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- Question 5 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... }{x})^{8-r}(b x)^r$$ To get middle term $T_5$, we put $r=4$ \begin{align}T_5&=\dfrac{8 !}{(8-4) ! 4 !}... 9 !}{(9-r) ! r !}(3 x)^{9-r}(-\dfrac{x^2}{2})^r$$ Putting $r=4$ to get first middle term \begin{align}... x^{13}\\ & T_5=\dfrac{15309}{8} x^{13}\end{align} Putting $r=5$ to get the $2^{\text {nd }}$ middle te
- Question 2 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... r !}(2)^{7-r } a^r $$ For $4^{\text {th }}$ term, putting $r=3$ \begin{align} & T_{3+1}=\dfrac{7 !}{(7... r}(-\dfrac{3}{y})^r$$ For $8^{\text {th }}$ term, putting $r=7$ \begin{align}T_{7+1}&=\dfrac{10 !}{(10... t}=x^0$ $$\Rightarrow 21-3 r=0 \Rightarrow r=7 $$ Putting $r=7$ in the above, we get \begin{align}T_{7
- Question 3 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ow 18-3 r=0 \Rightarrow 3 r=18 \Rightarrow r=6 $$ Putting $r=6$ in the above $T_{r+1}$ \begin{align}T_... $ $$\Rightarrow 10-5 r=0 \quad \Rightarrow r=2 $$ Putting $r=2$ in the above, we get \begin{align} T_{... t}=x^0$ $$\Rightarrow 21-3 r=0 \Rightarrow r=7 $$ Putting $r=7$ in the above, we get \begin{align}T_{7
- Question 4 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... row 40-r&=23\\ \Rightarrow r&=40-23=17\end{align} Putting $r=17$. in $T_{r+1}$ we get \begin{align}T_{... x^r}&=\dfrac{1}{x^4}\\ \Rightarrow 4=r\end{align} Putting $r=4$ in $T_{r+ 1}$ we get \begin{align}T_{4... ^3\\ \Rightarrow 9 -r=6 \text{or} r=3\end{align} Putting $r=3$ in the above, we get \begin{align}T_{3
- Question 10 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ray}\right) x^2-\ldots+i_n^*\right) x^n \cdot $$ Putting $x=1$ in the above equation, we have $(1 \di... nd{array}\right) 1^n \\ & \end{aligned} $$ If we put $x=-1$ in the above eyuation, we get $$ \begin{a
- Question 10 Exercise 7.3
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... -1 \Rightarrow n=-\frac{1}{2} . \end{aligned} $$ Putting $n=-\frac{1}{2}$ in Eq.(1), we get $$ \begin... \text { or } n=-\frac{15}{17} . \end{aligned} $$ Putting $n=\frac{15}{17}$ in Eq.(1), we get $$ -\fra
- Question 12 Exercise 7.3
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... 2 \text { or } n=-\frac{1}{2} . \end{aligned} $$ Putting $n=-\frac{1}{2}$ in Eq.(1), we get $-\frac{1... 2 \text { or } n=-\frac{1}{2} . \end{aligned} $$ Putting $n=-\frac{1}{2}$ in Eq.(1), we get $-\frac{1
- Question 10 Exercise 7.1
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ign} Which is the just the form taken by given propusition when $n$ is replaced by $k+1$. hence it is
- Question 15 Exercise 7.1
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... er $n$. ====Solution==== Since $n$ is even, so we put $n=2 n, \quad m \in \mathbb{Z}^{+}$. 1. For $m=
- Question 8 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... 5\end{array}\right) 3^{10} 5-2 \gamma^{15}$ we compute at $x=\frac{3}{4}$, so $$ \begin{aligned} & T_{
- Question 9 Exercise 7.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... (x-y)="$ when $x=12$ and $y-4$. Solution: When we put $x=12$, then the give becounes $$ \begin{aligned
- Question 11 Exercise 7.3
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... =2 n-2 \text { or } n=-\frac{1}{2} . \\ & \text { Putting } n=-\frac{1}{2} \text { in Eq.(1), we get }
- Question 5 & 6 Review Exercise 7
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ightarrow 4 r-20=0 \Rightarrow r=5 \text {. } $$ Putting in $T_{r+1}$ we get $$ T_{5+1}=\frac{10 !}{5
- Question 1 Exercise 7.1
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
- Question 2 Exercise 7.1
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB