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- Ch 07: Permutation, Combination and Probability @fsc-part1-ptb:important-questions
- mbination and Probability ====== <list-group> * Find $n$ when ${^nC_{12}}={^nC_6}$ ---// BISE Gujranwa... ^nC_4=^nC_{n-r}$ ---// BISE Gujrawala(2017)// * Find the numbers of diagonals of a $6-digits$ figures ... ujrawala(2017)// * A coin is tossed four times, find the probability that top shows all heads. ---// B... $6$ for $n=2,3$ ---// BISE Gujrawala(2017)// * Find the value of $n$ when $^nP_2=30$ ---// BISE Sargo
- Ch 03: Matrices and Determinants @fsc-part1-ptb:important-questions
- y}} \right]= 0$ --- // BISE Gujrawala(2015)// * Find inverse of $ \left[ {\begin{array}{c} 2&1&0\\ 1&1... {\begin{array}{c} 0&0\\ 0&0 \end{array}} \right]$ find the value of $a$ and $b$. --- // BISE Sargodha(2017), Gujrawala(2017)// * Find the value of $\lambda$ if $ A=\left[ {\begin{arr... t]$ is singular --- // BISE Sargodha(2015)// * Find the value of $x$, $ \left[ {\begin{array}{c} 3&1&
- Ch 08: Mathematical Induction and Binomial Theorem @fsc-part1-ptb:important-questions
- }{x^2}\right)$ --- // BISE Gujranwala(2015)// * Find the $6$th term in the expansion of $\left( x^2-\f... of decimials. --- // BISE Gujranwala(2017)// * Find the middle term of $(a+x)$? When $n$ is even. --- // BISE Gujranwala(2017)// * Find the term independent of $x$ in the following expa... 1}$ for $n=2,3$ --- // BISE Sargodha(2015)// * Find $13$th term of $x,1,2-x,3-2x,...$ --- // BISE Sar
- Ch 04: Quadratic Equations @fsc-part1-ptb:important-questions
- c} x^2-5xy+6y^2=0\\x^2+y^2=45\end{array}}$$ * Find the roots of the equation $4x^2+7x-1=0$ --- //BIS... $ is divided by $x-2$, then the reminder is $14$, find $k$. --- //BISE Gujrawala(2017)// * Show that ... $\alpha$, $\beta$ are the roots of $3x^2-2x+4=0$, find the values of $\frac{\alpha}{\beta}+\frac{\beta}{... 2-7x+6$ is divided by $x+2$ the reminder is $-4$? Find the value of $k$. --- //BISE Lahore(2017)// *
- Ch 06: Sequences and Series @fsc-part1-ptb:important-questions
- w that $AH=G^2$ ---// BISE Gujrawala(2015)// * Find $n$, so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ ma... frac{y-1}{y})$ --- //BISE Gujrawala(2017)// * Find the $9th$ term of harmonic sequence $\frac{1}{3},... //BISE Gujrawala(2017)// * If $a=-2$, $b=-6$, find $A.G$ --- //BISE Gujrawala(2017)// * If $\fra... If $15$ and $8$ are two A.Ms between $a$ and $b$, find $a$ and $b$. --- //BISE Sargodha(2015)// * If
- Ch 09: Fundamental of Trigonometry @fsc-part1-ptb:important-questions
- ndamental of Trigonometry ====== <list-group> * Find the value of the remaining trigonometric function... rc}$ into radian. --- //BISE Sargodha(2015)// * Find $\theta$ when $l=1.5cm$, $r=2.5cm$ --- //BISE Sar... theta+sin\theta}$ --- //BISE Sargodha(2015)// * Find $l$ when $\theta=65^{\circ}20'$, $r=18mm$ --- //BISE Sargodha(2015), BISE Lahore(2017)// * Find the value of remaining trigonometric functions if
- Ch 11: Trigonometric Functions and Their Graphs @fsc-part1-ptb:important-questions
- nctions and Their Graphs ====== <list-group> * Find the period of $\sin 4x$ --- //BISE Gujrawala(2015)// * Find the period of $\tan 4x$ --- //BISE Gujrawala(2017)// * Find the period of $\sin\frac{x}{5}$ --- //BISE Sargodha(2015), BISE Sargodha(2016)// * Find the period of $cosec10x$ --- //BISE Sargodha(201
- Ch 12: Applications of Trigonometry @fsc-part1-ptb:important-questions
- lications of Trigonometry ====== <list-group> * Find the value of $tan\frac{\alpha}{2}$ in term of $s$... $r=90^{\circ}$, $\alpha=62^{\circ}40'$, $b=796$, find $\beta$ anf $a$--- //BISE Gujrawala(2017)// * Find the area of $\triangle ABC$, if $a=18$, $b=24$,$c=... rc}$, $b=\sqrt{6}$--- //BISE Sargodha(2015)// * Find the area of the triangle $ABC$, when $a=18$, $b=2
- Ch 02: Functions and Groups @fsc-part1-ptb:important-questions
- ns are selected from old papers. <list-group> * Find multiplicative inverse $(2,4)$ --- // BISE Gujrawala(2015)// * Find power set of $\{a,\{b,c\}\}$ --- // BISE Gujra... // BISE Sargodha(2015)// * For $A=\{1,2,3\}$ find the relation $\{(x,y)| x+y<5\}$ --- // BISE S... $\{9,11\}$ --- // BISE Sargodha(2016)// * Find converse, inverse of the conditional $~p \longrig
- Ch 01: Number Systems @fsc-part1-ptb:important-questions
- frac{1}{b}}$ --- // BISE Sargodha(2015)// * Find multiplicative inverse $(\sqrt{2}, -\sqrt{5})$ -... t to "+" and "-". --- // BISE Lahore(2017)// * Find multiplicative inverse of $a \div ib$ --- // BI... \frac{-21}{2}$ --- // BISE Sargodha(2016)// * Find multiplicative inverse of $(0,1)$ --- // BISE
- Ch 10: Trigonometric Identities @fsc-part1-ptb:important-questions
- ala(2017)// * Using without table or calculator find $tan(1110^{\circ})$ --- // BISE Sargodha(2015), B... pha=2cot2\alpha$ --- // BISE Sargodha(2015)// * Find the value of $cos15^{circ}$ using without table o... rc}=\frac{1}{8}$ --- // BISE Sargodha(2016)// * Find the value of $cos\frac{\pi}{12}$ --- // BISE Sarg
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- l number. </panel> <panel> **Question 14(i) ** Find the multiplicative inverse of complex number $\le... 65},\frac{-7}{65} \right)$ **Question 14(ii) ** Find the multiplicative inverse of complex number $\le... rac{\sqrt{5}}{7} \right)$ **Question 14(iii) ** Find the multiplicative inverse of complex numbers $\l
- Ch 13: Inverse Trigonometry Functions @fsc-part1-ptb:important-questions
- se Trigonometry Functions ====== <list-group> * Find the value of $cos^{-1}(\frac{1}{2})$ --- //BISE G... 1}x)=\sqrt{1-x^2}$--- //BISE Sargodha(2016)// * Find the value of $tan(cos^{-1}\frac{\sqrt{3}}{2})$---
- Ch 14: Solutions of Trigonometric Equation @fsc-part1-ptb:important-questions
- e $x \in [0,2\pi]$--- //BISE Sargodha(2015)// * Find the solutions of $cosec\theta=2$ which is lie in
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- s a group under the operation $*$ and $a,b\in G$, find the solutions of the equations: $a*x=b$, $x*a=b$