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Ch 10: Trigonometric Identities
31 Hits, Last modified:
rc}\sin 30^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\frac{1}{16}$ --- // BISE Gujrawala(2015)// * Prove that $\sin(\frac{\pi}{4}-\theta)\sin(\frac{\pi}{4}+\theta)=\frac{1}{2}\csc^2\theta$ --- // BISE Gujrawala(2017)// * Prove that $\sin(\theta+\fra
Ch 08: Mathematical Induction and Binomial Theorem
28 Hits, Last modified:
-group> * 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)// *... 2015)// * Use binomial theorem to show that $1+\frac{1}{4}+\frac{1.3}{4.8}+\frac{1.3.5}{4.8.12},...=\s
Ch 06: Sequences and Series
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Sequences and Series ====== <list-group> * 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(20
Ch 12: Applications of Trigonometry
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ry ====== <list-group> * Find the value of $tan\frac{\alpha}{2}$ in term of $s$ --- //BISE Gujrawala(2... //BISE Gujrawala(2015)// * Show that $r_1=stan\frac{\alpha}{2}$ --- //BISE Gujrawala(2015)// * Defi... 30$ --- //BISE Gujrawala(2017)// * Prove that $\frac{1}{r^2}+\frac{1}{{r_1}^2}+\frac{1}{{r_2}^2}+\frac{1}{{r_3}^2}=\frac{a^2+b^2+c^2}{\triangle^2}$ --- //BI
Ch 13: Inverse Trigonometry Functions
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=== <list-group> * Find the value of $cos^{-1}(\frac{1}{2})$ --- //BISE Gujrawala(2015)// * Prove that $2tan^{-1}(\frac{1}{3})+tan^{-1}(\frac{1}{7})=\frac{\pi}{4}$ --- //BISE Gujrawala(2015), FBISE(2016)// * Prove that $sin^{-1}(\frac{1}{\sqrt
Ch 09: Fundamental of Trigonometry
13 Hits, Last modified:
gonometric functions of $\theta$, If $cos \theta=\frac{12}{13}$ and the terminal side of the angle is no... rawala(2017)// * Verify $2 $ $\sin 45^{\circ} +\frac{1}{2}\cos 45^{\circ}=\frac{3}{\sqrt{2}}$ --- //BISE Gujrawala(2017), BISE Sargodha(2017)// * Prove th... 5cm$ --- //BISE Sargodha(2015)// * Prove that $\frac{cos\theta+sin\theta}{cos\theta-sin\theta}+\frac{c
Ch 05: Partial Fraction
10 Hits, Last modified:
artial Fraction ====== <list-group> * Resolve $\frac{1}{(x^2+1)(x+1)}$ into partial fraction --- //BI... * 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 --- //... argodha(2015),BISE Sargodha(2017)// * Resolve $\frac{9}{(x+2)^2(x-1)}$ into partial fraction --- //BI
Ch 01: Number Systems
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_2$ --- // BISE Sargodha(2015)// * Simplify $\frac{2}{\sqrt{5}+\sqrt{-8}}$ in the form of $a+ib$ ... godha(2015)// * Simplify by justify each step $\frac{\frac{1}{a}-\frac{1}{b}}{1-\frac{1}{a}\frac{1}{b}}$ --- // BISE Sargodha(2015)// * Find multiplicative
Ch 04: Quadratic Equations
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$ 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// * Solve the f... * Show that the roots of the equation $x^2-2(m+\frac{1}{m})x+3=0$, $m \neq 0$ will be real --- //BIS
Ch 07: Permutation, Combination and Probability
6 Hits, Last modified:
{r-1}=^nC_r$ ---// BISE Sargodha(2015)// * If $\frac{a_5}{a_3}=\frac{4}{9}$, $a_2=\frac{4}{9}$ in $G.P$. Find $a_n$ ---// BISE Sargodha(2015)// * Find $n$, when $^{11}P_n... ---// BISE Sargodha(2015)// * Find the sum of $\frac{9}{4}+\frac{3}{2}+1+\frac{2}{3}+...\infty$ ---//
Ch 14: Solutions of Trigonometric Equation
4 Hits, Last modified:
tion ====== <list-group> * Solve $cose^2\theta=\frac{4}{3}$ in $[0,2\pi]$--- //BISE Gujrawala(2015), B... ha(2016), BISE Gujrawala(2017)// * Solve $sinx=\frac{1}{2}$ in $[0,2\pi]$--- //BISE Gujrawala(2015)// * Solve $cot\theta = \frac{1}{\sqrt{3}}$, $\theta \in [0,2\pi]$--- //BISE G... 7), BISE Sargodha(2016)// * Solve $sec^2\theta=\frac{4}{3}$ in $[0,2\pi]$--- //BISE Sargodha(2015)//
Ch 03: Matrices and Determinants
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show that $ \left[ {\begin{array}{c} ba&ca&ab\\ \frac{1}{a}&\frac{1}{b}&\frac{1}{c}\\a&b&c \end{array}} \right]=0$ --- // BISE Lahore(2017)// * Verify that $(AB)^t=B^
Ch 11: Trigonometric Functions and Their Graphs
2 Hits, Last modified:
SE Gujrawala(2017)// * Find the period of $\sin\frac{x}{5}$ --- //BISE Sargodha(2015), BISE Sargodha(2... ISE Sargodha(2015)// * Find the period of $\cot\frac{x}{2}$ --- //BISE Sargodha(2017), BISE Lahore(201