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- PPSC Paper 2015 (Lecturer in Mathematics) @ppsc
- ac{1}{2}\ln2+\dfrac{3\pi i}{4}$ - Which of the following space is complete. \\ - \(Q\) - \(]0,1]\)... }$ - $\dfrac{\sqrt{13}}{2}$ - Which of the following is convergent series? \\ - \(\sum\dfrac{1}{n... infty,+\infty)\) - \( x=0\) - Which of the following are in the usual metric space \( (R,d) \)? \\ ... (T_2\)-space - Normal space - Which of the following is connected in \(\mathbb{R}\) with usual topolog
- Software
- he Android devices. It can be downloaded from the following link: http://bit.ly/2vUbqMO * **Desmos Graphin... its features or download the app, please see the following: https://bit.ly/2Rs141c * **PhotoMath**: Photo... d or handwritten problems. It can downloaded from following page: https://bit.ly/3aZARPn ===== PDF Reader & ... full multimedia support. One can get it from the following link: https://get.adobe.com/reader/ * **Sumatr
- Mathematics 9 (Science Group) @matric
- ===== Unit 02: Real and Complex Numbers ===== The following MCQs was send by [[people:amir]]. We are very tha... essions and Algebraic Formulas===== In this unit, following topics has been covered: * Algebraic Expressio... ds and their Application * Rationalization The following notes of this chapter are provided by Mr. Adil As... } =====Unit 05: Factorization===== In this unit, following topics has been covered: After studying this unit
- Examples for the Wrap Plugin @wiki
- might come across something like this, where the following text protrudes into the space where only the floa... o be able to read its content. === Hide === The following text is hidden: <wrap hide>John, please revise that sentence.</wrap> The following text is hidden: <wrap hide>John, please revise th... ty risky secrets with it! === Pagebreak === The following will add a pagebreak: <WRAP pagebreak></WRAP>
- Mathematics 10 (Science Group) @matric
- rcise-3-7-maryam-jabeen.pdf |Download PDF}} The following notes are sent by Mr. [[:people:amir]]. We are ve... ercise_4-4-maryam-jabeen.pdf |Download PDF}} The following notes are sent by Mr. [[:people:amir]]. We are ve... erence, complement. * give formal proofs of the following fundamental properties of union and intersection ... ector of a circle is $\frac{1}{2}r^2 \theta$ The following Solutions was send by [[people:amir]]. We are ver
- Formatting Syntax @wiki
- . To remove this warning (for all users), put the following line in ''conf/lang/en/lang.php'' (more details a... ported Media Formats ==== DokuWiki can embed the following media formats directly. | Image | ''gif'', ''jpg... to show it's a reply or comment. You can use the following syntax: <code> I think we should do it > No we ... ld!"); //Display the string. } } </code> The following language strings are currently recognized: //4cs
- Exercise 2.1 (Solutions) @matric:9th_science:unit_02
- ====== ====Question 1==== Identify which of the following are rational and irrational numbers: (i) $\sqrt{... \pi$, $\sqrt{29}$ ====Question 2==== Convert the following fraction into decimal fraction. (i) $\frac{17}{2... tion. **False** ====Question 4==== Represent the following numbers on the number line. (i) $\frac{2}{3}$ (... epresents $\frac{2}{3}$ on the number line in the following figure. (ii) - To represent the rati
- Exercise 6.1 @matric:9th_science
- ====== Exercise 6.1 ====== On the following page we have given the solution of Exercise 6.1 of Mathematics 9 ... RAP> ====Question 1:==== Find the H.C.F of the following expressions.\\ (i) $39x^7y^3z$ and $91x^5y^6 z^7$... 17 xyz$ ====Question 2==== Find the H.C.F of the following expressions by factorization.\\ (i) $x^2+5x+6$, $... 3x-1)$ ====Question 4==== Find the L.C.M. of the following expressions by factorization.\\ (i) $39x^7y^3z$,
- Syllabus for PU @msc:syllabus
- ld papers. </callout> ===== Regulations ===== The following regulations will be observed by M.Sc. (Mathematic... y * c) Mechanics ===== M.Sc Part-I ===== The following five papers shall be studied in M.Sc. Part-I: -... I examinations, there are six written papers. The following three papers are compulsory. Each paper carries 1... Papers ==== A student may select any three of the following optional courses: * Paper IV-VI option (i) Math
- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- > **Question 2** Name the properties used in the following equations (Letters, where used, represent real nu... sqrt{7}= \sqrt{3}(\sqrt{5}+\sqrt{7})$ used in the following question. **Property:** Associative property w.r... > **Question 3** Name the properties used in the following inequalities: **Solution** (i) $-3<-2 \quad \Ri... col sm="6"> <panel> **Question 4(i)** Prove the following rules of addition: $$\frac{a}{c}+\frac{b}{c} = \
- MathCraft: PDF to LaTeX file: Sample-01 @mathcraft
- es}}\end{center} \vspace{2mm} Let us consider the following means $$ \begin{aligned} & E(x, y ; r, s)=\left... , Stolarsky means. } \vspace{2mm} We consider the following function $f(x)=p^{2} \varphi_{r}(x)+2 p q \varph... mathbb{R}$. And therefore $\log$-convex. We need following lemma which proof can be found in [2]. \vspace{4... 2}, x_{1} \neq x_{2}, y_{1} \neq y_{2}$, then the following inequality is valid: \begin{equation*} \left(\d
- PPSC Paper 2011 (Lecturer in Mathematics) @ppsc
- \(G\) be an abelian group. Then which one of the following is not true. \\ - every commutator of \(G\) i... ) - Let \(X=\{a,b,c,d,e\}\). Which one of the following classes of subsets of \(X\) is a topology on \(X\... {R}$ be the usual metric space. Then which of the following set is not closed. \\ - Set of integers -... i}{4}$ - $0$ - $\infty$ - Which of the following function is a bijection from \(\mathbb{R}\) to \(
- Ch 05: Partial Fraction @fsc-part1-ptb:important-questions
- ion --- //BISE Gujrawala(2015)// * Resolve the following into partial fractions $\frac{2x^4}{(x-3)(x+2)^2}... 1)}$ --- //BISE Sargodha(2015)// * Resolve the following into partial fractions $\frac{x^2+1}{(x^3+1)}$ --- //BISE Sargodha(2016)// * Resolve the following into partial fractions $\frac{1}{(x-1)^2(x^2+2)}$... ^2-1}$ --- //BISE Lahore(2017)// * Resolve the following into partial fractions $\frac{x^2}{(x-2)(x-1)^2}$
- Unit 05: Linear Inequalities and Linear Programming @fsc-part2-ptb:important-questions
- 6)// * Graph the feasible region subject to the following constraint: --- // BSIC Gujranwala (2016)// $2x-3... alpindi (2017)// * Graph the feasible region of following inequality $2x-3y\leq6$ --- // BSIC Sargodha(2016)// * Graph the feasible region of following system of linear inequalities, also find corner p... odha(2017)// * Graph the feasible region of the following system of linear inequalities, also find corner p
- Exercise 4.1 @matric:9th_science
- ====== Exercise 4.1 ====== On the following page we have given the solution of Exercise 4.1 of Mathematics 9 ... </WRAP> ====Question 1:==== Identify whether the following algebraic expressions are polynomials (Yes or No)... \\ ====Question 2:==== State whether each of the following expression is a rational expresion or not.\\ (i) ... \frac{1}{2x-1})$ ====Question 3:==== Reduce the following rational expressions to the lowest forms.\\ (i)