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B-Course of Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:55 +0000

B-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha.$(\lambda ,\mu )$

A-Course of Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:54 +0000

A-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha.

FSc Part 1 (KPK Boards)

anonymous@undisclosed.example.com (Anonymous) — Tue, 12 Dec 2023 17:30:33 +0000

FSc Part 1 (KPK Boards) These are the notes of old book. The notes of new book is AVAILABLE HERE [FSc Part 2 KPTP] Notes of FSc Part 1 of “A Textbook of Mathematics For Class XI” published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated.$P(z)$$(\sum)$$\sum n$$\sum n^2$$\sum n^3$$n$$n$$$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+...$$$^nP_r$$^nC_r=\left(\begin{smallm…

General Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:55 +0000

General Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha (UoS), Sargodha.

Syllabus & Paper Pattern for General Mathematics (Split Program)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:21 +0000

Syllabus & Paper Pattern for General Mathematics (Split Program) There was one examination after two years for BA/BSc Program from University of Punjab (PU), Lahore but from this year (2016), PU has made changes in its examination policies for the said program. The BA/BSc Program has been split into two parts. Syllabus is break into two part year wise. After the each year of the program candidate has to appeared in examination instead of appearing after two year. In this regards syllabus of Gen…

Short Questions by Mr. Akhtar Abbas

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:09 +0000

Short Questions by Mr. Akhtar Abbas * We are very thankful to Mr. Akhtar Abbas for sharing these short questions. * These short questions are selected from previous 5 years papers of different boards. Solve these at your own to perform well in annual exams.

Online View

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:19 +0000

Online View List of all chapters * Key to MCQs by Muhammad Imran Qureshi * Chapter 01 * Chapter 02 * Chapter 03 * Chapter 04 * Chapter 05 * Chapter 06 * Chapter 07 * Chapter 08 * Chapter 09 * Chapter 10 * Chapter 11 * Chapter 12 * Chapter 13 * Chapter 14

View

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:20 +0000

View * We are very thankful to Mr. Akhtar Abbas for sharing these short questions. These short questions are selected from previous five years papers of different boards. Solve these at your own to perform well in annual examination. Recommended book for these short questions is “Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore)”. But any student Mathematics can get benefit from it.

MCQs by Muhammad Imran Qureshi

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:06 +0000

MCQs by Muhammad Imran Qureshi MCQs of the Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. To see the keys of the MCQs, please see Key to MCQs by Muhammad Imran Qureshi. * Chapter 01 | View Online | Download PDF (166KB) * Chapter 02 | View Online | Download PDF (77KB)

MCQs by Nauman Idrees

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:06 +0000

Handwritten Notes of Real Analysis by Asim Marwat

anonymous@undisclosed.example.com (Anonymous) — Sat, 15 Apr 2023 17:26:13 +0000

Handwritten Notes of Real Analysis by Asim Marwat [Handwritten Notes of Real Analysis by Asim Marwat] Real analysis is a branch of mathematics that analyses how real numbers, sequences and series, and real functions behave. It focuses on real numbers and frequently extends the real line by including positive and negative infinity. Real analysis investigates a number of the properties of real-valued sequences and functions, including convergence, limits, continuity, smoothness, differentiabilit…

FSc-I Mathematics KPK: View Online

anonymous@undisclosed.example.com (Anonymous) — Tue, 12 Dec 2023 17:08:04 +0000

FSc-I Mathematics KPK: View Online These are the notes of old book. The notes of new book is AVAILABLE HERE On this page one can view the PDF of solutions of the A Textbook of Mathematics For Class XI” published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. These notes are written by

Vector Analysis by Hameed Ullah: Notes

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:13 +0000

Vector Analysis by Hameed Ullah: Notes [right triangle in semi circle] Note of vector analysis by Hammed Ullah. These notes are send by Umer Asghar, we are very thankful to him for providing these notes. These notes are for helpful for undergraduate level (BSc or BS). Name Notes of vector analysis

FSc-II Mathematics KPK: View Online

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:19 +0000

FSc-II Mathematics KPK: View Online On this page one can view the PDF of solutions of the “Textbook of Mathematics Grade 12” published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. These notes are written by khalid. Link to PDF is given at the end of preview.

