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- Quotes for the March @quote-of-the-day
- olor="#A11400" title="Quote by Mathematician"> <TEXT align="right">"نئی ریاضی" کی اہمیت بنیادی طور پر ... رمیان فرق سکھایا ہے۔ [اسحاق ٹودھنٹر (1820-1884)]</TEXT> The importance of the "New Mathematics" lies mai... sc and the circle. [Isaac Todhunter (1820-1884)] <TEXT align="right" type="danger" size="small">(Courtesy: MacTutor) ---: MathCity.org</TEXT> </callout></col><col lg="4"> <callout icon="f
- Quotes for the May @quote-of-the-day
- color="#A11400" title="Quote by Mathematician"> <TEXT align="right">مختصراً، پوری دنیا خلا اور وقت میں ... یار کی گئی مشین ہے۔۔۔ **مورس کلائن (1908-1992)**</TEXT> In brief, the whole world is the totality of mat... signed machine. --- **Morris Kline (1908-1992)** <TEXT align="right" type="danger" size="small">(Courtesy: MacTutor) ---: MathCity.org</TEXT> </callout></col><col lg="4"> <callout icon="f
- Quotes for the April @quote-of-the-day
- olor="#A11400" title="Quote by Mathematician"> <TEXT align="right">کاسمولوجسٹ اکثر غلط ہوتے ہیں، لیکن کبھی شک میں نہیں۔۔۔ **لیو لینڈاؤ (1908-1968)**</TEXT> Cosmologists are often wrong, but never in doubt. --- **Lev Landau (1908-1968)** <TEXT align="right" type="danger" size="small">(Courtesy: MacTutor) ---: MathCity.org</TEXT> </callout></col><col lg="4"> <callout icon="f
- Quotes for the February @quote-of-the-day
- ow to avoid them [Werner Heisenberg (1901-1976)] <TEXT align="right">ایک ماہر وہ ہوتا ہے جو اپنے مضمون م... چنے کا طریقہ جانتا ہو [ورنر ہیزنبرگ (1901-1976)]</TEXT> <TEXT align="right" type="danger" size="small">(Courtesy: MacTutor) ---: MathCity.org</TEXT> </callout></col><col lg="4"> <callout icon="f
- Question 2, Exercise 2.3 @math-11-kpk:sol:unit02
- 1 & 2 \\ 0 & 0 & 1 \end{matrix} \right. \right]\text{ by }R_1+3R_3\text{ and }R_2+2R_3 \\ \underset{\sim}{R}&\left[\begin{matrix} 1 & 4 & 14 \\ 0 & 5 & 6 ... 1 & 2 \\ 1 & 0 & 4 \end{matrix} \right. \right]\text{ by }R_3+R_1\\ \underset{\sim}{R}&\left[\begin{ma... -1 & 2 \\ 1 & 0 & 4 \end{matrix} \right. \right]\text{by}-R_2+R_3\\ \underset{\sim}{R}&\left[\begin{ma
- Question 1, Exercise 2.5 @math-11-nbf:sol:unit02
- & 8 & 3 \\ -4 & 6 & 5\end{array}\right]\\ \sim & \text{R} \left[\begin{array}{ccc} 1 & 3 & 5 \\ 0 & 26 &... right]\quad R_2 + 6R_1 \quad R_3 + 4R_1\\ \sim & \text{R} \left[\begin{array}{ccc} 1 & 3 & 5 \\ 0 & 1 & ... nd{array}\right] \quad \frac{1}{26}R_2 \\ \sim & \text{R} \left[\begin{array}{ccc} 1 & 3 & 5 \\ 0 & 1 & ... 26} \end{array}\right]\quad R_3 - 18R_2\\ \sim & \text{R} \left[\begin{array}{ccc} 1 & 3 & 5 \\ 0 & 1 &
- Examples for the Wrap Plugin @playground
- * (including alignments generated by changing the text direction) * **multi-columns** * and **widths... e a big headline with italic, bold and underlined text, e.g. ''%%//**__Emulated Big Headline__**//%%'' ... %//**Emulated Small Headline**//%%'' If you need text that is bold and italic, simply use it the other ... e across something like this, where the following text protrudes into the space where only the floating
- Formatting Syntax @wiki
