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- Question 18 and 19, Exercise 6.2 @math-11-nbf:sol:unit06
- ad, Pakistan. =====Question 18===== Howmany odd numbers less than $10,000$ can be formed using the digit... digits. ** Solution. ** We must make $4$ digit numbers to keep the number less that $10000$\\ and digit at unit place must be either $3$ or $5$ to make number odd.\\ Possible numbers starting with $0$ and end
- Unit 01: Complex Numbers (Solutions)
- ===== Unit 01: Complex Numbers (Solutions) ===== {{ :math-11-nbf:sol:math-11-nbf-sol-unit01.jpg?nolink&400x335|Unit 01: Complex Numbers (Solutions)}} This is a first unit of the book M... the students will be able to * Recall complex number $z$ and recognize its real and imaginary part. * Know the condition for equality of two complex numbers. * Revising the basic operations on complex nu
- Question 1, Exercise 1.4 @math-11-nbf:sol:unit01
- of Question 1 of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... kistan. =====Question 1(i)===== Write a complex number $2+i 2 \sqrt{3}$ in polar form. ** Solution. ** ... ) = \frac{\pi}{3}. \end{align} Since the complex number \( 2 + i 2 \sqrt{3} \) lies in the first quadrant... ==Question 1(ii)===== Write the following complex number $3-i \sqrt{3}$ in polar form. ** Solution. ** L
- Question 6(i-ix), Exercise 1.4 @math-11-nbf:sol:unit01
- stion 6(i-ix) of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... =====Question 6(i)===== Write a given complex number in the algebraic form: $\sqrt{2}\left(\cos 315^{\... n} =====Question 6(ii)===== Write a given complex number in the algebraic form: $5\left(\cos 210^{\circ}+i... } =====Question 6(iii)===== Write a given complex number in the algebraic form: $2\left(\cos \dfrac{3 \pi}
- Exercise 6.2 (Solutions) @math-11-nbf:sol:unit06
- ion 3 ]] **Question 4.** How many 3 -digit even numbers can be formed from the digits $1,2,3,4,5,6$, if ... & 5 ]] **Question 5.** How many 7 -digits mobile number can be made using the digits 0 to 9 , if each number starts with 5 and no digit is repeated?\\ [[math-11-... stion 4 & 5 ]] **Question 6.** How many 4 -digit numbers can be formed with the digits $1,2,3,4,5,6$ when
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- of Question 2 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... ====Question 2(i)==== Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)$ ** Solution.... ===Question 2(ii)==== Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)$ **Solution.*... ==Question 2(iii)==== Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)$ **Solution.*
- Question 6(x-xvii), Exercise 1.4 @math-11-nbf:sol:unit01
- ion 6(x-xvii) of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... . =====Question 6(x)===== Write a given complex number in the algebraic form: $7 \sqrt{2}\left(\cos \dfr... // =====Question 6(xi)===== Write a given complex number in the algebraic form: $10 \sqrt{2}\left(\cos \df... =====Question 6(xii)===== Write a given complex number in the algebraic form: $2\left(\cos\dfrac{5\pi}{2
- Question 1, Review Exercise 6 @math-11-nbf:sol:unit06
- "a1" collapsed="true">%%(b)%%: $6$</collapse> ii. Numbers of ways of arrangement of the word "GARDEN"\\ ... apse> iii. The product of $r$ consective positive numbers is divisible by \\ * (a) $r!$\\ * (b)$... llapsed="true">(a): $r!$</collapse> iv. The total number of $6$-digit number in which all the odd and only odd digits appear is:\\ * (a) $\dfrac{5}{2}\,\,6!$\
- Question 4 and 5, Exercise 6.2 @math-11-nbf:sol:unit06
- n. =====Question 4===== How many $3$-digit even numbers can be formed from the digits $1,2,3,4,5,6,$ if ... digits out of given $6$ digits to make a F3-digit number.\\ To ensure the created number is even we have to choose the right most digit of number to be even.\\ Case $\mathrm{I}:$ If unit digit (r
- Question 1, Review Exercise @math-11-nbf:sol:unit01
- Question 1 of Review Exercise of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... === Chose the correct option. i. Every real number is also a number. * (a) natural * (b) integer * %%(c)%% complex * (d) rational \\ <btn... ">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\mathrm{s})$. * (a
- Question 4, 5 and 6, Review Exercise 6 @math-11-nbf:sol:unit06
- kistan. =====Question 4===== How mant six-digit numbers can be formed using the digits $0,2,3,4,5,7$ wit... utations starting with $0$ results into $5$ digit number,\\ and number of such permutations is $$5!=120$$ Number of $6-$digits numbers formed $$=720-120=600$$ =====Question 5=
- Question 2, Exercise 1.2 @math-11-nbf:sol:unit01
- of Question 2 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... ion 2==== Use the algebraic properties of complex numbers to prove that $$ \left(z_{1} z_{2}\right)\left(z... quired result. **Remark:** For any three complex numbers $z_1$, $z_2$ and $z_3$, we have $$z_1 (z_2 z_3) ... $$ Logically, z_1 z_2 z_3 has no meaning as three number cannot be multiplies simultanously, but associate
- Question 16 and 17, Exercise 6.2 @math-11-nbf:sol:unit06
- d, Pakistan. =====Question 16===== How many odd numbers can be formed by using the digits $1,2,3,4,5,6$ ... ** Solution. ** If digit at units place is odd, number is odd.\\ We shall fix unit place with $1, 3$ or ... and calculate arrangements of remaining digits.\\ Number of six digit odd numbers $=3 \times{ }^{5} P_{5}=360$ =====Question 17===== How many $4$-digit odd numbe
- Question 4, Exercise 1.1 @math-11-nbf:sol:unit01
- of Question 4 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... . ====Question 4(i)==== Find the values of real number $x$ and $y$ in each of the following: $(2+3i)x+(1... ====Question 4(ii)==== Find the values of real number $x$ and $y$ in each of the following: $\dfrac{x}{... ====Question 4(iii)==== Find the values of real number $x$ and $y$ in each of the following: $\dfrac{x}{
- Question 6, Exercise 1.1 @math-11-nbf:sol:unit01
- of Question 6 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics f... estion 6(i)==== Find the conjugate of the complex number $4-3 i$. **Solution.** Given: $z=4-3 i$, then $... stion 6(ii)==== Find the conjugate of the complex number $3 i+8$. **Solution.** Do Yourself ====Question 6(iii)==== Find the conjugate of the complex number $2+\sqrt{\dfrac{-1}{5}}$. **Solution.** Given: