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Lahore School System
Mathematics - Class 9
Student Name
Roll Number
Section
Time Allowed
2 hours
Total Marks
50
Chapters
Date
Examiner Signature
Bubble Sheet for Q.No.1 (MCQs) Fill the correct option bubble for each question number.
1.
A B C D
2.
A B C D
3.
A B C D
4.
A B C D
5.
A B C D
6.
A B C D
7.
A B C D
8.
A B C D
9.
A B C D
10.
A B C D
MAXIMUM MARKS: 10 OBJECTIVE
حصہ معروضی
10 × 1 = 10 کل نمبر
سوال نمبر
Q.No.1
For each objective question four options (A–D) are given. Fill the bubble of the correct option against the question number on the bubble sheet.
Sr. No. Questions A B C D
(i)
\(\sqrt{7}\) is:
integer
rational number
irrational number
natural number
(ii)
\(\pi\) and \(e\) are:
natural numbers
integers
rational numbers
irrational numbers
(iii)
If \(n\) is not a perfect square, then \(\sqrt{n}\) is:
rational number
natural number
integer
irrational number
(iv)
\(\sqrt{3} + \sqrt{5}\) is:
whole number
integer
rational number
irrational number
(v)
For all \(x \in R, x = x\) is called:
reflexive property
transitive number
symmetric property
trichotomy property
(vi)
Let \(a, b, c \in R\), then \(a > b\) and \(b > c \Rightarrow a > c\) is called ________ property.
trichotomy
transitive
additive
multiplicative
(vii)
\(2^x \times 8^x = 64\) then \(x =\)
\(\frac{3}{2}\)
\(\frac{3}{4}\)
\(\frac{5}{6}\)
\(\frac{2}{3}\)
(viii)
Let \(a, b \in R\), then \(a = b\) and \(b = a\) is called ________ property.
reflexive
symmetric
transitive
additive
(ix)
\(\sqrt{75} + \sqrt{27} =\)
\(\sqrt{102}\)
\(9\sqrt{3}\)
\(5\sqrt{3}\)
\(8\sqrt{3}\)
(x)
The product of \((3 + \sqrt{5})(3 - \sqrt{5})\) is:
prime number
odd number
irrational number
rational number
(i)
\(\sqrt{7}\) is:
(a) integer (b) rational number (c) irrational number (d) natural number
(ii)
\(\pi\) and \(e\) are:
(a) natural numbers (b) integers (c) rational numbers (d) irrational numbers
(iii)
If \(n\) is not a perfect square, then \(\sqrt{n}\) is:
(a) rational number (b) natural number (c) integer (d) irrational number
(iv)
\(\sqrt{3} + \sqrt{5}\) is:
(a) whole number (b) integer (c) rational number (d) irrational number
(v)
For all \(x \in R, x = x\) is called:
(a) reflexive property (b) transitive number (c) symmetric property (d) trichotomy property
(vi)
Let \(a, b, c \in R\), then \(a > b\) and \(b > c \Rightarrow a > c\) is called ________ property.
(a) trichotomy (b) transitive (c) additive (d) multiplicative
(vii)
\(2^x \times 8^x = 64\) then \(x =\)
(a) \(\frac{3}{2}\) (b) \(\frac{3}{4}\) (c) \(\frac{5}{6}\) (d) \(\frac{2}{3}\)
(viii)
Let \(a, b \in R\), then \(a = b\) and \(b = a\) is called ________ property.
(a) reflexive (b) symmetric (c) transitive (d) additive
(ix)
\(\sqrt{75} + \sqrt{27} =\)
(a) \(\sqrt{102}\) (b) \(9\sqrt{3}\) (c) \(5\sqrt{3}\) (d) \(8\sqrt{3}\)
(x)
The product of \((3 + \sqrt{5})(3 - \sqrt{5})\) is:
(a) prime number (b) odd number (c) irrational number (d) rational number
Subjective Type (Part-I) / حصہ انشائیہ
Q. 2: Write short answers to any 5 questions. (2x5=10)
Max. Marks: 10
  1. (i)
    Identify each of the following as rational or irrational: \(e\)
    lines
  2. (ii)
    Define monomial and binomial surd.
    lines
  3. (iii)
    Rationalize the denominator: \(\frac{6 - 4\sqrt{2}}{6 + 4\sqrt{2}}\)
    lines
  4. (iv)
    Simplify: \(\left(\frac{3}{4}\right)^{-2} \div \left(\frac{4}{9}\right)^3 \times \frac{16}{27}\)
    lines
  5. (v)
    If \(x = 3 + \sqrt{8}\), find \(x^4 + \frac{1}{x^4}\)
    lines
Q. 3: Write short answers to any 4 questions. (2x4=8)
Max. Marks: 8
  1. (i)
    Simplify: \( \sqrt[5]{\frac{x^{15}y^{35}}{z^{20}}} \)
    lines
  2. (ii)
    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.
    lines
  3. (iii)
    Abdullah picked up 96 balls and placed them into two buckets. One bucket has twenty-eight more balls than the other bucket. How many balls were in each bucket?
    lines
  4. (iv)
    Simplify: \( \frac{6(3)^{n+2}}{3^{n+1} - 3^n} \)
    lines
Section-II: Attempt any 2 questions. (10x2=20 marks)
  1. Q. 4
    1. (i) Simplify: \(\sqrt[7]{\frac{x^{14} \times y^{21} \times z^{35}}{y^{14} z^7}}\)
      lines
    2. (ii) Simplify: \(\sqrt{\frac{(216)^{\frac{2}{3}} \times (25)^{\frac{1}{2}}}{(0.04)^{-\frac{3}{2}}}}\)
      lines
  2. Q. 5
    1. (i) Simplify: \(\frac{(25)^{\frac{3}{2}} \times (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times (8)^{\frac{4}{3}}}\)
      lines
    2. (ii) Simplify: \(\frac{54 \times \sqrt[3]{(27)^{2x}}}{9^{x+1} + 216(3^{2x-1})}\)
      lines
  3. Q. 6
    1. (i) If \(\frac{8 - 3\sqrt{2}}{4 + 3\sqrt{2}} = p + q\sqrt{2}\), find the rational numbers \(p\) and \(q\).
      lines