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- Question 9 Exercise 6.3 @math-11-kpk:sol:unit06
- Question 9(i)===== An $8$-persons committee is to be formed from a group of $6$ women and $7$ men. In how many ways can the committee be chosen if (i) committee must contain four men and... Total number of different ways that four men to be selected are: ${ }^7 C_4$. Total number of different ways that four women to be selected are ${ }^6 C_4$. By fundamental princip
- Question 7 and 8 Exercise 6.2 @math-11-kpk:sol:unit06
- stion 7(i)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if repetit... hundred digit, ten digit and unit digit place) to be filled by five digits, Moreover repetition is a... tion 7(ii)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if repetit... estion 8===== How many different arrangements can be formed of the word "equation" if all the vowels a
- Question 9 Exercise 6.5 @math-11-kpk:sol:unit06
- respectively. Find the probability that both will be selected. ====Solution==== \begin{align} P(\text ... ected In this case there are two chance. it may be Ajmal selected Bushra not selected that is $P(A \cap \bar{B})$. The second option is it may be Bushra selected but Ajmal not that is $P(\bar{A} ... respectively. Find the probability that none will be sclected. ====Solution==== \begin{align} P(\text
- Question 1 Review Exercise 6 @math-11-kpk:sol:unit06
- ollapse> ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}$ if rep... </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$ withou... e> v. In how many different ways can $5$ couples be seated around a circular table if the couple must not be separated? * (a) $768$ * %%(b)%% $724
- Question 1 Review Exercise 7 @math-11-kpk:sol:unit07
- ollapse> ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}$ if rep... </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$ withou... e> v. In how many different ways can $5$ couples be seated around a circular table if the couple must not be separated? * (a) $768$ * %%(b)%% $724
- Question 10 Exercise 6.2 @math-11-kpk:sol:unit06
- ion 10(i)===== In how many ways can five students be seated in a row of eight seals if a certain two s... The total number of ways these five students can be seated are: \begin{align}^8 P_5&=\dfrac{8 !}{(8-5... t next to each other then these two students will be handled as a single students and the eights seats will be considered as 7. In this case the total number o
- Question 1 Exercise 6.4 @math-11-kpk:sol:unit06
- =====Question 1(a)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... =====Question 1(b)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... =====Question 1(c)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... =====Question 1(d)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p
- Question 9 & 10 Review Exercise 6 @math-11-kpk:sol:unit06
- ===== How many numbers greater than a million can be formed with the digits $2,3,0,3,4,2,3$? ====Solut... otal numbers that do not start with zero. It can be formed using the given $7$ digits taking out $0$ ... . =====Question 10===== A party of $n$ men is to be seated around a circular table. Find the probabil... === The total number of ways that $n$ persons can be seated around a circular table are: $(n-1)$ ! If
- Multiple Choice Questions (MCQs)
- Here are the sample MCQs at this time. Page will be updated periodically. =====SAMPLE MCQs===== <gr... ty set * (C) Power set * (D) subset * Cube root of unity are * (A) $1, \omega, \omega^2$... D) $1, -1, 2$ * The equation $ax^2+bx+c=0$ will be quadratic if * (A) $a=0, b\neq 0$ * (B) $... ) permutation * The equation $ax^2+bx+c=0$ will be quadratic if * (A) $a=0, b\neq 0$ * (B) $
- Question 2 and 3 Exercise 3.3 @math-11-kpk:sol:unit03
- |&=\sqrt{169}=13\end{align} Now let say $\hat{c}$ be the unit vector $x$ the sum of $\vec{a}$ and $\ve... \vec{b}=-\hat{i}+\hat{j}+2 \hat{k}$. Let $\theta$ be the angle hetween $\vec{a}$ and $\vec{b}$ \begin{... $ and $\vec{b}=2 \hat{j}-5 \hat{k}$. Let $\theta$ be the angle between $\vec{a}$ and $\vec{b}$ \begin{... $\vec{b}=\hat{i}+\hat{j}+\hat{k}$. Let $\theta$ be the angle between $\vec{a}$ and $\vec{b}$ then $$
- Question 12 & 13 Exercise 4.2 @math-11-kpk:sol:unit04
- ====Solution==== Here $a=12, b=18$.\\ Let say $A$ be arithmetic means. Then \\ \begin{align}A&=\dfrac{... Here $a=\dfrac{1}{3}, b=\dfrac{1}{4}$,\\ Let $A$ be arithmetic mean. Then\\ \begin{align}A&=\dfrac{a+... ====Solution==== Here $a=-6, b=-216$.\\ Let $A$ be arithmetic mean. Then\\ $$A=\dfrac{a+b}{2}=\dfrac... \prime}=(a+b)^2$, $b^{\prime}=(a-b)^2$.\\ Let $A$ be arithmetic mean. Then\\ \begin{align} A&=\dfrac{a
- Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
- h term; 20 terms. GOOD ====Solution==== Let $a_1$ be first term and $d$ be common difference of given A.P. Then \begin{align}&a_1=9 \\ &d=7-9=-2 \\ &n=20... h term; 11 terms. GOOD ====Solution==== Let $a_1$ be first term and $d$ be common difference of given A.P. Then \begin{align}&a_1=3 \\ &d=\dfrac{8}{3}-3=
- Question 15 & 16 Exercise 4.5 @math-11-kpk:sol:unit04
- amount each day. If this continụed, how much must be set aside on the $15^{\text {th }}$ day? What is ... daily rate of increase if the rate is assumed to be constant. ====Solution==== The number of bacteria... _1=64000$ Let number of bacteria after first day be $a_2$, after second be $a_3$ and so on. The number of bacteria after $6$th day $a_7=729000$. Since t
- Question 5 and 6 Exercise 6.2 @math-11-kpk:sol:unit06
- In how many ways can letter of the word 'Fasting' be arranged? ====Solution==== The total number of al... ==Question 6===== How many four digits number can be formed from the digits $2,4,5,7,9$ ? (Repetition ... gits are: $$=5.4 .3 .2=120\quad \text{or}$$ can be found using permutation as: $$^5 P_4=\dfrac{5 !}{... f these for even number, the unit digit have to be filled by $2$ or $4$. So, we are left with $3$ nu
- Question 12 Exercise 6.2 @math-11-kpk:sol:unit06
- ==Question 12(i)===== How many different word can be formed from the letters "BOOKWORM" if the letters... =Question 12(ii)===== How many different word can be formed from the letters "BOOKKEEPER" if the lette... Question 12(iii)===== How many different word can be formed from the letters "ABBOTTABAD" if the lette... =Question 12(iv)===== How many different word can be formed from the letters "LETTER" if the letters a