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MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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====== MCQs: Ch 01 Number Systems ====== High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Cla... $ - $-2i$ - $2$ - $\sqrt{2}$ is ------- number. - natural - complex - irrational ... $\displaystyle{\frac{p}{q}}$ form - A rational number is a number which can be expressed in the form --
Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
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ptb:definitions-aurang-zaib]] ===== Chapter 01: Number system ===== * **Rational number:** A number which can be written in the form of $\frac{p}{q}$, where $p,q \in \mathbb{Z}$, $q\neq 0$, is called a rational number * **Irrational number:** A real number which c
Question 9 Exercise 6.3 @math-11-kpk:sol:unit06
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re $7$ and total women are $6.$ Therefore, Total number of persons $=7+6=13$ Committee consist of 8 pers... e contain exactly four men and four women. Total number of different ways that four men to be selected are: ${ }^7 C_4$. Total number of different ways that four women to be selected ... . By fundamental principle of counting the total number of different committees that will exactly contain
Question 7 Exercise 6.4 @math-11-kpk:sol:unit06
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5) & (6,6) \end{array}\right]\end{align} So total number of sample points are $$n(S)=6 \times 6=36$$ doub... nce the possibility of getting doublet of an even number is: $$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{3}{36}=\dfra... 5) & (6,6) \end{array}\right]\end{align} So total number of sample points are $$n(S)=6 \times 6=36$$ A sum less than $6$ Let $B=\{$ a number less than 6$\}$, then from sample space, we see
Question 13 Exercise 6.2 @math-11-kpk:sol:unit06
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war, Pakistan. =====Question 13(i)===== Find the number of permutation of word "Excellence." How many of ... in with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' are: $n=10$, out of wh... 2$ are $C$. Therefore, \begin{align}\text{total number of permutations are} &=\left(\begin{array}{c} n ... d $m_3=2$ are $C$. Therefore, \begin{align}\text{Number of permulations are} &=\left(\begin{array}{c} n \
Exercise 2.1 (Solutions) @matric:9th_science:unit_02
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e false? * (i) $\frac{2}{3}$ is an irrational number. * (ii) $\pi$ is an irrational number. * (iii) $\frac{1}{9}$ is a terminating fraction. * (iv) $\fr... uaton**\\ * (i) $\frac{2}{3}$ is an irrational number. **False** * (ii) $\pi$ is an irrational number. **True** * (iii) $\frac{1}{9}$ is a terminating fra
Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
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for his valuable contribution. =====Chapter 01: Number System===== ====Rational Number==== A number which can be expressed in the form \( \dfrac{p}{q} \), where \( p, q \in \mathbb{Z} \) and \( q \neq 0 \), is termed as a rational number. ===Example==== \( \dfrac{3}{4} \), \( \dfrac{7}{
Algebraic Number Theory Notes by Anwar Khan @notes
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====== Algebraic Number Theory Notes by Anwar Khan ====== {{ :notes:algebraic-number-theory-notes-anwar-khan.jpg?nolink|Algebraic Number Theory Notes by Anwar Khan}} Algebraic number theory is a subfield of number theory that studies integers
Number Theory: Handwritten Notes @notes
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====== Number Theory: Handwritten Notes ====== {{ :notes:number-theory-handwritten-notes.jpg?nolink&600|Number Theory: Handwritten Notes}} The study of the characteristi... of the positive integers (1, 2, 3,...) is called number theory. It is significant because it has numerous
Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
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l and irrational numbers? - Is there a rational number exists between any two rational numbers. - Is there a real number exists between any two real numbers. - Is the s... Multiple choice questions (MCQs) ===== ==== Real Number System==== <panel> 1. What is not true about number zero. * (A) Even * (B) Positive * (C) Ad
Number Theory by Dr Muhammad Umer Shuaib @notes
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====== Number Theory by Dr Muhammad Umer Shuaib ====== {{ :notes:number-theory-muzammil-tanveer.jpg?nolink&600|Number Theory Notes}} A subfield of mathematics called number theory studies the characteristics of positive int
MTH321: Real Analysis I (Spring 2023) @atiq
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om Chapter 02** - A convergent sequence of real number has one and only one limit (i.e. limit of the seq... }$ also converges to $s$. - For each irrational number $x$, there exists a sequence $\left\{ {{r}_{n}} \... _{n}}}$ is convergent if and only if for any real number $\varepsilon >0$, there exists a positive integer... r all $n$. Also suppose that for a fixed positive number $\lambda $ and positive integer $k$, $a_n<\lambda
Number Theory Notes by Anwar Khan @notes
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====== Number Theory Notes by Anwar Khan ====== {{ :notes:number-theory-notes-anwar-khan.jpg?nolink|Number Theory Notes by Anwar Khan}} Mathematicians who specialize in number theory examine the characteristics and connection
Number Theory by Prof. Asghar Ali @bsc
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======Number Theory by Prof. Asghar Ali====== {{ :bsc:number-theory-prof-asghar-ali.jpg?nolink|Number Theory by M Asghar Ali}} We are very thankful to Prof. [[:peopl... pful to prepare BSc or ADS mathematics portion of Number Theory. Number theory is a subject in which stude
