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- Question 9, Exercise 1.2 @math-11-nbf:sol:unit01
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... x_2 = 2, \quad y_2 = 5.\] First, we need to compute \(x_1^2 + y_1^2\): \[x_1^2 + y_1^2 = 4^2 + 2^2 = 20.\] Next, compute \(x_2^2 - y_2^2\): \[x_2^2 - y_2^2 = 2^2 - 5^2 = -21.\] Then, compute \(x_1^2 - y_1^2\): \[x_1^2 - y_1^2 = 4^2 - 2^
- Question 8, Exercise 1.2 @math-11-nbf:sol:unit01
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... $z=x+i y$. **Solution.** Given: $$|2z-i|=4.$$ Put $z=x+i y$, we have \begin{align} & |2(x+iy)-i|=4... y$. **Solution.** Given: $$|z-1|=|\bar{z}+i|.$$ Put $z=x+iy$, we have \begin{align} & |(x+iy)-1| = |... **Solution.** Given: $$|z-4i| + |z+4i| = 10.$$ Put $z = x + iy$, we have \begin{align} & |(x + iy)
- Question 2, Exercise 2.6 @math-11-nbf:sol:unit02
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... \\ \implies &x_2=\frac{11}{13}x_3\\ \end{align*} Put the value of $x_2$ in (vi), we have \begin{align... 2 \quad \lambda =-7 \end{align*} If $\lambda=2$, put the value of $\lambda$ we have \begin{align*} x_... &= 4x_{2} - 3x_{3} \quad \text{(iv)} \end{align*} Put the value if $x_1$ in (ii), we have \begin{align
- Question 4, Exercise 6.3 @math-11-nbf:sol:unit06
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... \end{array} \] \begin{align*}n & =9 \quad \text{put in (i)}\\ 10 r-3(9)-3 & =0 \\ 10 r-30 & =0 \\ r ... \ \end{array} \] \begin{align*} r&=27\quad \text{put in (i)}\\ 7(27)-3 n-3 & =0 \\ 186-3 n & =0 \\ n ... t{and}\\ n & =2 r \quad\cdots (ii)\\ \end{align*} Put (ii) in (i)\\ \begin{align*}6(2r)-11r-5&=0\\ 12r
- Question 6 Exercise 8.2 @math-11-nbf:sol:unit08
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... \sin\theta \cos\theta = \frac{1}{2}\sin 2\theta$$ Put $\theta = 15^{\circ}$ \begin{align*} \sin 15^{\c... $$\cos^2\theta -\sin^2\theta= \cos 2\theta = $$ Put $\theta = 15^{\circ}$ \begin{align*} \cos^2 15^\... pha.$$ That is $$1-2\sin^2 \alpha=\cos 2\alpha.$$ Put $\alpha= \dfrac{\pi}{8}$, we have \begin{align*}
- Question 4, Exercise 1.1 @math-11-nbf:sol:unit01
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... {align} &3x=-3y \\ x=-y \quad ... (3) \end{align} Putting value of $x$ in (1) \begin{align}2(-y)+y+2&=0\\ -2y+y&=-2\\ -y&=-2\\ y&=2\end{align} Putting in $(3)$, we have $x=-2$. Hence $x=-2$ and ... (2)$, we have &y=2x-1\cdots \cdots (3)\end{align} Put the value of $y$ in $(1)$ \begin{align}& x+(2x-1
- Question 26 and 27, Exercise 4.4 @math-11-nbf:sol:unit04
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... me. =====Question 27===== A city has a current population of 100,000 and the population is increasing by $3 \%$ each year. What will the population be in $15^{\text {th }}$ years? ** Solutio
- Question 7 and 8, Exercise 4.8 @math-11-nbf:sol:unit04
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... n*} 1 = (3k+1)A+(3k-2)B \ldots (2) \end{align*} Put $3k-2=0$ $\implies k=\dfrac{2}{3}$ in (2), we ha... 0 \\ \implies &A = \frac{1}{3}. \end{align*} Now put $3k+1=0$ $\implies k=-\dfrac{1}{3}$ in (2), we h... n*} 1 = (5k+1)A+(5k-4)B \ldots (2) \end{align*} Put $5k-4=0$ $\implies k=\dfrac{4}{5}$ in (2), we ha
- Question 11 and 12, Exercise 4.8 @math-11-nbf:sol:unit04
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... {align*} 1 = A(k+2) + Bk \ldots (2) \end{align*} Put $k=0$ in (2), we have \begin{align*} &1=2A + 0 \\ \implies & A = \frac{1}{2}. \end{align*} Put $k+2=0 \implies k=-2$ in (2), we have \begin{ali... n*} 1 = (3k+1)A+(3k-2)B \ldots (2) \end{align*} Put $3k-2=0$ $\implies k=\dfrac{2}{3}$ in (2), we ha
- Question 3, Exercise 1.2 @math-11-nbf:sol:unit01
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... hat for $z \in \mathbb{C}$. $z$ is either real or pure imaginary iff $(\overline{z})^{2}=z^{2}$. **So... For $z=x+iy$, first suppose that $z$ is real or pure imaginary, then $$z=x \quad \text{ or } \quad z... ither $z=iy$ or $z=x$. This gives $z$ is real or pure imaginary. ====Go to ==== <text align="left"><b
- Question 4, Exercise 1.3 @math-11-nbf:sol:unit01
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... {106}\\ &=\dfrac{2}{53}-\dfrac{7}{53}i\end{align} Put value of $\omega$ in (1), we have \begin{align} ... a= -\dfrac{288}{109}+ \dfrac{88}{109}i\end{align} Put vale of $\omega$ in $(1)$, we have \begin{align}... 53}\\ &=\dfrac{68}{53}-\dfrac{80}{53}i\end{align} Putting value of $\omega$ in $(3)$, we get \begin{al
- Question 7, Exercise 2.2 @math-11-nbf:sol:unit02
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... tical induction to prove the given fact. For C-1, put $n = 1$ \begin{align}A^1 =\begin{bmatrix} x^1 & ... $ ** Solution. ** we use mathematical induction. Put $n = 1$ \begin{align*} A^1 = \left[\begin{arra
- Question 13, Exercise 2.2 @math-11-nbf:sol:unit02
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... & 6 & -3 \\ 2 & 1 & 7 \end{pmatrix} \end{align*} Put value of $Y$ in (ii), we have \begin{align*} X ... & 3 & -1 \\ 1 & 0 & 3 \end{pmatrix} \end{align*} Put value of $X$ into value of $Y$. \begin{align*} Y
- Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... \end{array} \\ \implies &x_2=2x_3\\ \end{align*} Put the value of $x_3$ in (iii), we have \begin{alig... } \\ \implies & x_2 = \frac{2}{5}x_3 \end{align*} Put the value of $x_2$ in (iii), we have \begin{alig
- Question 3, Exercise 2.6 @math-11-nbf:sol:unit02
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... \ &\Rightarrow \quad z = -\frac{1}{2}\end{align*} Put $z = -\frac{1}{2}$ into the second row: \begin{a... }{2} \\ \Rightarrow & y = \frac{5}{4}\end{align*} Put values of $y = \frac{5}{4}$ and $z = -\frac{1}{2