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Ch 07: Permutation, Combination and Probability
17 Hits, Last modified:
Find the value of $n$ when $^nP_2=30$ ---// BISE Sargodha(2015)// * Find numbers of diagonals of $6-dided$ figure. ---// BISE Sargodha(2015)// * Find the value of $n$. $^nC_{12}=^nC_6$ ---// BISE Sargodha(2015)// * Determine the probability of getting ... ds in two successive tosses of a coin? ---// BISE Sargodha(2015)// * Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^
Ch 08: Mathematical Induction and Binomial Theorem
14 Hits, Last modified:
...=\sqrt{2}$ --- // BISE Gujranwala(2015), BISE Sargodha(2016)// * Evaluate $(1.03)^{\frac{1}{3}}$ by bi... ing expansion $(x-\frac{2}{x})^{10}$ --- // BISE Sargodha(2015), BISE Gujranwala(2017)// * Show that $n^3... result $4^n>3^n+2^{n-1}$ for $n=2,3$ --- // BISE Sargodha(2015)// * Find $13$th term of $x,1,2-x,3-2x,...$ --- // BISE Sargodha(2015)// * Expand $(1-2x)^{\frac{1}{3}}$ upto th
Ch 06: Sequences and Series
12 Hits, Last modified:
t{\frac{a}{c}}$ --- //BISE Gujranwala(2015),BISE Sargodha(2015), BISE Sargodha(2017),BISE Lahore(2017)// * With usual notation show that $AH=G^2$ ---// BISE Gujra... common difference is $\frac{a-c}{2ac}$ --- //BISE Sargodha(2015)// * If $15$ and $8$ are two A.Ms between $a$ and $b$, find $a$ and $b$. --- //BISE Sargodha(2015)// * If $S_2,S_3,S_5$ are the sum of $2n,
Ch 02: Functions and Groups
11 Hits, Last modified:
then verify associativity of union --- // BISE Sargodha(2015)// * If $A,B$ are elements of a group $G$ ... ow that $(ab)^{-1}=b^{-1}a^{-1}$ --- // BISE Sargodha(2015)// * For $A=\{1,2,3\}$ find the relation $\{(x,y)| x+y<5\}$ --- // BISE Sargodha(2015)// * Write the set $\{x|x \in Q \wedge x^2... $ in descriptive and tabular form --- // BISE Sargodha(2015)// * If $a,b$ being elements of a group $G
Ch 03: Matrices and Determinants
10 Hits, Last modified:
ight]$ find the value of $a$ and $b$. --- // BISE Sargodha(2017), Gujrawala(2017)// * Find the value of $\... &1 \end{array}} \right]$ is singular --- // BISE Sargodha(2015)// * Find the value of $x$, $ \left[ {\beg... 3&4\\ x&1&0 \end{array}} \right]=0 $ --- // BISE Sargodha(2015)// * Evaluate $ \left[ {\begin{array}{c} a... l\\ a-l&a&a+l \end{array}} \right]$ --- // BISE Sargodha(2015)// * If $ A=\left[ {\begin{array}{c} l\\1+
Ch 10: Trigonometric Identities
10 Hits, Last modified:
r calculator find $tan(1110^{\circ})$ --- // BISE Sargodha(2015), BISE Gujrawala(2017)// * Prove that $sin... {\circ}-\alpha)=-sin\alpha cos\alpha$ --- // BISE Sargodha(2015), BISE Lahore(2017)// * Prove that (withou... i}{3}sin\frac{4\pi}{9}=\frac{3}{16}$ --- // BISE Sargodha(2015)// * Prove that $cot\alpha-tan\alpha=2cot2\alpha$ --- // BISE Sargodha(2015)// * Find the value of $cos15^{circ}$ usin
Ch 12: Applications of Trigonometry
10 Hits, Last modified:
