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- MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
- ====== 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
- 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
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- 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}{
- Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
- is the difference between rational 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 set of rational numbers coun
- Question 7 Exercise 6.4 @math-11-kpk:sol:unit06
- . Find the probability of getting doublet of even numbers. ====Solution==== The sample space rolling a pai... 5) & (6,6) \end{array}\right]\end{align} So total number of sample points are $$n(S)=6 \times 6=36$$ doublet of even numbers. Let \begin{align}A&=\{(2,2),(4,4),(6,6)\}\\ n(... nce the possibility of getting doublet of an even number is: $$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{3}{36}=\dfra
- Question 9 Exercise 6.3 @math-11-kpk:sol:unit06
- 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
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- ad> The main topics of this exercise are complex numbers, real part and imaginary part of complex numbers, properties of the fundamental operation on complex numbers, complex number as ordered pair of real numbers and special subset of complex numbers. These notes are b
- Exercise 2.1 (Solutions) @matric:9th_science:unit_02
- hich of the following are rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$ ... 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
- Question 13 Exercise 6.2 @math-11-kpk:sol:unit06
- 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 \
- MTH321: Real Analysis I (Spring 2023) @atiq
- 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 $\left\{ {{r}_{n}} \right\}$ of distinct rational numbers such that $\underset{n\to \infty }{\mathop{\lim... _{n}}}$ is convergent if and only if for any real number $\varepsilon >0$, there exists a positive integer
- PPSC Paper 2011 (Lecturer in Mathematics) @ppsc
- 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
- CQs or short question will be posted here. - A number which is neither even nor odd is * (A) 0 ... ch that $n \in \mathbb{Z}$ * (D) $2\pi$ - A number which is neither positive nor negative is * ... exists in set of .............. * (A) natural numbers * (B) integers * (C) rational numbers * (D) real numbers - If a real number is not rationa
- Number Theory: Handwritten Notes @notes
- ====== 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
- MTH321: Real Analysis I (Fall 2021) @atiq
- opment. ===== Course contents ===== * The Real Number System: Ordered Fields. The Field of Reals. The Extended Real Number System. Euclidean Space. * Numerical Sequences... s in the 18th century used the entire set of real numbers without having defined them cleanly. The first r... is no difference between rational and irrational numbers in this regard. </callout> =====Schedule===== T
- Number Theory by Dr Muhammad Umer Shuaib @notes
- ====== 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
- Chapter 01: Viewer @bsc:notes_of_calculus_with_analytic_geometry:ch01_real_numbers_limits_and_continuity
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university