PPSC Paper 2011 (Lecturer in Mathematics) @ppsc
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ubgroup of $G$ \\ - $2$ - $4$ - Prime number - None of these - $nZ$ is a maximal ideal o... ng $Z$ if and only if $n$ is ------\\ - Prime number - Composite number - Natural number - None of these - Let $G$ be a cyclic group of order $24$ generated by $a$ the
MCQs or Short Questions @atiq:sp15-mth321
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Number Theory by Ms. Iqra Liaqat @msc:notes
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Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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MTH321: Real Analysis I (Fall 2021) @atiq
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Multiple Choice Questions (MCQs) @fsc-part1-ptb
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Notes of Mathematics
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MTH321: Real Analysis I (Spring 2020) @atiq
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Advanced Analysis: Handwritten Notes @notes
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Question 7 and 8 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 9 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 10 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 12 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 15 & 16 Exercise 4.5 @math-11-kpk:sol:unit04
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Question 10 Exercise 6.5 @math-11-kpk:sol:unit06
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ADS/BSc
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Number Theory by Prof. M. Tanveer @bsc
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What is the value of pi? @dyk
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Its about square root @dyk
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PPSC Paper 2015 (Lecturer in Mathematics) @ppsc
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Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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Question 1 Exercise 6.4 @math-11-kpk:sol:unit06
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Question 2 Exercise 6.4 @math-11-kpk:sol:unit06
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Question 5 Exercise 6.4 @math-11-kpk:sol:unit06
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MTH321: Real Analysis 1 @atiq
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MTH321: Real Analysis I (Fall 2015) @atiq
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MTH321: Real Analysis I (Fall 2018) @atiq
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MATH 103: Number Theory @atiq
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MTH321: Real Analysis 1 (Spring 2015) @atiq
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Notes of Number Theory by Umer Asghar @bsc
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Multiple Choice Questions (MCQs) @fsc-part1-kpk
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Multiple Choice Questions (MCQs) @math-11-kpk
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Real Analysis Notes by Prof Syed Gul Shah @notes
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MCQs with Answers @fsc:fsc_part_1_mcqs
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Chapter 01: Number System @fsc:fsc_part_1_solutions
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Question 5 and 6 Exercise 6.2 @math-11-kpk:sol:unit06
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MTH321: Real Analysis I (Fall 2019) @atiq
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MTH321: Real Analysis I (Fall 2022) @atiq
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MTH321: Real Analysis 1 @atiq
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Real Analysis Handwritten Notes by Kaushef Salamat @notes
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Question 5 and 6 Exercise 6.3 @math-11-kpk:sol:unit06
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Question 6 Exercise 6.4 @math-11-kpk:sol:unit06
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Exercise 2.6 (Solutions) @matric:9th_science:unit_02
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Preparation Guide @msc:syllabus:uos
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Khuram Ali Khan
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MathCraft
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CHEM-501: Basic Mathematics for Chemist @atiq
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MATH-300: Basic Mathematics for Chemist @atiq
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FSc Part 2 (KPK Boards) @fsc
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Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
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MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
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Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
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Question 4, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Question 5, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Question 4, Exercise 1.1 @math-11-kpk:sol:unit01
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Question 5, Exercise 1.1 @math-11-kpk:sol:unit01
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Question 3 and 4 Exercise 6.5 @math-11-kpk:sol:unit06
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Question 5 and 6 Exercise 6.5 @math-11-kpk:sol:unit06
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Question 5 Exercise 7.2 @math-11-kpk:sol:unit07
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Question 1 Review Exercise 7 @math-11-kpk:sol:unit07