* Show that $r_2=s tan\frac{\beta}{2}$--- //BISE Sargodha(2015)// * Show that $r=(s-a)tan\frac{\alpha}{2}$--- //BISE Sargodha(2015)// * The sides of a triangle are $x^2+x+1$... angle of the triangle is $120^{\circ}$ --- //BISE Sargodha(2015), FBISE(2017)// * Solve the triangle $ABC$... rc}$, $\gamma=15^{\circ}$, $b=\sqrt{6}$--- //BISE Sargodha(2015)// * Find the area of the triangle $ABC$,
Ch 09: Fundamental of Trigonometry
9 Hits, Last modified:
ac{3}{\sqrt{2}}$ --- //BISE Gujrawala(2017), BISE Sargodha(2017)// * Prove that $cosce \theta+tan\theta se... * Convert $150^{\circ}$ into radian. --- //BISE Sargodha(2015)// * Find $\theta$ when $l=1.5cm$, $r=2.5cm$ --- //BISE Sargodha(2015)// * Prove that $\frac{cos\theta+sin\theta... theta-sin\theta}{cos\theta+sin\theta}$ --- //BISE Sargodha(2015)// * Find $l$ when $\theta=65^{\circ}20'$,
Ch 01: Number Systems
7 Hits, Last modified:
z_2}=\overline z_1 +\overline z_2$ --- // BISE Sargodha(2015)// * Simplify $\frac{2}{\sqrt{5}+\sqrt{-8}}$ in the form of $a+ib$ --- // BISE Sargodha(2015)// * Simplify by justify each step $\frac{... 1}{b}}{1-\frac{1}{a}\frac{1}{b}}$ --- // BISE Sargodha(2015)// * Find multiplicative inverse $(\sqrt{2}, -\sqrt{5})$ --- //BISE Sargodha(2015)// * Does the set $\{0,-1\}$ possess the c
Ch 04: Quadratic Equations
6 Hits, Last modified:
$x(x+7)=(2x-1)(x+4)$ by factorization --- //BISE Sargodha(2015)// * If $\alpha$, $\beta$ are the roots o... c{\alpha}{\beta}+\frac{\beta}{\alpha}$ --- //BISE Sargodha(2015)// * For what value of $m$ will the roots... the equation $(m+1)x^2+2(m+3)x+m+8=0$ --- //BISE Sargodha(2015)// * Evaluate $(1+w-w^2)(1-w+w^2)$ --- //BISE Sargodha(2016)// * Discuse nature of roots of equation
Ch 05: Partial Fraction
6 Hits, Last modified:
1}{(x+1)(x-1)}$ into partial fraction --- //BISE Sargodha(2015),BISE Sargodha(2017)// * Resolve $\frac{9}{(x+2)^2(x-1)}$ into partial fraction --- //BISE Sargodha(2015)// * Solve the partial fraction $\frac{1}{(x-1)^2+(x+1)}$ --- //BISE Sargodha(2015)// * Resolve the following into partial fr
Ch 13: Inverse Trigonometry Functions
6 Hits, Last modified:
}{\sqrt{5}})+cot^{-1}(3)=\frac{\pi}{4}$--- //BISE Sargodha(2015), BISE Sargodha(2016), BISE Gujrawala(2017) // * Prove that $cos^{-1}(-x)=\pi-cos^{-1}x$--- //BISE G... (\frac{12}{13})=sin^{-1}(\frac{5}{13})$--- //BISE Sargodha(2015)// * Show that $cos(sin^{-1}x)=\sqrt{1-x^2}$--- //BISE Sargodha(2016)// * Find the value of $tan(cos^{-1}\frac{
Ch 14: Solutions of Trigonometric Equation
6 Hits, Last modified:
3}$ in $[0,2\pi]$--- //BISE Gujrawala(2015), BISE Sargodha(2016), BISE Gujrawala(2017)// * Solve $sinx=\fr... eta \in [0,2\pi]$--- //BISE Gujrawala(2017), BISE Sargodha(2016)// * Solve $sec^2\theta=\frac{4}{3}$ in $[0,2\pi]$--- //BISE Sargodha(2015)// * Solve $4cos^2x-3=0$, $x \in [0,2\pi]$--- //BISE Sargodha(2015)// * Solve the equation $secx=-2$ where $x
Ch 11: Trigonometric Functions and Their Graphs
4 Hits, Last modified:
* Find the period of $\sin\frac{x}{5}$ --- //BISE Sargodha(2015), BISE Sargodha(2016)// * Find the period of $cosec10x$ --- //BISE Sargodha(2015)// * Find the period of $\cot\frac{x}{2}$ --- //BISE Sargodha(2017), BISE Lahore(2017)// * Show that $\sin x$