MTH321: Real Analysis I (Spring 2023)

anonymous@undisclosed.example.com (Anonymous) — Wed, 14 Jun 2023 14:47:57 +0000

MTH321: Real Analysis I (Spring 2023) ~~DISCUSSION~~ [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform con…

Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad

anonymous@undisclosed.example.com (Anonymous) — Sat, 24 May 2025 18:13:54 +0000

Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad [Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book.

Definitions: FSc Part 1 (Mathematics): PTB

anonymous@undisclosed.example.com (Anonymous) — Sun, 22 Sep 2024 17:12:21 +0000

Definitions: FSc Part 1 (Mathematics): PTB On this page, all the definitions of “Textbook of Algebra and Trigonometry Class XI, published by Punjab Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to Muhammad Waqas Sulaiman for his valuable contribution.$\frac{p}{q}$$p,q \in \mathbb{Z}$$q\neq 0$$\frac{p}{q}$$p,q \in \mathbb{Z}$$q\neq 0$$\mathbb{R}$$0.3333....,21.134134$$\pi = 3.1415...$$\divideontimes$$z=x+iy$$x,y \in \mathbb{R}, i = \sqrt{-1}$$x$$y$$z$$2, 3+\sqrt{3}i, \fra…

Complex Analysis (Notes) by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Sun, 06 Aug 2023 09:33:02 +0000

Complex Analysis (Notes) by Ms. Iqra Liaqat [Notes of Complex Analysis by Ms. Iqra Liaqat] These notes are send by Ms. Iqra Liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org Complex analysis is the study of functions of complex numbers. It is useful in a variety of mathematical fields, such as algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics fields like…

FBISE Annual 2009

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:16 +0000

FBISE Annual 2009 * FSc part 1 (HSSC-I) mathematics paper conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been analyse on this web page with the help of chart. Three type of chart are given in which one includes bar chart between chapters and marks, 2nd one include relation between algebraic and trigonometric portion and 3rd one contains pie chart which show the portion of questions from exercises to non-exercise question from book a

FBISE Annual 2011

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:18 +0000

FBISE Annual 2011 * FSc part 1 (HSSC-I) mathematics paper conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been analyse on this web page with the help of chart. Three type of chart are given in which one includes bar chart between chapters and marks, 2nd one include relation between algebraic and trigonometric portion and 3rd one contains pie chart which show the portion of questions from exercises to non-exercise question from book a

FBISE Annual 2012

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:18 +0000

FBISE Annual 2012 * FSc part 1 (HSSC-I) mathematics paper conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been analyse on this web page with the help of chart. Three type of chart are given in which one includes bar chart between chapters and marks, 2nd one include relation between algebraic and trigonometric portion and 3rd one contains pie chart which show the portion of questions from exercises to non-exercise question from book a

Notes of Vector Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:54 +0000

Notes of Vector Analysis [Vector Ananlysis] Notes of the vector analysis are given on this page. These notes are helpful for BSc or equivalent classes. These notes are written by Amir Taimur Mohmand of University of Peshawar. The books of these notes is not known. If you know about the book, please inform us.$f$$P$

Real Analysis Notes by Prof Syed Gul Shah

anonymous@undisclosed.example.com (Anonymous) — Mon, 17 Apr 2023 04:04:23 +0000

Real Analysis Notes by Prof Syed Gul Shah [Real Analysis Notes by Prof Syed Gul Shah] Real analysis, a discipline that explores the complexities of mathematical functions, limits, and sequences, can often be a difficult topic for students. Prof. Syed Gul Shah, as a true analyst, not only excelled in the subject but also gained fame for his extraordinary qualities as a human being.$s_n\frac{1}{2}s$$\{s_n\}$…

Syllabus & Paper Pattern for A and B Course of Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:18 +0000

Syllabus & Paper Pattern for A and B Course of Mathematics This is a new page created to discuss the syllabus or course outline of PU splitted into two part. It will take some time to complete this page. Please stay in touch with this page to be updated.

Applied Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:54 +0000

Applied Mathematics Paper pattern for Applied Mathematics chapter-wise for University of Sargodha is given on this page. This pattern is extracted from syllabus, so use your own risk. Syllabus of Applied Mathematics can be seen here. Applied Mathematics is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. In every paper there are three sections with four questions each. A student have to attempt two questions from each section.

MTH321: Real Analysis I (Fall 2021)

anonymous@undisclosed.example.com (Anonymous) — Fri, 28 Oct 2022 11:10:02 +0000

MTH321: Real Analysis I (Fall 2021) Discussion is available at the end of this page. One is free to ask any question or comment. [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphas…

MTH321: Real Analysis I (Spring 2020)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:41 +0000

MTH321: Real Analysis I (Spring 2020) Discussion is available at the end of this page. One is free to ask any question or comment. ~~DISCUSSION~~ [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and fun…

Notes of Calculus with Analytic Geometry

anonymous@undisclosed.example.com (Anonymous) — Mon, 30 May 2022 17:44:37 +0000

Notes of Calculus with Analytic Geometry [Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin] Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore-Pakistan is one of the books studied widely in Bachelor and undergraduate classes inclduing different engineering programs. There are total of ten chapters. Solutions of the books are given in the chapters listed below. The only aim to publish the soltuions is to pro…

Tests by Mobeen Munir

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:13 +0000

Tests by Mobeen Munir Calculus Chapter 01 ARW Chapter 1,2 & 5 (Important Questions) NEW Download PDF (6KB) ARW Chapter 01, Test 01 Download PDF (51KB) Method Chapter 01 ARW Chapter 01, Test 03 Download PDF (52KB) Chapter 03 ARW Chapter 03, Test 01 Download PDF (67KB) Calculus & Methods (Mixed)

Fundamental of Complex Analysis (Solutions of Some Exercises)

anonymous@undisclosed.example.com (Anonymous) — Sat, 15 Apr 2023 18:26:12 +0000

Fundamental of Complex Analysis (Solutions of Some Exercises) [Fundamental of Complex Analysis, Solutions of Some Exercises] Complex analysis is the study of functions that exist in the complex plane, that is, functions with complex arguments and complex outputs. With roots in the 18th century and the years just before, it is one of the classical branches of mathematics. In the 20th century, significant figures in mathematics who are connected to complex numbers include Euler, Gauss, Riemann, …

Vector & Tensor Analysis by Dr Nawazish Ali (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Sun, 06 Aug 2023 18:20:39 +0000

Vector & Tensor Analysis by Dr Nawazish Ali (Solutions) [Vector & Tensor Analysis by Dr Nawazish Ali (Solutions)] We are very thankful to Prof. Fazal Abbas Sajid for sharing these solutions. Vector & Tensor Analysis for Scientists and Engineers, by Prof. Dr. Nawazish Ali Shah is a famous book taught in different universities of the Pakistan. On this page, we have added the solutions of the exercises of the book. Solutions of Chapter 5 is written by

Chapter 12: Application of Trigonometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:34 +0000

Chapter 12: Application of Trigonometry [Chapter 12: Application of Trigonometry] Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction

General Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:58 +0000

General Mathematics Paper pattern for General Mathematics chapter-wise for University of Sargodha is given on this page. This pattern is provided by Muhammad Siraj (+92-345-5365318). Syllabus of General Mathematics can be seen here. General Mathematics is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. In every paper there are three sections with four questions. A student have to attempt two questions from each section.

Pure Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:03 +0000

Pure Mathematics Paper pattern for Pure Mathematics chapter-wise for University of Sargodha is given on this page. This pattern is extracted from syllabus, so use your own risk. Syllabus of Pure Mathematics can be seen here. Pure Mathematics is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. In every paper there are three sections with four questions each. A student have to attempt two questions from each section.

Fundamental of Complex Analysis: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:41 +0000

Fundamental of Complex Analysis: Viewer Solutions of some exercises from Fundamental of Complex Analysis written by Dr. M. Iqbal and published by Ilmi Kitab Khana, Lahore- PAKISTAN. These are handwritten notes by Prof.(Rtd) Muhammad Saleem. You can also download PDF of solutions from this page.

MTH321: Real Analysis 1

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:06 +0000

MTH321: Real Analysis 1 At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous func…

MTH321: Real Analysis I (Fall 2019)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:11 +0000

MTH321: Real Analysis I (Fall 2019) [Photo-illustration of Zeno's Paradox by Juliana Jiménez Jaramillo. Photo by Twildlife/Thinkstock] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Def…

MTH321: Real Analysis 1 (Spring 2015)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:32 +0000

MTH321: Real Analysis 1 (Spring 2015) At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about c…

MTH322: Real Analysis II (Spring 2016)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:34 +0000

MTH322: Real Analysis II (Spring 2016) This course was teach to MSc III and IV. Course Contents: Sequences of functions: convergence, uniform convergence, uniform convergence and continuity, uniform convergence and integration, uniform convergence and differentiation, the exponential and logarithmic function, the trigonometric functions.

