)c=ac+bc \)
Question 3: If \(a=\frac{4}{3}\), \(b=\frac{5}{2}\), \(c=\frac{7}{4}\) then verify the associative property of real numbers w.r.t. addition and multiplication.
Question 4: Is \(0\) a rational number? Explain.
Question 5: State trichotomy property of real numbers.
Question 6: Find two rational numbers between \(4\) and \(5\).
Question 7: Simplify the following:
\((i)\) \(\quad\) \(\large{\sqrt[5]{\frac{x^{15} y^{35}}{z^{20}}}}\)
\((ii)\) \(\quad\) \(\large{\sqrt[3]{( 27)^{2x}}} \)
\((iii)\) \(\quad\) \(\large{\frac{6( 3)^{n+2}}{3^{n+1} -3^{n}}}\)