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- Unit 04: Introduction to Analytic Geometry @fsc-part2-ptb:important-questions
- the list of important questions. <list-group> * Find the area between $x-axis$ and the curve $y=4x-x^2$ --- // BSIC Gujranwala (2016)// * Find $h$ if $A(-1,h)$, $B(3,2)$, $C(7,3)$ are collinear --- // BSIC Gujranwala (2016)// * Find the point three fifth of the way along the line s... to $B(5,3)$ --- // BSIC Gujranwala (2016)// * Find equation of straight line if its slop is $2$ and
- Unit 02: Differentiation @fsc-part2-ptb:important-questions
- SIC Gujranwala (2016)// * If $x=at^2$, $y=2at$. Find $\frac{dy}{dx}$ --- // BSIC Gujranwala (2016)// ... ujranwala (2016)// * If $y=x^2ln(\frac{1}{x})$. Find $\frac{dy}{dx}$. --- // BSIC Gujranwala (2016)// * If $x=sin\theta$, $y=sin m\theta$. Find $\frac{dy}{dx}$. --- // BSIC Gujranwala (2016)//... / BSIC Gujranwala (2016)// * Using differential find $\frac{dy}{dx}$, When $x^2+2y^2=16$ --- // BSIC G
- Unit 06: Conic section @fsc-part2-ptb:important-questions
- the list of important questions. <list-group> * Find the centre and radius of the circle given by the ... x+12y-25=0$ --- // BSIC Gujranwala (2016)// * Find equation of tangent to the circle $x^2+y^2=2$ par... e $x-2y+1=0$ --- // BSIC Gujranwala (2016)// * Find focus and directrix of parabola $x^2=-16y$ --- // BSIC Gujranwala (2016)// * Find equation of ellipse with vertices $(0,\pm5)$, ecc
- Unit 07: Vectors @fsc-part2-ptb:important-questions
- he list of important questions. <list-group> * Find position vector of a point which divide the join ... ratio $4:3$. --- // BSIC Gujranwala (2016)// * Find $a$ and $b$ so that the vectors $3\underline i-\u... re parallel. --- // BSIC Gujranwala (2016)// * Find $\cos$ of angle between $u.v$ if $u=3\underline i... nderline k$. --- // BSIC Gujranwala (2016)// * Find the unit vector perpendicular to the plane of vec
- Ch 07: Permutation, Combination and Probability @fsc-part1-ptb:important-questions
- mbination and Probability ====== <list-group> * Find $n$ when ${^nC_{12}}={^nC_6}$ ---// BISE Gujranwa... ^nC_4=^nC_{n-r}$ ---// BISE Gujrawala(2017)// * Find the numbers of diagonals of a $6-digits$ figures ... ujrawala(2017)// * A coin is tossed four times, find the probability that top shows all heads. ---// B... $6$ for $n=2,3$ ---// BISE Gujrawala(2017)// * Find the value of $n$ when $^nP_2=30$ ---// BISE Sargo
- Unit 03: Vectors (Solutions) @math-11-kpk:sol
- definitions using analytical representation. * Find a unit vector in the direction of another given vector. * Find the position vector of a point which divides the ... * Give analytic representation of a vector. * Find magnitude of a vector. * Repeat all fundamental... * Express dot product in terms of components. * Find the condition for orthogonality of two vectors.
