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Ch 07: Permutation, Combination and Probability
19 Hits, Last modified:
BISE Gujrawala(2017)// * Find the numbers of diagonals of a $6-digits$ figures ---// BISE Gujrawala... nd 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 $n$. $^nC_{12}=^nC_6$ ---/
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... expansion $(x-\frac{2}{x})^{10}$ --- // BISE Sargodha(2015), BISE Gujranwala(2017)// * Show that $... ult $4^n>3^n+2^{n-1}$ 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
Ch 09: Fundamental of Trigonometry
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====== Ch 09: Fundamental of Trigonometry ====== <list-group> * Find the value of the remaining trigonometric functions of $\theta$, If $cos \theta=\fr... 3}{\sqrt{2}}$ --- //BISE Gujrawala(2017), BISE Sargodha(2017)// * Prove that $cosce \theta+tan\theta... Convert $150^{\circ}$ into radian. --- //BISE Sargodha(2015)// * Find $\theta$ when $l=1.5cm$, $r=2
Ch 02: Functions and Groups
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stions of Chapter 2 of Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook B... n verify associativity of union --- // BISE Sargodha(2015)// * If $A,B$ are elements of a group $... 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 $\{x|x \in Q \wedge
Ch 06: Sequences and Series
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frac{a}{c}}$ --- //BISE Gujranwala(2015),BISE Sargodha(2015), BISE Sargodha(2017),BISE Lahore(2017)// * With usual notation show that $AH=G^2$ ---// B... mon 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 $
Ch 10: Trigonometric Identities
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====== Ch 10: Trigonometric Identities ====== <list-group> * Prove that (without calculator) $\sin 1... alculator find $tan(1110^{\circ})$ --- // BISE Sargodha(2015), BISE Gujrawala(2017)// * Prove that $... irc}-\alpha)=-sin\alpha cos\alpha$ --- // BISE Sargodha(2015), BISE Lahore(2017)// * Prove that (wit... 3}sin\frac{4\pi}{9}=\frac{3}{16}$ --- // BISE Sargodha(2015)// * Prove that $cot\alpha-tan\alpha=2c
Ch 12: Applications of Trigonometry
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====== Ch 12: Applications of Trigonometry ====== <list-group> * Find the value of $tan\frac{\alpha}... 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... le of the triangle is $120^{\circ}$ --- //BISE Sargodha(2015), FBISE(2017)// * Solve the triangle $A
Ch 03: Matrices and Determinants
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t]$ find the value of $a$ and $b$. --- // BISE Sargodha(2017), Gujrawala(2017)// * Find the value of... \end{array}} \right]$ is singular --- // BISE Sargodha(2015)// * Find the value of $x$, $ \left[ {\... \\ x&1&0 \end{array}} \right]=0 $ --- // BISE Sargodha(2015)// * Evaluate $ \left[ {\begin{array}{c... a-l&a&a+l \end{array}} \right]$ --- // BISE Sargodha(2015)// * If $ A=\left[ {\begin{array}{c} l\
Ch 01: Number Systems
7 Hits, Last modified:
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 $\fr... b}}{1-\frac{1}{a}\frac{1}{b}}$ --- // BISE Sargodha(2015)// * Find multiplicative inverse $(\sqrt{2}, -\sqrt{5})$ --- //BISE Sargodha(2015)// * Does the set $\{0,-1\}$ possess th
Ch 04: Quadratic Equations
7 Hits, Last modified:
rac{p}{q}}=0$$ --- //BISE Gujrawala(2017),BISE Sagodha(2017// * Solve the following system of equa... x+7)=(2x-1)(x+4)$ by factorization --- //BISE Sargodha(2015)// * If $\alpha$, $\beta$ are the root... alpha}{\beta}+\frac{\beta}{\alpha}$ --- //BISE Sargodha(2015)// * For what value of $m$ will the ro... e equation $(m+1)x^2+2(m+3)x+m+8=0$ --- //BISE Sargodha(2015)// * Evaluate $(1+w-w^2)(1-w+w^2)$ --
Ch 13: Inverse Trigonometry Functions
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====== Ch 13: Inverse Trigonometry Functions ====== <list-group> * Find the value of $cos^{-1}(\frac... sqrt{5}})+cot^{-1}(3)=\frac{\pi}{4}$--- //BISE Sargodha(2015), BISE Sargodha(2016), BISE Gujrawala(2017) // * Prove that $cos^{-1}(-x)=\pi-cos^{-1}x$---... rac{12}{13})=sin^{-1}(\frac{5}{13})$--- //BISE Sargodha(2015)// * Show that $cos(sin^{-1}x)=\sqrt{1-
Ch 14: Solutions of Trigonometric Equation
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====== Ch 14: Solutions of Trigonometric Equation ====== <list-group> * Solve $cose^2\theta=\frac{4}... in $[0,2\pi]$--- //BISE Gujrawala(2015), BISE Sargodha(2016), BISE Gujrawala(2017)// * Solve $sinx=... \in [0,2\pi]$--- //BISE Gujrawala(2017), BISE Sargodha(2016)// * Solve $sec^2\theta=\frac{4}{3}$ in $[0,2\pi]$--- //BISE Sargodha(2015)// * Solve $4cos^2x-3=0$, $x \in [0,2\p
Ch 05: Partial Fraction
6 Hits, Last modified:
(x+1)(x-1)}$ 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
Ch 11: Trigonometric Functions and Their Graphs
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====== Ch 11: Trigonometric Functions and Their Graphs ====== <list-group> * Find the period of $\s... ind 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