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- Definitions: FSc Part 1 (Mathematics): PTB
- itions-Muzzammil-Subhan ]] ===== 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
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
- r 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
- 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 ... - $-2i$ - $2$ - $\sqrt{2}$ is ------- number. - natural - complex - irrational ... displaystyle{\frac{p}{q}}$ form - A rational number is a number which can be expressed in the form -
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- binary operation, semi-group, monoid, groups and abelian groups. These notes are based on the new Stud... # 1** Operation $\oplus$ performed on the two-member set $G=\{0,1\}$ is shown in the adjoining table. \[ \begin{array}{|c|c|c|} \hline \oplus & 0 & 1 \\ \h... the set $G$, under the given operation a group? Abelian or non-abelian? **Solutions**\\ (i) From the
- Trigonometric Formulas
- oard Lahore. This handout is very helpful to remember the formulas. All these formulas are given for r... d defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word f... anel><grid><col sm="6"> * $\sin \left( \alpha +\beta \right)=\sin \alpha \cos \beta +\cos \alpha \sin \beta$ * $\sin \left( \alpha -\beta \right)=\s
- MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
- uations ====== High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry ... - Linear - Cubic - None of these - Number of basic techniques for solving a quadratic equa... - Coefficients - None of these - Maximum number of roots of a quadratic equation are - One ... -4ac}}{2a}$ - A quadratic equation which cannot be solved by factorization, that will be solved by
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- 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
- Ch 03: Matrices and Determinants @fsc-part1-ptb:important-questions
- == <list-group> * Fin $x$ and $y$ if $ \left[ {\begin{array}{c} x+3&1\\ -3& 3y-4 \end{array}} \right]= \left[ {\begin{array}{c} 2&1\\ -3&2 \end{array}} \right]$ -... ala(2015)// * Solve for matrix $A$ if $\left[ {\begin{array}{c}4&3\\ 2&2 \end{array}} \right]A-\left[ {\begin{array}{c} 2&3\\ -1&-2 \end{array}} \right]= \l
- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- topics of this exercise are properties of real numbers, binary operation, addition and multiplication ... or '$\times$'. **Solutions** Addition Table \[\begin{array}{|c|c|} \hline + & 0 \\ \hline 0 & 0 ... ure property w.r.t. '+'. Multiplication Table \[\begin{array}{|c|c|} \hline \times & 0 \\ \hline 0... or '$\times$'. **Solutions** Addition Table \[\begin{array}{|c|c|} \hline + & 1 \\ \hline 1 & 2
- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- hese - The objects in a set are called - Numbers - Terms - Elements - None of these - A set can be describing in different no. of ways are - One... - Capital letters - None of these - The members of different sets usually denoted by - Capi... rs - None of these - The symbol used for membership of a set is - $\forall$ - $\wedge$
- Solution and Area of Oblique Triangle
- oard Lahore. This handout is very helpful to remember the formulas. All these formulas are given for r... d defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word f... b^2+c^2-2bc\cos \alpha$ * $b^2=c^2+a^2-2ca\cos \beta$ * $c^2=a^2+b^2-2ab\cos \gamma$ </col><col s... $\cos\alpha =\dfrac{b^2+c^2-a^2}{2bc}$ * $\cos\beta =\dfrac{c^2+a^2-b^2}{2ac}$ * $\cos\gamma =\df
- Multiple Choice Questions (MCQs)
- the above mentioned book. MCQs are very important because most of entry tests, admission tests and job... n$ is prime, then $\sqrt{n}$ is * rational number * whole number * natural number * irrational number - Multiplicative property of order of real numbers is
- Ch 07: Permutation, Combination and Probability @fsc-part1-ptb:important-questions
- BISE Gujranwala(2015)// * How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How many of them with lie between $400,000$ and $430,000$? ---// BISE Gujrawala(2015)// * How many words can be formed from the letter $``PLANE"$ using all lette
- Ch 04: Quadratic Equations @fsc-part1-ptb:important-questions
- * If the roots of $px^2+qx+q=0$ are $\alpha$, $\beta$,then prove that $$\sqrt {\frac{\alpha}{\beta}}+\sqrt {\frac{\beta}{\alpha}}+\sqrt{\frac{p}{q}}=0$$ --- //BISE Gujrawala(2017),BISE Sagodha(2017... tem of equations --- //BISE Gujrawala(2017)// $${\begin{array}{c} x^2-5xy+6y^2=0\\x^2+y^2=45\end{array
- Ch 06: Sequences and Series @fsc-part1-ptb:important-questions
- $n$, so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ maybe $A.M$ between $a$ and $b$. --- //BISE Gujrawala(2015)// * If $y=1+\frac{x}{2}+\frac{x^4}{4}+...$ ... argodha(2015)// * If $15$ and $8$ are two A.Ms between $a$ and $b$, find $a$ and $b$. --- //BISE Sa... -- //BISE Sargodha(2015)// * Find three $A.Ms$ between $3$ and $11$ --- //BISE Sargodha(2016)//