Measure Theory Handwritten Notes by Asim Marwat

anonymous@undisclosed.example.com (Anonymous) — Fri, 10 Feb 2023 17:43:56 +0000

Measure Theory Handwritten Notes by Asim Marwat [Measure Theory Notes by Asim Marwat] These notes are made and shared by Mr. Asim Marwat. He has our sincere gratitude for supplying these notes, and we value his effort in having them published on MathCity.org. Measure Theory is an important subject in BS Mathematics. These notes contain topic from base level, like equivalence set, to advance level, like convergent in measure.$L_p$$L_p$$L^\infty$$L_p$

Fill in the blanks by Rauf & Nabeel

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:06 +0000

Fill in the blanks by Rauf & Nabeel * Fill in the blanks, provided by Adil Rauf & Muhammad Nabil (F.Sc. Part I, Session: 2003-05, FAZMIC Sargodha) * Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) Chapter 02 Download PDF (93KB)

Chapter 01: Number System

anonymous@undisclosed.example.com (Anonymous) — Sat, 03 Jun 2023 16:30:31 +0000

Chapter 01: Number System [Chapter 01: Number System] Notes (Solutions) of Chapter 01: Number System, Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Rational numbers and irrational numbers$\mathbb{C}$$(x+iy)^n$$\left(\frac{x_1+iy_1}{x_2+iy_2}\right)^n, x_2+iy_2\neq 0$$\sqrt{-1}=i$$\sqrt{-1}$$i$$-i$$i$$-i$$-1$$i^2=-1$$\sqrt{-1}=i$$\sqrt{-1}$

Chapter 02: Sets, Functions and Groups

anonymous@undisclosed.example.com (Anonymous) — Wed, 05 Apr 2023 12:54:57 +0000

Chapter 02: Sets, Functions and Groups Notes (Solutions) of Chapter 02: Sets, Functions and Groups, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. [Chapter 02: Sets, Functions and Groups] Contents & summary * Introduction$p\leftrightarrow q$

Chapter 06: Sequences and Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:29 +0000

Chapter 06: Sequences and Series [Chapter 06: Sequences and Series] Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction * Types of Sequences$l,m,n$$p$$q$$r$$$l(q-r)+m(r-p)+n(p-q)=0$$$a_1$$d$$$\begin{align}l=a_1+(p-1)d,\\ m=a_1+(q-1)d,\\ n=a_1+(r-1)d.\end{align}$$ Now $$\begin{align}L.H.S &= l(q-r)+m(r-p)+n(p-q)\\ &= lq-lr+mr-mp+np-nq\\ &=…

Chapter 09: Fundamentals of Trigonometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 04 Jun 2023 16:03:04 +0000

Chapter 09: Fundamentals of Trigonometry [Chapter 09: Fundamentals of Trigonometry] Notes (Solutions) of Chapter 09: Fundamentals of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. This chapter has four exercise and solutions of those exercises are given below which can be downloaded in PDF format or can be viewed online.$D^\circ M'S''$$45^\circ , 30^\circ , 60^\circ$$0^\circ , 90^\circ , 180^\circ , 270^\circ , 36…

Chapter 10: Trigonometric Identities

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:32 +0000

Chapter 10: Trigonometric Identities [Chapter 10: Trigonometric Identities] Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. There are four exercise in this chapter.

Short Questions by Mr. Akhtar Abbas

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:47 +0000

Preparation Guide

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:44 +0000

Preparation Guide This guide is made by Mr. Anwar Khan, PhD. We are very thankful to him for sharing. This guide is helpful to prepare papers for MSc Mathematics (annual system) from University of Sargodha. Part 1 1. REAL ANAYSIS * Real Analysis (Notes by Syed Gul Shah) * Chapter # 08 sequences and series of Mathematical Method by SM Yousaf (solutions are available $z= f(x,y)$

MTH321: Real Analysis I (Fall 2015)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:08 +0000

MTH321: Real Analysis I (Fall 2015) At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about con…

MTH322: Real Analysis II (Fall 2016)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:09 +0000

~~DISCUSSION:off~~ MTH322: Real Analysis II (Fall 2016) Do you have questions or comments? Please use Discussion at the end of this page. This course is offered to MSc, Semester III at Department of Mathematics, COMSATS Institute of Information Technology, Attock campus. The is course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in

