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- Question 13 Exercise 6.2 @math-11-kpk:sol:unit06
- of permutation of word "Excellence." How many of these permutations begin with $\mathrm{E}$ ? ====Soluti... of permutation of word "Excellence." How many of these permutations begin with $\mathrm{E}$ and end with... of permutation of word "Excellence." How many of these permutations begin with $\mathrm{E}$ and end with... of permutation of word "Excellence." How many of these permutations do not begin with $\mathrm{E}$ ? ===
- Question 5 and 6 Exercise 6.2 @math-11-kpk:sol:unit06
- er of possible arrangements to fill $7$ places by these $7$ letters are: \begin{align}^7 P_7&=\dfrac{7 !}... ,9$ ? (Repetition not being allowed). How many of these are even? ====Solution==== We have to fill four places with these five digits $2,4,5,7,9$, so that repetition is ... m{n} . \mathrm{m}$ ber that can $e$ formed though these 5 digits are: $$=5.4 .3 .2=120\quad \text{or}$$
- Question 10 Exercise 6.2 @math-11-kpk:sol:unit06
- nts are five so, $r=5$. The total number of ways these five students can be seated are: \begin{align}^8 ... wo students insist to sit next to each other then these two students will be handled as a single students... nts are five so, $r=5$. The total number of ways these five students can be seated are: \begin{align}^8 ... to each other, then the total number ways sitting these students in a row are: \begin{align}^7 P_4&= \dfr
- Question 9 & 10 Review Exercise 6 @math-11-kpk:sol:unit06
- are computing the total number of ways arranging these digits using repeated permutation as: $$=\dfrac{7... 1)$ ! If two persons sit together, we shall deal these two as one man, then in this case total will be $(n - 1)$. and the total number of ways these $(n-1)$ can sit around table are: $(n-2) !$ the ... e of counting the total number of ways of sitting these $n$ people in which two men want to sit together
- Solutions: Math 11 KPK
- is plan (SLOs based). But there is no doubt that these solutions are valid for all the boards of Khyber Pakhtunkhwa. These boards include Board of Intermediate and Secondar
- Question 2 and 3 Exercise 3.3 @math-11-kpk:sol:unit03
- ow|\vec{b}|&=\sqrt{29}\end{align} Now putting all these in (1) \begin{align}\cos \theta&=\dfrac{8}{5 \cdo... row|\vec{b}|&=\sqrt{3}\end{align} Now putting all these in (1) \begin{align}\cos \theta&=\dfrac{-1}{\sqrt
- Question 1 Review Exercise 3 @math-11-kpk:sol:unit03
- %%(c)%% $|\vec{a}|=|\vec{b}|$ * (d) None of these \\ <btn type="link" collapse="a4">See Answer</btn... * %%(c)%% $\dfrac{3}{14}$ * (d) None of these \\ <btn type="link" collapse="a5">See Answer</btn
- Question 1 Review Exercise 5 @math-11-kpk:sol:unit05
- %% $n^2+n$ * %%(c)%% $n^2$ * (d) None of these \\ <btn type="link" collapse="a4">See Answer</btn... 1}$ * %%(c)%% $n+2(2^n-1)$ * (d) None of these \\ <btn type="link" collapse="a5">See Answer</btn
- Question 5 Exercise 6.4 @math-11-kpk:sol:unit06
- +4=10$. Total number of ways to select $5$ out of these $10$ are: \begin{align}{ }^{10)} C_5 &=\dfrac{10 ... +4=10$. Total number of ways to select $5$ out of these $10$ are: \begin{align}{ }^{10} C_5 &=\dfrac{10 !
- Question 9 Exercise 6.5 @math-11-kpk:sol:unit06
- oes not depend on the other sclection, therefore these two events are independent. Thus \begin{align}P(\... but Ajmal not that is $P(\bar{A} \cup B)$. Also these both are independent events. Thus the probabilit
- Question 7 & 8 Review Exercise 6 @math-11-kpk:sol:unit06
- It means have to fill the first two places with these two digits, then the remaining digits are: $$10-2... $$ We have to fill the remaining four places with these $8$ digits, so the event $E_1$ occurs with $m_1=
- Multiple Choice Questions (MCQs)
- e is * (A) negative * (B) positive * (C) non-negative * (D) none of these </col> </grid>
- Question 1, Review Exercise 1 @math-11-kpk:sol:unit01
- axis$ * %%(c)%% line $y=5$ * (d) None of these \\ <btn type="link" collapse="a5">See Answer</btn
- Question 4 Review Exercise @math-11-kpk:sol:unit05
- \quad 15 A+6 B-3 C=0$$ $$4 A+8 B-2 C=1$$ Solving these three equations for the constants $A, B$ and $C$
- Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
- i) Numbers greater than $10$ but less than $100$ These numbers will consist just two digits ten digit an