Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 08:55:13 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/fsc-part1-ptb/important-questions/ch05-partial-fractions Ch 05: Partial Fraction * Resolve $\frac{1}{(x^2+1)(x+1)}$ into partial fraction --- BISE Gujrawala(2015) * Resolve the following into partial fractions $\frac{2x^4}{(x-3)(x+2)^2}$ --- BISE Gujrawala(2017) * Resolve $\frac{x^2+1}{(x+1)(x-1)}$ into partial fraction --- BISE Sargodha(2015),BISE Sargodha(2017) * Resolve $\frac{9}{(x+2)^2(x-1)}$$\frac{1}{(x-1)^2+(x+1)}$$\frac{x^2+1}{(x^3+1)}$$\frac{1}{(x-1)^2(x^2+2)}$$\frac{1}{x^2-1}$$\frac{x^2}{(x-2)(x-1)^2}$$\frac{3x-1}{(x^2+1)(x+3)}… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:40 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch03-matrices-and-determinants Ch 03: Matrices and Determinants * 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]$ --- BISE Gujrawala(2015) * Solve for matrix $A$ if $\left[ {\begin{array}{c}4&3\\ 2&2 \end{array}} \right]A-\left[ {\begin{array}{c} 2&3\\ -1&-2 \end{array}} \right]= \left[ {\begin{array}{c} -1&-4\\ 3&6 \end{array}} \right]$ --- BISE Gujrawala(2015) * Prove without expansion $ \left[ {\begin{array}{c} 6&7&… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:39 +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 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch04-quadratic-equations Ch 04: Quadratic Equations * Reduce $x^{-2}-10=3x^{-1}$ to quadratic form --- BISE Gujrawala(2015) * Show that $x^3-y^3=(x-y)(x-wy)(x-w^2y)$ --- BISE Gujrawala(2015) * If $n$ is an odd integer, is $(x+a)$ factor of $(x^n+a^n)$? --- BISE Gujrawala(2015) * 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$${\begin{array}{c} x^2-5xy+6y^2=0\\x^2… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:40 +0000