MTH321: Real Analysis I (Fall 2018)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:10 +0000

MTH321: Real Analysis I (Fall 2018) At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about cont…

MTH321: Real Analysis I (Fall 2022)

anonymous@undisclosed.example.com (Anonymous) — Mon, 15 May 2023 07:16:43 +0000

MTH321: Real Analysis I (Fall 2022) ~~DISCUSSION~~ [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform conti…

MTH322: Real Analysis II (Spring 2023)

anonymous@undisclosed.example.com (Anonymous) — Thu, 15 Jun 2023 01:08:47 +0000

MTH322: Real Analysis II (Spring 2023) [MTH322: Real Analysis II (Spring 2023)] This course is offered to BS, Semester VI at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notions included in $f\in \mathcal{R}[a,b]$$b\ge a$$f(x)\ge 0$$x\ge a$$\int_{\,a}^{\,\infty }{f(x)\,dx}$$M>0$$\int\limits_{a}^{b}{f(x)\,dx}\leq M$$b\ge a$$f(x)$$g(x)$$x>a$$\li…

Quantitative Reasoning II (QR2: Tools for Reasoning Skills)

anonymous@undisclosed.example.com (Anonymous) — Fri, 01 Aug 2025 18:31:56 +0000

Quantitative Reasoning II (QR2: Tools for Reasoning Skills) [Quantitative Reasoning II (Tools for Reasoning Skills)] This handout provides a comprehensive exploration of fundamental mathematical and logical concepts, making it an essential read for students and professionals alike. It begins with an introduction to enumeration and its practical applications, followed by an in-depth discussion on quantitative reasoning, number systems, and arithmetic operations. The book highlights the contribut…

Vector & Tensor Analysis by Prof Fazal Abbas

anonymous@undisclosed.example.com (Anonymous) — Wed, 24 Aug 2022 07:12:53 +0000

Vector & Tensor Analysis by Prof Fazal Abbas [Vector & Tensor Analysis by Prof Fazal Abbas] Solution of Chapter 6: Curvilinear Coordinates of the book Vector & Tensor Analysis by Prof. Dr. Nawazish Ali Shah written by Prof. Fazal Abbas Sajid. Here solutions of chapter 6 are provided by the author of the book, for the solutions of all the chapters of the book, please buy the solution manual from the market.

Notes of Vector Analysis (Online View)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:01 +0000

Notes of Vector Analysis (Online View) PDF View of Notes of the Vector Analysis is given on this page. These notes are helpful for BSc or equivalent classes. PDF file of the notes can also be downloaded from this page. Contents of these notes are available

Chapter 03: Matrices and Determinants

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:27 +0000

Chapter 03: Matrices and Determinants [Chapter 03: Matrices and Determinants] Notes (Solutions) of Chapter 03: Matrices and Determinants, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction$2\times2$$2\times2$$2\times2$$n\geq 3$$n\geq 3$

Chapter 04: Quadratic Equations

anonymous@undisclosed.example.com (Anonymous) — Sun, 04 Jun 2023 16:13:15 +0000

Chapter 04: Quadratic Equations [Chapter 04: Quadratic Equations] Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board, Lahore. Contents & summary * Introduction * Solutions of Quadratic Equations

Chapter 05: Partial Fractions

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:29 +0000

Chapter 05: Partial Fractions [Chapter 05: Partial Fractions] Notes (Solutions) of Chapter 05: Partial Fractions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction * Rational Fraction$\frac {P(x)}{Q(x)}$

Chapter 07: Permutation, Combination and Probability

anonymous@undisclosed.example.com (Anonymous) — Sat, 26 Mar 2022 16:28:40 +0000

Chapter 07: Permutation, Combination and Probability [Chapter 07: Permutation , Combination and Probability] Notes (Solutions) of Chapter 07: Permutation , Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary

Chapter 08: Mathematical Induction and Binomial Theorem

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:30 +0000

Chapter 08: Mathematical Induction and Binomial Theorem [Chapter 08 Mathematical Induction and Binomial Theorem] Notes (Solutions) of Chapter 08: Mathematical Induction and Binomial Theorem, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.$(a+x)^n$$(a+x)^n$

Chapter 11: Trigonometric Functions and their Graphs

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Chapter 11: Trigonometric Functions and their Graphs [Chapter 11: Trigonometric Functions and their Graphs] Notes (Solutions) of Chapter 11: Trigonometric Functions and their Graphs, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary $ y = \sin x$$-2\pi \hbox{ to } 2\pi$$ y = \cos x$$-2\pi \hbox{ to } 2\pi$$ y = \tan x$$-\pi \hbox{ to } \pi$$ y = \cot x$$-2\pi \hbox{ to } \pi$$ y = \sec x$$-2\pi \hbox{ to } 2\pi…

Chapter 13: Inverse Trigonometric Functions

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Chapter 13: Inverse Trigonometric Functions [Chapter 13: Inverse Trigonometric Functions] Notes (Solutions) of Chapter 13: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * ${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqrt {1 - {…

Chapter 14: Solutions of Trigonometric Equation

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Chapter 14: Solutions of Trigonometric Equation [Chapter 14: Solutions of Trigonometric Equation] Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary ${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqr…

Ch 01: Number System: Mathematics FSc Part 1

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Ch 01: Number System: Mathematics FSc Part 1 Notes (Solutions) of Chapter 01: Number System, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 02: Sets, Functions and Groups: Mathematics FSc Part 1

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Ch 02: Sets, Functions and Groups: Mathematics FSc Part 1 Notes (Solutions) of Chapter 02: Sets, Functions and Groups, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are eight exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 05: Partial Fractions: Mathematics FSc Part 1

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Ch 05: Partial Fractions: Mathematics FSc Part 1 Notes (Solutions) of Chapter 05: Partial Fractions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 06: Sequences and Series: Mathematics FSc Part 1

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Ch 06: Sequences and Series: Mathematics FSc Part 1 Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are eleven exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1

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Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 Notes (Solutions) of Chapter 07: Permutation, Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are eight exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1

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Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 Notes (Solutions) of Chapter 08: Mathematical Induction and Binomial Theorem, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 09: Fundamentals of Trigonometry: Mathematics FSc Part 1

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Ch 09: Fundamentals of Trigonometry: Mathematics FSc Part 1 Notes (Solutions) of Chapter 09: Fundamentals of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 10: Trigonometric Identities: Mathematics FSc Part 1

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Ch 10: Trigonometric Identities: Mathematics FSc Part 1 Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

View Online (Solutions of Chapter 11)

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View Online (Solutions of Chapter 11) Notes (Solutions) of Chapter 11: Trigonometric Functions and their Graphs, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. There are two exercise in this chapter.

Ch 12: Application of Trigonometry: Mathematics FSc Part 1

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Ch 12: Application of Trigonometry: Mathematics FSc Part 1 Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Ch 13: Inverse Trigonometric Functions: Mathematics FSc Part 1

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Ch 13: Inverse Trigonometric Functions: Mathematics FSc Part 1 Notes (Solutions) of Chapter 10: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are two exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

Chapter 03: Matrices

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Chapter 03: Matrices Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The difficulty level of this chapter is very low. Most of the questions involve calculations. This chapter is wide range of applications in Linear Algebra. In many universities teachers include this chapter in the syllabus of Linear Algebra for BS students of mathematics and other subjects.

Chapter 04: System of Linear Equations

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Chapter 04: System of Linear Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The difficulty level of this chapter is low. Most of the questions involve calculations. This chapter is wide range of applications in Linear Algebra and Operations Research. In many universities teachers include this chapter in the syllabus of Linear Algebra and Operations Research for BS students of mathematics and other …

Chapter 11: The Laplace Transform

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Chapter 11: The Laplace Transform Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin. This book is published by Ilmi Kitab Khana, Lahore - PAKISTAN. Solutions of Chapter 11: The Laplace Transform are given here in pdf form. $f$$[0,\infty)$$f$$\mathcal{L}(f)$$F$$ provided the above improper integral converges. We have $

Chapter 03: PDF Viewer

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Chapter 03: PDF Viewer Notes of the Chapter 03: General Theorem, Intermediate Forms with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter.

Chapter 04: PDF Viewer

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Chapter 04: PDF Viewer Notes of the Chapter 04: Techniques of integration written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter. List of all exercise of chapter 04

Chapter 05: PDF Viewer

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Chapter 05: PDF Viewer Notes of the Chapter 05: The Definite Integral, Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter.