- Question 7 Exercise 6.4 @math-11-kpk:sol:unit06
- ion 7(i)===== Two dice are thrown simultaneously. Find the probability of getting doublet of even number... on 7(ii)===== Two dice are thrown simultaneously. Find the probability of getting a sum less than $6$. ... n 7(iii)===== Two dice are thrown simultaneously. Find the probability of getting a sum more than $7.$ =... on 7(iv)===== Two dice are thrown simultaneously. Find the probability of getting a sum greater than $10
- FSc Part 1 (KPK Boards) @fsc
- ric series. * recognize a harmonic sequence and find its nth term. * define harmonic mean and insert... ces and its uses. * use the partial fraction to find the sum to $n$ terms and to infinity of the serie... . * expand $(x+y)^n$ using binomial theorem and find its general form. * understand pascal's triangl... l number. * know binomial series and its use to find the sum of the given series. ===Download=== <cal
- MTH604: Fixed Point Theory and Applications (Fall 2022) @atiq
- xed points. - Consider a function $f(x)=x^2-1$. Find its fixed points and also find the nature of fixed point. - Define orbit of the point $x_0$ under fun... er a function $L(x)=mx$, where $m\in \mathbb{R}$. Find the value of $m$ for which $x=0$ is attracting fixed point. - Let $F(x)=2(\sin x)^2$. Find the interval in which $F$ has attracting fixed po
- MTH604: Fixed Point Theory and Applications (Spring 2020) @atiq
- nt theorem. - Consider a function $f(x)=x^2-1$. Find its fixed points and also find the nature of fixed point. - Define orbit of the point $x_0$ under fun... er a function $L(x)=mx$, where $m\in \mathbb{R}$. Find the value of $m$ for which $x=0$ is attracting fixed point. - Let $F(x)=2(\sin x)^2$. Find the interval in which $F$ has attracting fixed po
- Exercise 6.1 @matric:9th_science
- ch with this page. </WRAP> ====Question 1:==== Find the H.C.F of the following expressions.\\ (i) $39... s 17 xyz^2$\\ H.C.F= $17 xyz$ ====Question 2==== Find the H.C.F of the following expressions by factori... nd{align}$ H.C.F= $18(3x-1)$ ====Question 4==== Find the L.C.M. of the following expressions by factor... &=5610 x^2y^2z^2\end{align}$ ====Question 5==== Find the L.C.M. of the following expressions by factor
- Question 2 Exercise 4.3 @math-11-kpk:sol:unit04
- components $a_1, a_n, n, d$ and $S_n$ are given. Find the one that is missing: $a_1=2, n=17, d=3$. GOOD... ution==== Given: $a_1=2, n=17, d=3$ \\ We need to find $a_{17}$ and $S_{17}$. As we know $$a_{n}=a_1+(n-... components $a_1, a_n, n, d$ and $S_n$ are given. Find the one that are missing $a_1=-40, S_{21}=210$. G... $S_{21}=210$.\\ So we have $n=21$ and we have to find $a_{21}$ and $d$. As \begin{align}&S_{21}=\dfrac{
- Ch 03: Matrices and Determinants @fsc-part1-ptb:important-questions
- y}} \right]= 0$ --- // BISE Gujrawala(2015)// * Find inverse of $ \left[ {\begin{array}{c} 2&1&0\\ 1&1... {\begin{array}{c} 0&0\\ 0&0 \end{array}} \right]$ find the value of $a$ and $b$. --- // BISE Sargodha(2017), Gujrawala(2017)// * Find the value of $\lambda$ if $ A=\left[ {\begin{arr... t]$ is singular --- // BISE Sargodha(2015)// * Find the value of $x$, $ \left[ {\begin{array}{c} 3&1&
- Ch 08: Mathematical Induction and Binomial Theorem @fsc-part1-ptb:important-questions
- }{x^2}\right)$ --- // BISE Gujranwala(2015)// * Find the $6$th term in the expansion of $\left( x^2-\f... of decimials. --- // BISE Gujranwala(2017)// * Find the middle term of $(a+x)$? When $n$ is even. --- // BISE Gujranwala(2017)// * Find the term independent of $x$ in the following expa... 1}$ for $n=2,3$ --- // BISE Sargodha(2015)// * Find $13$th term of $x,1,2-x,3-2x,...$ --- // BISE Sar
- Question 1, Exercise 3.2 @math-11-kpk:sol:unit03
- -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $\vec{a}+2\vec{b}$. ====Solution==== \begin{ali... -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $3\vec{a}-2\vec{b}$. ====Solution==== \begin{al... -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $2(\vec{a}-\vec{b})$. ====Solution==== First we... -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $|\vec{a}+\vec{b}|$. ====Solution==== We have,