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Mathematician of the day
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MATH-305: Real Analysis-I @atiq
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Are the functions are same? @dyk
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Definitions: FSc Part1 KPK @fsc-part1-kpk
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Definitions: FSc Part1 KPK @math-11-kpk
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Advance Analysis by Ms. Iqra Liaqat @notes
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Complex Analysis (Quick Review) @notes
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Metric Spaces (Notes) @notes
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PPSC Paper 2021 (Lecturer in Mathematics) @ppsc
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PPSC Mock Interview Lecturer Mathematics @ppsc
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Formatting Syntax @wiki
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Targets @msc:notes
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Syllabus for UoS (Private only) @msc:syllabus
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Question 3 & 4, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Question 3 & 4, Exercise 1.2 @math-11-kpk:sol:unit01
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Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
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Question 13 & 14 Exercise 4.3 @math-11-kpk:sol:unit04
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Question 3 and 4 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 14 and 15 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 7 and 8 Exercise 6.3 @math-11-kpk:sol:unit06
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Question 8 Exercise 6.5 @math-11-kpk:sol:unit06
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Question 1 Review Exercise 6 @math-11-kpk:sol:unit06
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Dr. Muhammad Ahsan Binyamin
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Mathematics CUI: LaTeX Resources
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MTH322: Real Analysis II (Fall 2021) @atiq
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MTH103: Exploring Quantitative Skills @atiq
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MATH-301: Complex Analysis @atiq
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MATH-505: Complex Analysis @atiq
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MTH633: Advanced Convex Analysis (Spring 2019) @atiq
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Important Questions @fsc-part1-ptb
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Short Term Preparation FSc 1 @fsc-part1-ptb
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FSc Part 1 (KPK Boards) @fsc
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Mathematics 9 (Science Group) @matric
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Complex Analysis (Notes) by Ms. Iqra Liaqat @notes
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Complex Analysis by M Usman Hamid @notes
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Computing Tools for Mathematics by Asif Arshad @notes
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General Topology by Azhar Hussain @notes
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Handwritten Notes of Real Analysis by Asim Marwat @notes
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Measure Theory Notes by Anwar Khan @notes
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Notes for Numerical Methods by M Usman Hamid @notes
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Topology: Handwritten Notes @notes
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Muzammil Tanveer @people
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Umer Asghar @people
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Quotes for the April @quote-of-the-day
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Quotes for the February @quote-of-the-day
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Quotes for the May @quote-of-the-day
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DokuWiki @wiki
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Unit 01: Functions and Limits @fsc:fsc_part_2_solutions
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Syllabus for PU @msc:syllabus
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Pure Mathematics @bsc:paper_pattern:sargodha_university
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Question 3 & 4, Exercise 3.2 @math-11-kpk:sol:unit03
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Question 3 and 4 Exercise 4.2 @math-11-kpk:sol:unit04
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Question 5 and 6 Exercise 4.2 @math-11-kpk:sol:unit04
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Question 11 Exercise 4.2 @math-11-kpk:sol:unit04
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Question 9 & 10 Exercise 4.3 @math-11-kpk:sol:unit04
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Question 4 & 5 Exercise 4.4 @math-11-kpk:sol:unit04
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Question 7 & 8 Exercise 4.5 @math-11-kpk:sol:unit04
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Question 2 & 3 Exercise 5.1 @math-11-kpk:sol:unit05
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Question 11 Review Exercise 6 @math-11-kpk:sol:unit06
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Question 2 Review Exercise 7 @math-11-kpk:sol:unit07
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Exercise 2.2 (Solutions) @matric:9th_science:unit_02
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