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- Exercise 6.2 (Solutions) @math-11-nbf:sol:unit06
- ====== Exercise 6.2 (Solutions) ====== The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published b... }^n P_{n-2}$\\ [[math-11-nbf:sol:unit06:ex6-2-p1|Solution Question 1]] **Question 2.** Find $n$, if:\\ (i)... -1}=22: 7$ \\ [[math-11-nbf:sol:unit06:ex6-2-p2|Solution: Question 2 ]] **Question 3.** Find $r$, if:\\ (
- Exercise 6.3 (Solutions) @math-11-nbf:sol:unit06
- ====== Exercise 6.3 (Solutions) ====== The solutions of the Exercise 6.3 of book “Model Textbook of Mathematics for Class XI” published b... ^{n+1} C_{r}$\\ [[math-11-nbf:sol:unit06:ex6-3-p1|Solution: Question 1(i-v)]] **Question 1(vi-x).** Prove t... ible by $k$ !\\ [[math-11-nbf:sol:unit06:ex6-3-p2|Solution: Question 1(vi-x) ]] **Question 2.** Find $n$, i
- Exercise 2.2 (Solutions) @math-11-nbf:sol:unit02
- ====== Exercise 2.2 (Solutions) ====== The solutions of the Exercise 2.2 of book “Model Textbook of Mathematics for Class XI” published b... {2 i-3 j}{3}$\\ [[math-11-nbf:sol:unit02:ex2-2-p1|Solution:Question 1]] **Question 2.** Construct a matrix ... +j^{2}}{i+j}$\\ [[math-11-nbf:sol:unit02:ex2-2-p2|Solution:Question 2]] **Question 3.** If $A=\left[\begin{
- Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
- ====== Question 1, Exercise 2.6 ====== Solutions of Question 1 of Exercise 2.6 of Unit 02: Matrices and Dete... em of homogeneous linear equation for non-trivial solution if exists\\ $ 2 x_{1}-3 x_{2}+4 x_{3}=0$\\ $x_{1}... _{2}+3 x_{3}=0$\\ $4 x_{1}+x_{2}-6 x_{3}=0$\\ ** Solution. ** \begin{align*} &2 x_{1}-3 x_{2}+4 x_{3}=0\cdo... 4+36=0 \end{align*} So the system has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*
- Exercise 1.4 (Solutions) @math-11-nbf:sol:unit01
- ====== Exercise 1.4 (Solutions) ====== The solutions of the Exercise 1.4 of book “Model Textbook of Mathematics for Class XI” published b... rac{\pi}{3}}$\\ [[math-11-nbf:sol:unit01:ex1-4-p1|Solution: Question 1]] **Question 2.** Write the followin... {3}\right)}$ \\ [[math-11-nbf:sol:unit01:ex1-4-p2|Solution: Question 2]] **Question 3.** If $\left(x_{1}+i
- Exercise 1.2 (Solutions) @math-11-nbf:sol:unit01
- ====== Exercise 1.2 (Solutions) ====== The solutions of the Exercise 1.2 of book “Model Textbook of Mathematics for Class XI” published b... rname{Re}(z)$\\ [[math-11-nbf:sol:unit01:ex1-2-p1|Solution: Question 1]] **Question 2.** Use the algebraic ... ght) z_{4} $$\\ [[math-11-nbf:sol:unit01:ex1-2-p2|Solution: Question 2]] **Question 3.** Prove that for $z
- Question 1, Exercise 1.3 @math-11-nbf:sol:unit01
- ====== Question 1, Exercise 1.3 ====== Solutions of Question 1 of Exercise 1.3 of Unit 01: Complex Numbers. ... polynomial into linear functions: $z^{2}+169$. **Solution.** \begin{align} & z^{2} + 169 \\ = & z^{2} - (... olynomial into linear functions: $2 z^{2}+18$. **Solution.** \begin{align} & 2z^2 + 18 \\ = &2(z^2 - (3i)^... nomial into linear functions: $3 z^{2}+363$. **Solution.** \begin{align} & 3z^2 + 363 \\ = & 3(z^2 - (1
- Exercise 6.1 (Solutions) @math-11-nbf:sol:unit06
- ====== Exercise 6.1 (Solutions) ====== The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published b... !}{(6!)^2}$ \\ [[math-11-nbf:sol:unit06:ex6-1-p1|Solution: Question 1]] **Question 2.** Write the followin... -1)}{n(n-4)}$\\ [[math-11-nbf:sol:unit06:ex6-1-p2|Solution: Question 2 ]] **Question 3.** Prove the followi
- Question 6(i-ix), Exercise 1.4 @math-11-nbf:sol:unit01
- ====== Question 6(i-ix), Exercise 1.4 ====== Solutions of Question 6(i-ix) of Exercise 1.4 of Unit 01: Compl... os 315^{\circ}+i \sin 315^{\circ}\right)$ ** Solution. ** \begin{align} &\sqrt{2}\left(\cos 315^{\circ... t(\cos 210^{\circ}+i \sin 210^{\circ}\right)$ ** Solution. ** \begin{align*} &5\left(\cos 210^\circ + i \s... c{3 \pi}{2}+i \sin \dfrac{3 \pi}{2}\right)$ ** Solution. ** \begin{align*} &2\left(\cos \frac{3\pi}{2} +
- Review Exercise 1 (Solutions) @math-11-nbf:sol:unit01
- ====== Review Exercise 1 (Solutions) ====== The solutions of the Review Exercise 1 of book “Model Textbook of Mathematics for Class XI” publis... rrect option.\\ [[math-11-nbf:sol:unit01:re-ex-p1|Solution: Question 1]] **Question 2.** Find the value of ... \right)^{-1}$\\ [[math-11-nbf:sol:unit01:re-ex-p2|Solution: Question 2 ]] **Question 3.** Factorize the fol
- Question 2, Exercise 6.2 @math-11-nbf:sol:unit06
- ====== Question 2, Exercise 6.2 ====== Solutions of Question 2 of Exercise 6.2 of Unit 06: Permutation and C... )===== Find $n$, if: $\quad ^nP_4=20\, ^nP_2$ ** Solution. ** \begin{align*} \dfrac{m}{(n-4)!}&=20 \cdot \... = Find $n$, if: $\quad ^{2n}P_3=100 \, ^nP_2$ ** Solution. ** \begin{align*} \dfrac{(2 n)!}{(2 n-3)!}&=100... ind $n$, if: $\quad16\, ^nP_3=13\, ^{n+1}P_3$ ** Solution. ** \begin{align*}16 \dfrac{n!}{(n-3)!}&=13 \dfr
- Unit 04: Sequences and Seeries
- abad, Pakistan. On this page we have provided the solutions of the questions. After reading this unit the s... ries. <panel type="default" title="Exercise 4.1 (Solutions)"> * [[math-11-nbf:sol:unit04:ex4-1-p1|Questio... nel> <panel type="default" title="Exercise 4.2 (Solutions)"> * [[math-11-nbf:sol:unit04:ex4-2-p1|Questio... anel> <panel type="default" title="Exercise 4.3 (Solutions)"> * [[math-11-nbf:sol:unit04:ex4-3-p1|Questio
- Exercise 1.1 (Solutions) @math-11-nbf:sol:unit01
- ====== Exercise 1.1 (Solutions) ====== The solutions of the Exercise 1.1 of book “Model Textbook of Mathematics for Class XI” published b... {58}+i^{21}$ \\ [[math-11-nbf:sol:unit01:ex1-1-p1|Solution: Question 1]] **Question 2.** Write the followin... ac{1}{2+3i}$ \\ [[math-11-nbf:sol:unit01:ex1-1-p2|Solution: Question 2]] **Question 3.** Simplify the follo
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- ====== Question 2, Exercise 1.1 ====== Solutions of Question 2 of Exercise 1.1 of Unit 01: Complex Numbers. ... ex number in the form $x+iy$: $(3+2i)+(2+4i)$ ** Solution. ** \begin{align}&(3+i2)+(2+i4)\\ =&(3+2)+(i2+i... lex number in the form $x+iy$: $(4+3i)-(2+5i)$ **Solution.** \begin{align}&(4+3i)-(2+5i)\\ =&(4-2)+(3i-5i... lex number in the form $x+iy$: $(4+7i)+(4-7i)$ **Solution.** \begin{align} &(4+7i)+(4-7i)\\ =&(4+4)+(7i-7
- Question 3, Exercise 1.3 @math-11-nbf:sol:unit01
- ====== Question 3, Exercise 1.3 ====== Solutions of Question 3 of Exercise 1.3 of Unit 01: Complex Numbers. ... ratic equation: $\dfrac{1}{3} z^{2}+2 z-16=0$. **Solution.** Given \begin{align}&\dfrac{1}{3}z^{2}+2 z-16=0... 57}}}{2} \\ &= -3 \pm \sqrt{57} \end{align} Hence Solution set $=\{ -3 \pm \sqrt{57} \}$. ====Question 3(i... uadratic equation: $z^{2}-\frac{1}{2} z+17=0$. **Solution.** Given $$ z^{2} - \frac{1}{2}z + 17 = 0 $$ Usi