Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 17:05:00 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/wiki/welcome Welcome to your new DokuWiki Congratulations, your wiki is now up and running. Here are a few more tips to get you started. Enjoy your work with DokuWiki, -- the developers Create your first pages Your wiki needs to have a start page. As long as it doesn't exist, this link will be red: anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:13 +0000 https://www.mathcity.org/math-11-kpk/sol/unit06/re-ex6-p6 Question 9 & 10 Review Exercise 6 Solutions of Question 9 & 10 of Review Exercise 6 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$2,3,0,3,4,2,3$$1$$=100,0000$$$=\dfrac{7 !}{3 ! \cdot 2 !}=420 $$$1$$0$$7$$0$$$=\dfrac{6 !}{2 ! 3 !}=60 $$$1$$420-50=360$$n$$n$$(n-1)$$(n - 1)$$(n-1)$$(n-2) !$$2$$2 !$$n$$$(n-2) ! \cdot 2 !=2(n-2) ! $$ anonymous@undisclosed.example.com (Anonymous) Thu, 01 Feb 2024 02:36:03 +0000 https://www.mathcity.org/math-11-nbf/sol/unit01/ex1-2 Exercise 1.2 (Solutions) The solutions of the Exercise 1.2 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to real and imaginary part of complex numbers, modulus and conjugate of the complex numbers.$\operatorname{Re}(i z)=-\operatorname{Im}(z)$$\operatorname{Im}(i z)=\operatorname{Re}(z)$$$\left(z_{1} z_{2}\right)\left(z_{3} z_{4… anonymous@undisclosed.example.com (Anonymous) Mon, 27 Oct 2025 18:50:09 +0000 https://www.mathcity.org/atiq/fa23-mth480 MTH480: Introductory Quantum Mechanics Objective The physical principles and mathematical formalism of quantum theory, with emphasis on applications to atomic, molecular, and many-body physics; scattering phenomena; and electromagnetism (photon physics). $x(t)={{t}^{3}}+2\sin t$$t=\dfrac{\pi }{6}$$v(t)={{t}^{2}}+t{{e}^{t}}$ anonymous@undisclosed.example.com (Anonymous) Sat, 07 Oct 2023 18:27:32 +0000 https://www.mathcity.org/quote-of-the-day/apr Quotes for the April کاسمولوجسٹ اکثر غلط ہوتے ہیں، لیکن کبھی شک میں نہیں۔۔۔ لیو لینڈاؤ (1908-1968) Cosmologists are often wrong, but never in doubt. --- Lev Landau (1908-1968) (Courtesy: MacTutor) anonymous@undisclosed.example.com (Anonymous) Fri, 28 Apr 2023 18:32:46 +0000 https://www.mathcity.org/quote-of-the-day/mar Quotes for the March “نئی ریاضی” کی اہمیت بنیادی طور پر اس حقیقت میں پنہاں ہے کہ اس نے ہمیں ڈسک اور دائرے کے درمیان فرق سکھایا ہے۔ [اسحاق ٹودھنٹر (1820-1884)] anonymous@undisclosed.example.com (Anonymous) Fri, 28 Apr 2023 18:08:23 +0000 https://www.mathcity.org/wiki/syntax Formatting Syntax DokuWiki supports some simple markup language, which tries to make the datafiles to be as readable as possible. This page contains all possible syntax you may use when editing the pages. Simply have a look at the source of this page by pressing anonymous@undisclosed.example.com (Anonymous) Sat, 10 Feb 2024 11:07:05 +0000 https://www.mathcity.org/math-11-kpk/sol/unit04/ex4-5-p10 Question 15 & 16 Exercise 4.5 Solutions of Question 15 & 16 of Exercise 4.5 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$2$$4$$15^{\text {th }}$$a_1=R s .1$$a_2=R s .2$$a_3=R s .4$$1,2,4,8, \ldots$$a_1=1 . \quad r=2 . \quad n=15$$a_n=a_1 r^{n-1}$$15^{1 / 2}$$$a_{15}=a_1 r^{14} $$$$a_{15}=1 .(2)^{1 4}=R s .16384 $$$$S_{30}=\dfrac{a_1(r^{30}-1)}{r-1} $$$r-2$$a_1=1$\begi… anonymous@undisclosed.example.com (Anonymous) Fri, 05 Jan 2024 17:30:06 +0000 https://www.mathcity.org/math-11-kpk/sol/unit10/ex10-1-p6 Question 6, Exercise 10.1 Solutions of Question 1 of Exercise 10.1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$\cos \alpha =2{{\cos }^{2}}\dfrac{\alpha }{2}-1=1-2{{\sin }^{2}}\dfrac{\alpha }{2}$\begin{align}\cos \alpha &=\cos 2\dfrac{\alpha }{2}\\ &={{\cos }^{2}}\dfrac{\alpha }{2}-{{\sin }^{2}}\dfrac{\alpha }{2}\\ &={{\cos }^{2}}… anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 02:45:42 +0000 https://www.mathcity.org/math-11-nbf/sol/unit01/ex1-2-p7 Question 7, Exercise 1.2 Solutions of Question 7 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. Question 7 $\sqrt{2}|z| \geq|\operatorname{Re}(z)|+|\operatorname{Im}(z)| \quad$$\left(|x|-|y|)^{2} \geq 0\right)$\begin{align} &\left(|x|-|y|)^{2} \geq 0\right) \\ \implies & |x|^2+|y|^2-2|x||y| \geq 0 \\ \implies & |x|^2+|y|^2 \geq 2|x||y| \\ \implie… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Jul 2024 13:32:58 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p4 Question 4 and 5, Exercise 6.2 Solutions of Question 4 and 5 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $3$$1,2,3,4,5,6,$$3$$6$$\mathrm{I}:$$2$$$\underline{ },\underline{ },\underline{2}$$$={ }^{5} P_{2}=20$$4$$$\underline{ },\underline{ },\underline{4}$$$={ }^{5} P_{2}=20$$6$$$\underline{ },\underline{ },\underline{6}$$$={ }^{5} P_… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:51 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p6 Question 8 and 9, Exercise 6.2 Solutions of Question 8 and 9 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $4$$5$$5$$4$$41$$=41 \times 41=576$$2$$3$$4$$$\text{Total flags} =9$$$$\text{Repetition of blue }=2$$$$\text{Repetition of yellow}=3$$$$\text{Repetition of green}=4$$\begin{align*}\text{Total signals }&=\dfrac{9!}{2!3!4!}\\ &=\dfr… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:54 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p12 Question 20 and 21, Exercise 6.2 Solutions of Question 20 and 21 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $6$$6$$5!$$6$$6!$$=5! \times 6!=86400$$= n = 4$$= {}^4P_4 = 24.$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:45 +0000