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- Unit 04: Sequences and Seeries
- n this page we have provided the solutions of the questions. After reading this unit the students will be a... olutions)"> * [[math-11-nbf:sol:unit04:ex4-1-p1|Question 1 & 2]] * [[math-11-nbf:sol:unit04:ex4-1-p2|Question 3 & 4]] * [[math-11-nbf:sol:unit04:ex4-1-p3|Question 5 & 6]] * [[math-11-nbf:sol:unit04:ex4-1-p4|Questi
- Exercise 6.2 (Solutions) @math-11-nbf:sol:unit06
- given on this page. This exercise consists of the question related to factorial function. The book misses t... t{ if } n=0. \end{array} \right. $$ </callout> **Question 1.** Prove the following for $n \in \mathbb{N}$.\... -2}$\\ [[math-11-nbf:sol:unit06:ex6-2-p1|Solution Question 1]] **Question 2.** Find $n$, if:\\ (i) $\quad n P_4=20^n P_2$ (ii) ${ }^{2 n} P_3=100{ }^n P_2$ (iii) $16
- Unit 08: Fundamental of Trigonometry
- n this page we have provided the solutions of the questions. After reading this unit the students will be a... olutions)"> * [[math-11-nbf:sol:unit08:ex8-1-p1|Question 1]] * [[math-11-nbf:sol:unit08:ex8-1-p2|Question 2 ]] * [[math-11-nbf:sol:unit08:ex8-1-p3|Question 3]] * [[math-11-nbf:sol:unit08:ex8-1-p4|Question 4]]
- Exercise 6.3 (Solutions) @math-11-nbf:sol:unit06
- given on this page. This exercise consists of the question related to factorial function. **Question 1(i-v).** Prove the following for $n \in \mathbb{N}$.\\ (i) ${ ... r}$\\ [[math-11-nbf:sol:unit06:ex6-3-p1|Solution: Question 1(i-v)]] **Question 1(vi-x).** Prove the following for $n \in \mathbb{N}$.\\ (vi) ${ }^{2 n} \mathrm{C}_{\
- Exercise 2.2 (Solutions) @math-11-nbf:sol:unit02
- given on this page. This exercise consists of the question related to sum, product and different operations on matrices. **Question 1.** Construct a matrix $A=\left[a_{i j}\right]$ ... {3}$\\ [[math-11-nbf:sol:unit02:ex2-2-p1|Solution:Question 1]] **Question 2.** Construct a matrix $B=\left[a_{\ell}\right]$ of order $3 \times 3$ for which:\\ (i) $b
- Exercise 1.4 (Solutions) @math-11-nbf:sol:unit01
- given on this page. This exercise consists of the question related to polar form of the complex numbers. **Question 1.** Write the following complex number in polar ... }}$\\ [[math-11-nbf:sol:unit01:ex1-4-p1|Solution: Question 1]] **Question 2.** Write the following complex number in rectangular form.\\ (i) $\left(\cos \dfrac{\pi}{
- Unit 05: Polynomials
- n this page we have provided the solutions of the questions. After reading this unit the students will be a... olutions)"> * [[math-11-nbf:sol:unit05:ex5-1-p1|Question 1]] * [[math-11-nbf:sol:unit05:ex5-1-p2|Question 2 & 3]] * [[math-11-nbf:sol:unit05:ex5-1-p3|Question 4 & 5]] * [[math-11-nbf:sol:unit05:ex5-1-p4|Questi
- Unit 09: Trigonometric Functions
- n this page we have provided the solutions of the questions. After reading this unit the students will be a... olutions)"> * [[math-11-nbf:sol:unit09:ex9-1-p1|Question 1]] * [[math-11-nbf:sol:unit09:ex9-1-p2|Question 2 ]] * [[math-11-nbf:sol:unit09:ex9-1-p3|Question 3]] * [[math-11-nbf:sol:unit09:ex9-1-p4|Question 4(i-
- Exercise 1.2 (Solutions) @math-11-nbf:sol:unit01
- given on this page. This exercise consists of the question related to real and imaginary part of complex num... modulus and conjugate of the complex numbers. **Question 1.** Show that for any complex number :\\ (i) $\o... z)$\\ [[math-11-nbf:sol:unit01:ex1-2-p1|Solution: Question 1]] **Question 2.** Use the algebraic properties of complex numbers to prove that $$\left(z_{1} z_{2}\righ
- Exercise 6.1 (Solutions) @math-11-nbf:sol:unit06
- given on this page. This exercise consists of the question related to factorial function. The book misses t... t{ if } n=0. \end{array} \right. $$ </callout> **Question 1.** Evaluate the following:\\ (i) $10!$ (ii) $\d... $ \\ [[math-11-nbf:sol:unit06:ex6-1-p1|Solution: Question 1]] **Question 2.** Write the following in factorial form:\\ (i) 14.13 .12 .11 (ii) 1.3.5.7.9 (iii) $n\lef
- Review Exercise 1 (Solutions) @math-11-nbf:sol:unit01
- given on this page. This exercise consists of the question related to polar form of the complex numbers. **Question 1.** Choose the correct option.\\ [[math-11-nbf:sol:unit01:re-ex-p1|Solution: Question 1]] **Question 2.** Find the value of the following:\\ (i) $i^{2}+i^{4}+i^{6}+\cdots+i^{100}$\\ (ii) $\l
- Exercise 1.1 (Solutions) @math-11-nbf:sol:unit01
- given on this page. This exercise consists of the question related to sum, product and division of the complex numbers. **Question 1.** Evaluate :\\ (i) ${{i}^{31}}$ (ii) ${{\left(... }$ \\ [[math-11-nbf:sol:unit01:ex1-1-p1|Solution: Question 1]] **Question 2.** Write the following complex number in the form $x+iy$:\\ (i) $(3+2i)+(2+4i)$ (ii) $(4+
- Exercise 2.3 (Solutions) @math-11-nbf:sol:unit02
- given on this page. This exercise consists of the question related to determinant and inverse of the matrix. **Question. 1** Evaluate the determinant of the following ma... ht]$\\ [[math-11-nbf:sol:unit02:ex2-3-p1|Solution:Question 1]] **Question. 2** Evaluate the determinants of the following matrices using cofactor method.\\ (i) $\l
- 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. This is unit of... ederal Textbook Board, Islamabad, Pakistan. ====Question 1(i)==== Factorize the polynomial into linear fun... (13i)^2 \\ = &(z + 13i)(z - 13i). \end{align} ====Question 1(ii)==== Factorize the polynomial into linear fu
- 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: Complex Numbers. Thi... deral Textbook Board, Islamabad, Pakistan. =====Question 6(i)===== Write a given complex number in the al... {i}{\sqrt{2}} \right) \\ =& 1-i. \end{align} =====Question 6(ii)===== Write a given complex number in the al