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- Question 2 & 3, Exercise 1.1 @math-11-kpk:sol:unit01
- ====== Question 2 & 3, Exercise 1.1 ====== Solutions of Question 2 & 3 of Exercise 1.1 of Unit 01: Complex Numbers. This is... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== Prove that ${{i}^{107}}+{{i}^{112}}+{{i}^{... \\ &=-i+1-1+i\\ &=0=R.H.S.\end{align} GOOD =====Question 3(i)===== Add the complex numbers $3\left( 1+2i \
- Question 1, Exercise 1.1 @math-11-kpk:sol:unit01
- ====== Question 1, Exercise 1.1 ====== Solutions of Question 1 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Simplify ${{i}^{9}}+{{i}^{19}}$. GOOD =... -1 \right)\\ &=i-i\\ &=0.\end{align} GOOD =====Question 1(ii)===== Simplify ${{\left( -i \right)}^{23}}$.
- Question 1, Review Exercise 10 @math-11-kpk:sol:unit10
- ====== Question 1, Review Exercise 10 ====== Solutions of Question 1 of Review Exercise 10 of Unit 10: Trigonometric Ident... Board (KPTB or KPTBB) Peshawar, Pakistan. ===== Question 1 ===== Chose the correct option. i. $\cos {{5... <text align="right"><btn type="success">[[math-11-kpk:sol:unit10:re-ex10-p2|Question 2 & 3 >]]</btn></text>
- Question 3 & 4 Exercise 4.3 @math-11-kpk:sol:unit04
- ====== Question 3 & 4 Exercise 4.3 ====== Solutions of Question 3 & 4 of Exercise 4.3 of Unit 04: Sequence and Series. This... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3===== Find sum of all the numbers divisible by $... ghtarrow S_{66}&=33(375)=12375 .\end{align} =====Question 4===== The sum of three numbers in an arithmetic
- Question 2 Exercise 4.3 @math-11-kpk:sol:unit04
- ====== Question 2 Exercise 4.3 ====== Solutions of Question 2 of Exercise 4.3 of Unit 04: Sequence and Series. This is unit... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Some of the components $a_1, a_n, n, d$... n} Hence $a_{17}=50$ and $S_{17}=442$. GOOD =====Question 2(ii)===== Some of the components $a_1, a_n, n, d
- Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
- ====== Question 1 Exercise 4.3 ====== Solutions of Question 1 of Exercise 4.3 of Unit 04: Sequence and Series. This is unit... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Find indicated term and sum of the indi... -29 and sum of first 20 terms is -200. GOOD =====Question 1(ii)===== Find indicated term and sum of the ind
- Question 14 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 14 Exercise 4.2 ====== Solutions of Question 14 of Exercise 4.2 of Unit 04: Sequence and Series. This is un... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 14(i)===== Insert three arithmetic means between ... 3}{4},23\dfrac{1}{2},32\dfrac{1}{4}.$$ GOOD =====Question 14(ii)===== Insert four arithmetic means between
- Question 17 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 17 Exercise 4.2 ====== Solutions of Question 17 of Exercise 4.2 of Unit 04: Sequence and Series. This is un... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 17===== There are $n$ arithmetic means between 5 ... text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p12 |< Question 16 ]]</btn></text>
- Question 16 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 16 Exercise 4.2 ====== Solutions of Question 16 of Exercise 4.2 of Unit 04: Sequence and Series. This is un... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 16===== Insert five arithmetic means between $5$ ... e="primary">[[math-11-kpk:sol:unit04:ex4-2-p11 |< Question 15 ]]</btn></text> <text align="right"><btn type=
- Question 15 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 15 Exercise 4.2 ====== Solutions of Question 15 of Exercise 4.2 of Unit 04: Sequence and Series. This is un... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 15===== For what value of $n, \dfrac{a^{n+1}+b^{n... e="primary">[[math-11-kpk:sol:unit04:ex4-2-p10 |< Question 14 ]]</btn></text> <text align="right"><btn type=
- Question 12 & 13 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 12 & 13 Exercise 4.2 ====== Solutions of Question 12 & 13 of Exercise 4.2 of Unit 04: Sequence and Series. ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 12===== A man earned dollars 3500 the first year ... s 21st year of work is dollars 18,500. GOOD =====Question 13(i)===== Find the arithmetic mean between $12$
- Question 11 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 11 Exercise 4.2 ====== Solutions of Question 11 of Exercise 4.2 of Unit 04: Sequence and Series. This is un... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 11===== Ahmad and Akram can climb 1000 feet in th... pe="primary">[[math-11-kpk:sol:unit04:ex4-2-p7 |< Question 10]]</btn></text> <text align="right"><btn type="
- Question 10 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 10 Exercise 4.2 ====== Solutions of Question 10 of Exercise 4.2 of Unit 04: Sequence and Series. This is un... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 10===== The population of a town is decreasing by... pe="primary">[[math-11-kpk:sol:unit04:ex4-2-p6 |< Question 9]]</btn></text> <text align="right"><btn type="s
- Question 9 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 9 Exercise 4.2 ====== Solutions of Question 9 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 9===== A ball rolling up an incline covered $24m$... pe="primary">[[math-11-kpk:sol:unit04:ex4-2-p5 |< Question 8]]</btn></text> <text align="right"><btn type="s
- Question 8 Exercise 4.2 @math-11-kpk:sol:unit04
- ====== Question 8 Exercise 4.2 ====== Solutions of Question 8 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8===== If $\dfrac{b+c-a}{a}, \dfrac{c+a-b}{b}, \d... pe="primary">[[math-11-kpk:sol:unit04:ex4-2-p4 |< Question 7]]</btn></text> <text align="right"><btn type="s