- [[doku>toolbar|quickbuttons]], too. ===== Basic Text Formatting ===== DokuWiki supports **bold**, //i... by a whitespace or the end of line. This is some text with some linebreaks\\ Note that the two backslas... espace \\this happens without it. This is some text with some linebreaks\\ Note that the two backsl... m or simply www.google.com - You can set the link text as well: [[http://www.google.com|This Link points
- Question 2, Exercise 2.5 @math-11-nbf:sol:unit02
- & 6 \\ 2 & 10 & 6 \end{array} \right]\\ \sim & \text{R}\left[ \begin{array}{ccc} 1 & \frac{9}{5} & \fr... \end{array} \right]\quad \frac{1}{5} R1\\ \sim & \text{R}\left[ \begin{array}{ccc} 1 & \frac{9}{5} & \fr... end{array} \right]\quad R2 - 3 \cdot R1\\ \sim & \text{R}\left[ \begin{array}{ccc} 1 & \frac{9}{5} & \fr... nd{array} \right]\quad R3 - 2 \cdot R1 \\ \sim & \text{R}\left[ \begin{array}{ccc} 1 & \frac{9}{5} & \fr
- Question 1, Exercise 2.3 @math-11-kpk:sol:unit02
- -1 \\ 0 & -5 & 6 \\ 0 & -5 & -2 \end{bmatrix} \text{ by } R_2-2R_1 \text{ and } R_3-3R_1 \\ \underset{\sim}{R}&\begin{bmatrix} 1 & 3 & -1 \\ 0 & -5 & 6 \\ 0 & -5 & -2 \end{bmatrix} \text{ by } R_3-R_2 \\ \underset{\sim}{R}&\begin{bmatri... 1 & 9 \\ 3 & \quad 1 & 3 & \quad 2 \end{bmatrix}\text{ by } R_1\leftrightarrow R_2\\ \underset{\sim}{R}
- Question 4, Exercise 2.6 @math-11-nbf:sol:unit02
- & 7 \\ 4 & 2 & -5 & : & 10 \end{bmatrix}\\ &\sim \text{R}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2}... ert & 10 \end{bmatrix}\quad \dfrac{1}{2}\\ &\sim \text{R}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2}... 5 & : & 10 \end{bmatrix}\quad R_2 - 3R_1\\ &\sim \text{R}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2}... -3 & : & 6 \end{bmatrix}\quad R_3 - 4R_1\\ &\sim \text{R}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2}
- Question 9 Exercise 6.5 @math-11-kpk:sol:unit06
- ll be selected. ====Solution==== \begin{align} P(\text { Ajmal scicction })&=\dfrac{1}{7} \\ \Rightarrow P(\text { Ajmal not selected })&=\dfrac{6}{7} \\ P(\text { Bushra selection })&=\dfrac{1}{5} \\ \Rightarrow P(\text { Bushra not selected })&=\dfrac{4}{5}\end{align}
- Question 9 & 10 Exercise 4.3 @math-11-kpk:sol:unit04
- ots, 693$$.\\ Here, $a=306$,\\ $$d=(315-306) = 9 \text { and } a_n=693 .$$\\ Let the number of terms be $n$. Then\\ \begin{align}a_n&=a_1+(n-1) d \text { becomes } \\ \Rightarrow a_1+(n-1) d&=693 \\ \R... 1000$, \\ therefore we have $n=4$\\ \begin{align}\text{Let the first person receives}&=R s . a\\ \text{Then the seçond receives}&=\operatorname{Rs}(a-20)\\ \
- Question 13 Exercise 6.2 @math-11-kpk:sol:unit06
- $ and $m_3=2$ are $C$. Therefore, \begin{align}\text{total number of permutations are} &=\left(\begin... L$ and $m_3=2$ are $C$. Therefore, \begin{align}\text{Number of permulations are} &=\left(\begin{array}... L$ $m_3=2$ are $C$. Therefore, \begin{align}\text{total number of permutations are} & =\left(\begin... and $m_3=1$ are $C$. $\therefore$ \begin{align}\text{Number of permutations are}& =\left(\begin{array}
- Question 3, Exercise 9.1 @math-11-nbf:sol:unit09
- Domain of $y=\left\{\theta: \theta\in \mathbb{R} \text{ and } \theta \neq n\pi, n\text{ is integer} \right\}$ Range of $y=\mathbb{R}$ As \begin{align*} & ... } Hence domain of $y=\left\{x: x\in \mathbb{R} \text{ and } x \neq 2n, n\text{ is integer} \right\}$ Range of $y=\mathbb{R}$. GOOD =====Question 3(v)=====
- Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch07
- Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch08