Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 05:01:10 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-7-p8 Question 17 and 18, Exercise 4.7 Solutions of Question 17 and 18 of Exercise 4.7 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n$$2^{2}+5^{2}+8^{2}+\ldots$$2+5+8+\ldots$$a_k=2+(k-1)(3)=2+3k-3=3k-1$$T_k$$k$\begin{align*}T_k&=(3k-1)^2 \\ &=9k^2-6k+1. \end{align*}\begin{align*}\sum_{k=1}^{n} T_{k} &= \sum_{k=1}^{n} (9k^{2} - 6k + 1)\\ & = 9\sum_{k=1}^{n} k^{2} … anonymous@undisclosed.example.com (Anonymous) Fri, 04 Oct 2024 19:06:41 +0000 https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-7-p11 Question 21 and 22, Exercise 4.7 Solutions of Question 21 and 22 of Exercise 4.7 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n$$1 \times 4+2 \times 7+3 \times 10+\cdots$$4+7+10+\ldots$$a_k=4+(k-1)(3)=4+3k-3=3k+1$$1+2+3+...$$k$$k(3k+1)$$T_k$$k$\begin{align*}T_k&=k(3k+1) \\ &=3k^2+k. \end{align*}\begin{align*}\sum_{k=1}^{n} T_{k} &= \sum_{k=1}^{n} (3k^2 +k)\… anonymous@undisclosed.example.com (Anonymous) Fri, 04 Oct 2024 19:06:33 +0000 https://www.mathcity.org/math-11-nbf/definitions Definitions: Mathematics 11 NBF Model Textbook of Mathematics for Class XI is published by National Book Foundation (NBF), Islamabad, Pakistan. NBF can be considered as Federal Textbook Board Islamabad. The book has total of nine (9) chapters. Definition of the book provide the quick overview of the book.$x+iy$$x,y\in\mathbb{R}$$i^2=1$$\mathbb{C}$$x+i y$$x$$y$$x$$y$$Re(z)=x$$Im(z)=y$$z=x+i y$$\bar{z}$$\bar{z}=x-i y$$z=x+i y$$|z|$$|z|=\sqrt{x^{2}+y^{2}}$$z=x+iy$$Re(z)=x$$Im(z)=y$$Re(z^{-1})= \d… anonymous@undisclosed.example.com (Anonymous) Wed, 10 Jul 2024 18:51:53 +0000 https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-2-p9 Question 14 and 15, Exercise 4.2 Solutions of Question 14 and 15 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $b$$10$$b$$20$$a= b$$b=20$\begin{align*} &\text{A.M.} = \frac{a + b}{2} \\ \implies & 10 = \frac{b + 20}{2} \\ \implies & 20 = b + 20 \\ \implies & b = 20 - 20 \\ \implies & b = 0 \end{align*}$b = 0$$b$$25$$b$$20$$b$$10$$b$$-10$$x$$y$… anonymous@undisclosed.example.com (Anonymous) Fri, 20 Sep 2024 18:31:40 +0000 https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-4-p10 Question 20 and 21, Exercise 4.4 Solutions of Question 20 and 21 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $$3 , \_\_\_ , \_\_\_ , \_\_\_ , 48$$$a_1=3$$a_5=48$$r$$$ a_n=ar^{n-1}. $$\begin{align*} &a_5=a_1 r^4 \\ \implies & 48=3r^4 \\ \implies & r^4 = 16 \\ \implies & r^4 = 2^4 \\ \implies & r = 2. \end{align*}\begin{align*} & a_2=a_1 r= (3… anonymous@undisclosed.example.com (Anonymous) Sun, 22 Sep 2024 18:26:02 +0000 https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-4-p15 Question 30, Exercise 4.4 Solutions of Question 30 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $=a_1= 1$$=a_2= 3$$=a_3=3\times 3 = 9$$=a_4=3\times 9 = 27$$=a_5=3\times 27 = 81$$81$$a_1=1$$r=3$$a_5=?$$$a_n=a_1 r^{n-1}.$$\begin{align*} a_5&=a_1 r^4 \\ &=(1)(3)^4 = 81 \end{align*}$$S_n=a_1+a_2+a_3+a_4+a_5.$$ anonymous@undisclosed.example.com (Anonymous) Sun, 22 Sep 2024 18:26:05 +0000 https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-7-p9 Question 19 and 20, Exercise 4.7 Solutions of Question 19 and 20 of Exercise 4.7 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n$$1^{3}+3^{3}+5^{3}+$$1+3+5+\ldots$$a_k=1+(k-1)(2)=1+2k-2=2k-1$$T_k$$k$\begin{align*}T_k&=(2k-1)^3 \\ &=(2k)^3+3(2k)^2(-1)+3(2k)(-1)^2+(-1)^3 \\ &=8k^3-12k^2+6k+1 \end{align*}\begin{align*}\sum_{k=1}^{n} T_{k} &= \sum_{k=1}^{n} (8k^… anonymous@undisclosed.example.com (Anonymous) Fri, 04 Oct 2024 19:06:43 +0000 https://www.mathcity.org/math-11-nbf/sol/unit04/ex4-7-p10 Question 19 and 20, Exercise 4.7 Solutions of Question 19 and 20 of Exercise 4.7 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n$$1^{3}+3^{3}+5^{3}+$$1+3+5+\ldots$$a_k=1+(k-1)(2)=1+2k-2=2k-1$$T_k$$k$\begin{align*}T_k&=(2k-1) \\ &=9k^2-6k+1. \end{align*}\begin{align*}\sum_{k=1}^{n} T_{k} &= \sum_{k=1}^{n} (2k - 1)\\ & = 2 \sum_{k=1}^{n} k - \sum_{k=1}^{n} 1 \… anonymous@undisclosed.example.com (Anonymous) Fri, 04 Oct 2024 19:06:32 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-1 Exercise 6.1 (Solutions) The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n!$$$ n!=\left\{\begin{array}{l} n(n-1)(n-2)\cdot \ldots \cdot 3 \cdot 2 \cdot 1 \text{ if } n\geq 1,\\ 1 \text{ if } n=0. \end{array} \right. $$$10!$$\dfrac{12!}{7! 3! 2!}$$\dfrac{4!-2!}{3!+5!}$$\dfrac… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:40 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2 Exercise 6.2 (Solutions) The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n!$$$ n!=\left\{\begin{array}{l} n(n-1)(n-2)\cdot \ldots \cdot 3 \cdot 2 \cdot 1 \text{ if } n\geq 1,\\ 1 \text{ if } n=0. \end{array} \right. $$$n \in \mathbb{N}$${ }^n P_r=\frac{n!}{(n-r)!}$$\quad{ }^… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:59 +0000