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- Question 1 Review Exercise 7
- id="a1" collapsed="true">(a): $2520$</collapse> ii. How many two digits odd numbers can be formed fo... id="a2" collapsed="true">(c): $28$ </collapse> iii. How many six digits number can be formed from th... id="a6" collapsed="true">(d): $4775$</collapse> vii. The number of all possible matrices of order $3 ... id="a7" collapsed="true">(c): $512$</collapse> viii. How many diagonals can be drawn in plane figure
- Question 7 Exercise 7.2
- ^5+(2-\sqrt{3})^5=724\end{align} =====Question 7(ii)===== $(1+\sqrt{2})^4-(1-\sqrt{2})^{-}$ ====Solut... t{2})^4&=24 \sqrt{2}\end{align} =====Question 7(iii)===== Find $(a+b)^5+(a-b)^5$ ====Solution==== (iii) $(a+b)^5+(a-b)^5$ Solution: Using binomial theor
- Question 1 Exercise 7.2
- {y^3}+\dfrac{1}{y^4} \end{align} =====Question 1(ii)===== Expand by using Binomial theorem: $(1+x y)^... +x^7 y^7 \text {. } \end{align} =====Question 1(iii)===== Expand by using Binomial theorem: $(\sqrt{y
- Question 2 Exercise 7.2
- htarrow T_4=560 a ^3 \end{align} =====Question 2(ii)===== Find the indicate term in the expansion $8^... x^3 \cdot y^{-7} \end{align} =====Question 2(iii)===== Find the indicate term in the expansion $8^
- Question 3 Exercise 7.2
- dependent of $x$ and is $2268.$ =====Question 3(ii)===== Find the term independent of $x$ in the exp... ependemt of $x$ which is $405$ =====Question 3(iii)===== Find the term independent of $x$ in the exp
- Question 4 Exercise 7.2
- ion of $(x^2-x^{20})$ is $-1140$ =====Question 4(ii)===== Find the coefticient of $\dfrac{1}{x^4}$ in... frac{9}{x})$, is $^8C_4\, 2^4$ =====Question 4(iii)===== Find the coefticient of $a^6 b^3$ in $(2 a-
- Question 5 Exercise 7.2
- xpansion which is $70 a^4 b^4$. =====Question 5(ii)===== Find middle term in the expansion of $(3 x-... T_6=-\dfrac{5103}{16} x^{14}$$ =====Question 5(iii)===== Find middle term in the expansion of $(3 x^
- Question 1 Exercise 7.3
- c{3 x^2}{8}+\frac{5 x^3}{16}+\ldots \\ & \text { (ii) }(1-x)^{\frac{3}{2}} \\ & (1-x)^{\frac{3}{2}}=1-... 2}-2\right)}{3 !}(-x)^3+\ldots \end{aligned} $$ (iii) $(8+12 x)^{\frac{2}{3}}$ Solution: $$ \begin{al
- Question 2 Exercise 7.3
- .] \cong 5.099 \text {. } \\ & \end{aligned} $$ (ii) $\frac{1}{\sqrt{0.998}}$ Solution: We are given... 0005+\ldots \\ & \cong 1.001 . \end{aligned} $$ (iii) Find cube root of 126 correct to five decimal pl
- Question 12 Exercise 7.1
- rue for all $n \in \mathbf{N}$. =====Question 12(ii)===== Show by mathematical induction that $\dfrac
- Question 13 Exercise 7.1
- true for all $n \in \mathbf{N}$. =====Question 13(ii)===== $n$ ! $>n^2$ for every integer $n \geq 4$ =
- Question 14 Exercise 7.1
- rue for all $n \in \mathbf{N}$. =====Question 14(ii)===== Prove that $2^{2 n}-1$ is a multiple of $3$
- Question 7 and 8 Exercise 7.3
- ook Board (KPTB or KPTBB) Peshawar, Pakistan. Q7 II $x^4$ and higher powers are neglected and $(1-x)^
- Question 10 Exercise 7.3
- e the sum of the series is $\sqrt{\frac{2}{3}}$. (ii) $1+\frac{5}{8}+\frac{5.8}{8.12}+\frac{5.8 .11}{8