Chapter 06: PDF Viewer

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Chapter 06: PDF Viewer Notes of the Chapter 06: Plane Curves I, Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter. List of all resources of chapter 06

View Online (Solutions of Chapter 10)

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View Online (Solutions of Chapter 10) Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. There are total of four exercise in this chapter.

View Online (Solutions of Chapter 12)

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View Online (Solutions of Chapter 12) Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. There are eight exercises in this chapter.

Ch 14: Solutions of Trigonometric Equation

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Ch 14: Solutions of Trigonometric Equation Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at

View Online (Solutions of Chapter 14)

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View Online (Solutions of Chapter 14) Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. In this chapter there is only one exercise.

Unit 02: Differentiation: Mathematics FSc part 2

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Unit 02: Differentiation: Mathematics FSc part 2 Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are ten exercises in this chapter. Please see the main page of this chapter for MCQs and important question

Unit 03: Differentiation: Mathematics FSc part 2

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Unit 03: Differentiation: Mathematics FSc part 2 Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are eight exercises in this chapter. Please see the main page of this chapter for MCQs and important question

Unit 04: Introduction to Analytic Geometry: Mathematics FSc part 2

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Unit 04: Introduction to Analytic Geometry: Mathematics FSc part 2 Notes (Solutions) of Unit 04: Introduction to Analytic Geometry, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are five exercises in this chapter. Please see the main page of this chapter for MCQs and important question

MTH322: Real Analysis II (Fall 2021)

anonymous@undisclosed.example.com (Anonymous) — Thu, 30 Dec 2021 19:16:17 +0000

MTH322: Real Analysis II (Fall 2021) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in $\int_{1}^{\infty }{{{x}^{-p}} dx}$$p$$f\in \mathcal{R}[a,b]$$b\ge a$$f(x)\ge 0$$x\ge a$$\int_{a}^{\infty }{f(x) dx}$$M>0$$\int\limits_{a}^{b}{f(x)\,dx} \le M$$b\ge a$$f\in \mathcal{R}[a,b]$$b\ge a$…

Notes of Mathematical Method

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Notes of Mathematical Method [BSc Mathematical Method] Notes of the Mathematical Method written by by S.M. Yusuf, A. Majeed and M. Amin and published by Ilmi Kitab Khana, Lahore. This is an old and good book of mathematical method. The notes given here are provided by awesome peoples, who dare to help others. Some of the notes are send by the authors of these notes and other are send by people who didn't write but share these notes as Open Educational Resources (OER). We are thankful to

Mathematics 9 (Science Group)

anonymous@undisclosed.example.com (Anonymous) — Wed, 08 Mar 2023 18:04:36 +0000

Mathematics 9 (Science Group) [Mathematics 9 (Science Group)] Mathematics 9 is written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq and this book is published by Carvan Book House, Lahore, Pakistan. This book consist of 302 pages and there are 17 units. Notes of Unit 1 and 3 are provided by $ka + kb + kc$$ac + ad + bc + bd$$a^2 + 2ab + b^2$$a^2 – b^2$$a^2 + 2ab + b^2 – c^2$$a^4 + a^2b^2 + b^4$$a^4 + 4b^4$$x^2 + px + q$$ax^2 + bx + c$$(ax^2 + bx + c) (ax2 + bx + d) + k$$(x + a) (x + b) (x + c) …

Functional Analysis by Mr. Tahir Hussain Jaffery

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Functional Analysis by Mr. Tahir Hussain Jaffery [Functional Analysis by Prof Mumtaz Ahmad] Functional analysis is a branch of mathematics concerned with vector space theory and linear algebra. It requires looking into the relationships between various roles, objects, incidents, actions, and results. The term $M$$M+N$

Chapter 01: Real Numbers, Limits and Continuity

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Chapter 01: Real Numbers, Limits and Continuity [Chapter 01 of Calculus with Analytic Geometry] Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The notes of this chapter is written by Prof. $\mathbb{R}$$\mathbb{R}$$\mathbb{R}$

Chapter 03: General Theorem, Intermediate Forms

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Apr 2023 13:46:07 +0000

Chapter 03: General Theorem, Intermediate Forms [BSc Calculus 3rd Chapter] What is in the this chapter? * Rolle's theorem * Geometrical interpretation of Rolle's theorem * The mean value theorems * Another form of mean value theorem * Increasing and decreasing functions$\frac{0}{0}$$\frac{\infty}{\infty}$$0\times \infty$$\infty \times 0$$\infty-\infty$$0^\infty, 1^\infty, \infty^0$

