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- Question 1 Exercise 7.1
- Question 2 Exercise 7.1
- Question 3 Exercise 7.1
- Question 4 Exercise 7.1
- Question 5 Exercise 7.1
- Question 6 Exercise 7.1
- Question 7 Exercise 7.1
- Question 8 Exercise 7.1
- Question 9 Exercise 7.1
- Question 10 Exercise 7.1
- Question 11 Exercise 7.1
- Question 12 Exercise 7.1
- Question 13 Exercise 7.1
- Question 14 Exercise 7.1
- Question 15 Exercise 7.1
- Question 1 Exercise 7.2
- Question 2 Exercise 7.2
- Question 3 Exercise 7.2
- Question 4 Exercise 7.2
- Question 5 Exercise 7.2
- Question 6 Exercise 7.2
- Question 7 Exercise 7.2
- Question 8 Exercise 7.2
- Question 9 Exercise 7.2
- Question 10 Exercise 7.2
- Question 11 Exercise 7.2
- Question 1 Exercise 7.3
- Question 2 Exercise 7.3
- Question 3 Exercise 7.3
- Question 4 Exercise 7.3
- Question 5 and 6 Exercise 7.3
- Question 7 and 8 Exercise 7.3
- Question 9 Exercise 7.3
- Question 10 Exercise 7.3
- Question 11 Exercise 7.3
- Question 12 Exercise 7.3
- Question 13 Exercise 7.3
- Question 14 Exercise 7.3
- Question 1 Review Exercise 7
- Question 2 Review Exercise 7
- Question 3 & 4 Review Exercise 7
- Question 5 & 6 Review Exercise 7
- Question 7 & 8 Review Exercise 7
- Question 9 and 10 Review Exercise 7
- Question 11 Review Exercise 7
Fulltext results:
- Question 2 Exercise 7.2
- ====== Question 2 Exercise 7.2 ====== Solutions of Question 2 of Exercise 7.2 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Find the indicate term in the expansion... 3 \\ & \Rightarrow T_4=560 a ^3 \end{align} =====Question 2(ii)===== Find the indicate term in the expansio
- Question 3 Exercise 7.2
- ====== Question 3 Exercise 7.2 ====== Solutions of Question 3 of Exercise 7.2 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(i)===== Find the term independent of $x$ in the... $T_7$ is independent of $x$ and is $2268.$ =====Question 3(ii)===== Find the term independent of $x$ in th
- Question 4 Exercise 7.2
- ====== Question 4 Exercise 7.2 ====== Solutions of Question 4 of Exercise 7.2 of Unit 07: Permutation, Combination and Prob... Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 4(i)===== Find the coefticient of $x^{23}$ in $(x... the expansion of $(x^2-x^{20})$ is $-1140$ =====Question 4(ii)===== Find the coefticient of $\dfrac{1}{x^4
- Question 5 Exercise 7.2
- ====== Question 5 Exercise 7.2 ====== Solutions of Question 5 of Exercise 7.2 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Find middle term in the expansion of $(... rm of the expansion which is $70 a^4 b^4$. =====Question 5(ii)===== Find middle term in the expansion of $
- Question 7 Exercise 7.2
- ====== Question 7 Exercise 7.2 ====== Solutions of Question 7 of Exercise 7.2 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Find $(2+\sqrt{3})^5+(2-\sqrt{3})^5$ ==... 2+\sqrt{3})^5+(2-\sqrt{3})^5=724\end{align} =====Question 7(ii)===== $(1+\sqrt{2})^4-(1-\sqrt{2})^{-}$ ====
- Question 12 Exercise 7.1
- ====== Question 12 Exercise 7.1 ====== Solutions of Question 12 of Exercise 7.1 of Unit 07: Permutation, Combination and Pr... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 12(i)===== Show by mathematical induction that $\... tion it is true for all $n \in \mathbf{N}$. =====Question 12(ii)===== Show by mathematical induction that $
- Question 13 Exercise 7.1
- ====== Question 13 Exercise 7.1 ====== Solutions of Question 13 of Exercise 7.1 of Unit 07: Permutation, Combination and Pr... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 13(i)===== $2^n>n \forall n \in \mathbf{N}$. ====... ction it is true for all $n \in \mathbf{N}$. =====Question 13(ii)===== $n$ ! $>n^2$ for every integer $n \ge
- Question 14 Exercise 7.1
- ====== Question 14 Exercise 7.1 ====== Solutions of Question 14 of Exercise 7.1 of Unit 07: Permutation, Combination and Pr... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 14 (i)===== Show that $5$ is a factor $3^{2 n-1}+... tion it is true for all $n \in \mathbf{N}$. =====Question 14(ii)===== Prove that $2^{2 n}-1$ is a multiple
- Question 1 Exercise 7.2
- ====== Question 1 Exercise 7.2 ====== Solutions of Question 1 of Exercise 7.2 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Expand by using Binomial theorem: $(x^2... dfrac{4x^2}{y^3}+\dfrac{1}{y^4} \end{align} =====Question 1(ii)===== Expand by using Binomial theorem: $(1+
- Question 2 Exercise 7.1
- ====== Question 2 Exercise 7.1 ====== Solutions of Question 2 of Exercise 7.1 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== Establish the formulas below by mathematic... pe="primary">[[math-11-kpk:sol:unit07:ex7-1-p1 |< Question 1 ]]</btn></text> <text align="right"><btn type=
- Question 3 Exercise 7.1
- ====== Question 3 Exercise 7.1 ====== Solutions of Question 3 of Exercise 7.1 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3===== Establish the formulas below by mathematic... pe="primary">[[math-11-kpk:sol:unit07:ex7-1-p2 |< Question 2 ]]</btn></text> <text align="right"><btn type=
- Question 4 Exercise 7.1
- ====== Question 4 Exercise 7.1 ====== Solutions of Question 4 of Exercise 7.1 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 4===== Establish the formulas below by mathematic... pe="primary">[[math-11-kpk:sol:unit07:ex7-1-p3 |< Question 3 ]]</btn></text> <text align="right"><btn type=
- Question 5 Exercise 7.1
- ====== Question 5 Exercise 7.1 ====== Solutions of Question 5 of Exercise 7.1 of Unit 07: Permutation, Combination and Prob... Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5===== Establish the formulas below by mathematic... pe="primary">[[math-11-kpk:sol:unit07:ex7-1-p4 |< Question 4 ]]</btn></text> <text align="right"><btn type=
- Question 6 Exercise 7.1
- ====== Question 6 Exercise 7.1 ====== Solutions of Question 6 of Exercise 7.1 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6===== Establish the formulas below by mathematic... pe="primary">[[math-11-kpk:sol:unit07:ex7-1-p5 |< Question 5 ]]</btn></text> <text align="right"><btn type=
- Question 7 Exercise 7.1
- ====== Question 7 Exercise 7.1 ====== Solutions of Question 7 of Exercise 7.1 of Unit 07: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7===== Establish the formulas below by mathematic... pe="primary">[[math-11-kpk:sol:unit07:ex7-1-p6 |< Question 6 ]]</btn></text> <text align="right"><btn type=