Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 16:38:00 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/fsc-part1-ptb/important-questions/ch06-sequence-and-series Ch 06: Sequences and Series * If $\frac{1}{a}$, $\frac{1}{b}$ and $\frac{1}{c}$ are in $G.P$. Show that $r=\pm \sqrt{\frac{a}{c}}$ --- BISE Gujranwala(2015),BISE Sargodha(2015), BISE Sargodha(2017),BISE Lahore(2017) * With usual notation show that $AH=G^2$ --- BISE Gujrawala(2015) * Find $n$, so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ maybe $A.M$ between $a$ and $b$$y=1+\frac{x}{2}+\frac{x^4}{4}+...$$x=2(\frac{y-1}{y})$$9th$$\frac{1}{3}, \frac{1}{5}, \frac{1}{7},...$$a=-2$$b=-6$$A.G$$\f… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:42 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch07-permutation-combination-and-probablity Ch 07: Permutation, Combination and Probability * Find $n$ when ${^nC_{12}}={^nC_6}$ --- BISE Gujranwala(2015) * Evaluate ${^{20}C_{17}}$ without calculator --- 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 $430,000$? ---$``PLANE"$$^nC_4=^nC_{n-r}$$6-digits$$n^3-n$$6$$n=2,3$$n$$^nP_2=30$$6-dided$$n$$^nC_{12}=^nC_6$$^{n-1}C_r+^{n-1}C_{r-1}=^nC_r$$\frac{a_5}{a_3}=\frac{4}{9}$$a_2=\frac{4}{9}$… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:42 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch08-mathematical-induction-and-binomial-theorem Ch 08: Mathematical Induction and Binomial Theorem * Using binomial theorem,expand $\left(\frac{x}{2}-\frac{2}{x^2}\right)$ --- BISE Gujranwala(2015) * Find the $6$th term in the expansion of $\left( x^2-\frac{3}{2x}\right)$ --- BISE Gujranwala(2015) * Expand $\left( 8-2x\right)^{-1}$ up to two terms. --- BISE Gujranwala(2015) * Use binomial theorem to show that $1+\frac{1}{4}+\frac{1.3}{4.8}+\frac{1.3.5}{4.8.12},...=\sqrt{2}$$(1.03)^{\frac{1}{3}}$$(a+x)$$n$$x$$(x-\frac{2}{x})^{10}$$… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:43 +0000