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- Question 12 & 13 Exercise 4.2 @math-11-kpk:sol:unit04
- his salary during his twenty first year of work? GOOD ====Solution==== Suppose $a_1$ represents salar... n during his 21st year of work is dollars 18,500. GOOD =====Question 13(i)===== Find the arithmetic mean between $12$ and $18$. GOOD ====Solution==== Here $a=12, b=18$.\\ Let say $... 15.\end{align} Hence 15 is A.M between 12 and 18. GOOD =====Question 13(ii)===== Find the arithmetic
- Question 1, Exercise 1.1 @math-11-kpk:sol:unit01
- estion 1(i)===== Simplify ${{i}^{9}}+{{i}^{19}}$. GOOD ====Solution==== \begin{align}{{i}^{9}}+{{i}^{1... i\cdot\left( -1 \right)\\ &=i-i\\ &=0.\end{align} GOOD =====Question 1(ii)===== Simplify ${{\left( -i \right)}^{23}}$. GOOD ====Solution==== \begin{align}{{\left( -i \righ... 1}}\\ &=-i\cdot\left( -1 \right)\\ &=i\end{align} GOOD =====Question 1(iii)===== Simplify ${{\left( -1
- Question 2 Exercise 4.3 @math-11-kpk:sol:unit04
- Find the one that is missing: $a_1=2, n=17, d=3$. GOOD ====Solution==== Given: $a_1=2, n=17, d=3$ \\ W... 2.\end{align} Hence $a_{17}=50$ and $S_{17}=442$. GOOD =====Question 2(ii)===== Some of the component... d the one that are missing $a_1=-40, S_{21}=210$. GOOD ====Solution==== Given: $a_1=-40$ and $S_{21}=2... \end{align} Hence $a_{21}=60$, $d=5$ and $n=21$. GOOD =====Question 2(iii)===== Some of the component
- Question 10 Exercise 6.5 @math-11-kpk:sol:unit06
- obability that either both are apples or both are good? ====Solution===== Total number of Apples $=20$... es $=5$ number of defective oranges $=3$. Totál good apples $=15$ Defective apples $=5$ Total good oranges $=10$ number of defective oranges $=3$ number of good fruits $=22$ Now two fruits are chosen at rand
- Question 14 Exercise 4.2 @math-11-kpk:sol:unit04
- = Insert three arithmetic means between 6 and 41. GOOD ====Solution==== Let $A_1, A_2, A_3$ be three a... $$14\dfrac{3}{4},23\dfrac{1}{2},32\dfrac{1}{4}.$$ GOOD =====Question 14(ii)===== Insert four arithmetic means between 17 and 32. GOOD ====Solution==== Let $A_1, A_2, A_3, A_4$ be fo... etic means between 17 and 32 are $$20,23,26,29.$$ GOOD ====Go To==== <text align="left"><btn type=
- Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
- sequence: $9,7,5,3, \ldots$; 20th term; 20 terms. GOOD ====Solution==== Let $a_1$ be first term and $d... th term is -29 and sum of first 20 terms is -200. GOOD =====Question 1(ii)===== Find indicated term a... }, \dfrac{7}{3}, 2, \ldots$; 11th term; 11 terms. GOOD ====Solution==== Let $a_1$ be first term and $d... 3}$ and sum of first 11 terms is $\dfrac{44}{3}$. GOOD ====Go To==== <text align="right"><btn type="
- Question 5 and 6 Exercise 4.2 @math-11-kpk:sol:unit04
- dent of $n$. Thus, the given sequence is in A.P. GOOD =====Question 6===== Find the value of $k$, if... k-2$, $8 k-4$ are in A.P. Also find the sequence. GOOD ====Solution==== Since the given terms are in A... ac{7}{2}$ and the sequence is $14,19,24, \ldots$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p2 |< Question
- Question 2 & 3, Exercise 1.1 @math-11-kpk:sol:unit01
- i}^{107}}+{{i}^{112}}+{{i}^{122}}+{{i}^{153}}=0$. GOOD ====Solution==== \begin{align}L.H.S.&={{i}^{107... ght)}^{76}}\\ &=-i+1-1+i\\ &=0=R.H.S.\end{align} GOOD =====Question 3(i)===== Add the complex number... right)+\left( 1+\sqrt{2} \right)i\end{align} ====Go to ==== |<text align="left"><btn type="primary">
- Question 6 Exercise 4.1 @math-11-kpk:sol:unit04
- $n=5$ by using its general recursive definition. GOOD ====Solution==== For $n=5$, we have Pascal se... $n=6$ is $1,8,28,56,70,56,28,8,1,0,0,0, \ldots$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-1-p3 |< Question
- Question 1 and 2 Exercise 4.2 @math-11-kpk:sol:unit04
- h term of the arithmetic sequence $2,5,8, \ldots$ GOOD ====Solution==== Here $a_1=2$, $d=5-2=3$ and $n... ence is 8 and the 21st is 108. Find the 7th term. GOOD ====Solution==== Since $a_1=8$ and $a_{21}=108$... e the 7th term of the given sequence is 38. ====Go To==== <text align="right"><btn type="success">[[
- Question 3 and 4 Exercise 4.2 @math-11-kpk:sol:unit04
- he number of terms in given progression are $25$. GOOD =====Question 4===== The $n$th term of sequenc... =14+7=21.$$ Hence the 7th term of given AP is 21. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p1 |< Question
- Question 7 Exercise 4.2 @math-11-kpk:sol:unit04
- -a_4=\dfrac{2}{3}$, find the arithmetic sequence. GOOD ====Solution==== Let $a_1$ be first term and $d... d A.P is $\dfrac{5}{3}, 2, \dfrac{7}{3}, \ldots$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p3 |< Question
- Question 9 Exercise 4.2 @math-11-kpk:sol:unit04
- d how many meters it covered in the eight second? GOOD ====Solution==== Suppose that $$a_1=24,$$ $$a_... tance covered by the ball in 8th second is $3m$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p5 |< Question
- Question 10 Exercise 4.2 @math-11-kpk:sol:unit04
- 1960 was 20135, what was its population in 1970? GOOD ====Solution==== Suppose $a_1$ represents the p... the population of the town in $1070$ was $15135$. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p6 |< Questi
- Question 11 Exercise 4.2 @math-11-kpk:sol:unit04
- When will they reach the top of a 5400 feet hill? GOOD ====Solution==== Suppose $a_1$ represent the di... ll take 45 hours to reach at the top of the hill. GOOD ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p7 |< Question