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- Ch 03: Matrices and Determinants
- == <list-group> * 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]$ -... ala(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]= \l
- Ch 07: Permutation, Combination and Probability
- 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 $430,000$? ---// BISE Gujrawala(2015)// * How many words can be formed from the letter $``PLANE"$ using all lette
- Ch 04: Quadratic Equations
- * 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... tem of equations --- //BISE Gujrawala(2017)// $${\begin{array}{c} x^2-5xy+6y^2=0\\x^2+y^2=45\end{array
- Ch 06: Sequences and Series
- $n$, so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ maybe $A.M$ between $a$ and $b$. --- //BISE Gujrawala(2015)// * If $y=1+\frac{x}{2}+\frac{x^4}{4}+...$ ... argodha(2015)// * If $15$ and $8$ are two A.Ms between $a$ and $b$, find $a$ and $b$. --- //BISE Sa... -- //BISE Sargodha(2015)// * Find three $A.Ms$ between $3$ and $11$ --- //BISE Sargodha(2016)//
- Ch 12: Applications of Trigonometry
- $ --- //BISE Gujrawala(2015)// * Define an escribed circle.--- //BISE Gujrawala(2015)// * With usu... {\circ}$, $\alpha=62^{\circ}40'$, $b=796$, find $\beta$ anf $a$--- //BISE Gujrawala(2017)// * Find t... Gujrawala(2017)// * Show that $r_2=s tan\frac{\beta}{2}$--- //BISE Sargodha(2015)// * Show that $... FBISE(2017)// * Solve the triangle $ABC$, if $\beta=60^{\circ}$, $\gamma=15^{\circ}$, $b=\sqrt{6}$-
- Ch 10: Trigonometric Identities
- r.--- // BISE Sargodha(2015)// * If $\alpha$, $\beta$, $\gamma$ are the angles of $\triangle ABC$, show that $cot\frac{\alpha}{2}+cot\frac{\beta}{2}+cot\frac{\gamma}{2}=cot\frac{\alpha}{2}cot\frac{\beta}{2}cot\frac{\gamma}{2}$ --- // BISE Sargodha(2015)// * If $\alpha$, $\beta$, $\gamma$ are the angles of triangle $ABC$, pr
- Ch 01: Number Systems
- ====== Ch 01: Number Systems ====== <list-group> * Simplify $(i)^{19}$ --- //BISE Gujrawala(2015)// * If $z$ be a complex number then prove that $\overline{z_1 + z_2}=\overline z_1 +\overline z_2$ --- // BISE Sa
- Ch 02: Functions and Groups
- Punjab Textbook Board (PTB) Lahore, Pakistan has been given on this page. These questions are selecte... BISE Gujrawala(2015)// * What is the difference between $\{a,b \}$ and $\{\{a,b\}\}$ --- // BISE G... orm --- // BISE Sargodha(2015)// * If $a,b$ being elements of a group $G$ then solve (a) $ax=b$
- Ch 08: Mathematical Induction and Binomial Theorem
- s so small that bits square and higher powers can be neglected then show that $\frac{1-x}{\sqrt{1+x}}