Mathematical Method by Khalid Latif Mir (Solutions)

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Mathematical Method by Khalid Latif Mir (Solutions) [Mathematical Method by Khalid Latif Mir (Solutions)] We are very thankful to Prof. Fazal Abbas Sajid for sharing these solutions. Problems & Methods Mathematical Method by Khalid Latif Mir is a famous book taught in different universities of the Pakistan at BS and Master level. On this page, we have added the solutions of the exercises of the book. The solutions of Chapter 06: The Laplace Transform and its Applications is written by Marrium …

Chapter 01: Viewer

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Chapter 01: Viewer Notes of “Chapter 01: Real numbers, limits and continuity” of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. You can also download a PDF file of respective exercise from this page.

Chapter 02: Viewer

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Chapter 02: Viewer Notes of Chapter 02: The Derivatives of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. You can also download a PDF file of respective exercise from this page.

Chapter 07: Viewer

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Chapter 07: Viewer Notes of “Chapter 07: Plane Curve II” of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. You can also download a PDF file of respective exercise from this page.

Chapter 08: PDF Viewer

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Chapter 08: PDF Viewer Notes of the Chapter 08: Analytic Geometry of Three Dimensions of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are thirteen exercises in this chapter.

Chapter 09: PDF Viewer

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Chapter 09: PDF Viewer Notes of the Chapter 09: Functions of Several Variables of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are thirteen exercises in this chapter.

Chapter 02: Viewer

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Chapter 02: Viewer Notes of Chapter 02: Groups of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercises of Chapter 02

Chapter 03: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:53:09 +0000

Chapter 03: Viewer Notes of Chapter 03: Matrices of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercise of Chapter 03

Chapter 04: Viewer

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Chapter 04: Viewer Notes of Chapter 04: System of linear equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page.

Chapter 04: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:53:27 +0000

Chapter 05: Viewer

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Chapter 05: Viewer Notes of Chapter 05: Determinants of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Notes of two exercises are given here.

Chapter 06: Viewer

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Chapter 06: Viewer Notes of Chapter 06: Vector space of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercises of Chapter 06

Chapter 07: Viewer

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Chapter 07: Viewer Notes of Chapter 07: Inner Product Spaces of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercise of Chapter 07

Chapter 08: Viewer

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Chapter 08: Viewer Notes of Chapter 08: Infinite Series of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercise of Chapter 08

Chapter 09: Viewer

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Chapter 09: Viewer Notes of Chapter 09: First Order Partial Differential Equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page.

Chapter 10: Viewer

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Chapter 10: Viewer Notes of Chapter 10: Higher Order Linear Differential Equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page.

Chapter 11: Viewer

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Chapter 11: Viewer Notes of Chapter 11: The Laplace Transform of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page.

Chapter 02: Composition of Forces

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Chapter 02: Composition of Forces Notes of Chapter 02: Composition of Forces: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Notes of this chapter is send by Mr. Tahir Aziz. We are very thankful for his such effort.$(\lambda,\mu)$

Chapter 06: Virtual Work

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Chapter 06: Virtual Work Notes of Chapter 06: Virtual Work: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Notes of this chapter is provide by *Prof. M. Tanveer*. We are very thankful to him for such a kind effort.

Chapter 07: Kinematics

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Chapter 07: Kinematics Notes of Chapter 07: Kinematics: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Notes of this chapter is send by Mr. Tahir Aziz and Mr. Umair Sabi Ullah. We are very thankful to them for such a kind effort.

View Online (Notes of Chapter 04)

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View Online (Notes of Chapter 04) Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board, Lahore. These notes are provided by M. Shahid Nadeem, Lecturer in Mathematics, Punjab College Wah Cantt. One can also download PDF of the notes from this page.

View Online (Solutions of Chapter 07)

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View Online (Solutions of Chapter 07) Notes (Solutions) of Chapter 07: Permutation , Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Here is the list of all exercises of Chapter 07

View Online (Solutions of Chapter 13)

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View Online (Solutions of Chapter 13) Notes (Solutions) of Chapter 13: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. In this chpater, there are two exercise.

Unit 05: Linear Inequalities and Linear Programming: Mathematics FSc part 2

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Unit 05: Linear Inequalities and Linear Programming: Mathematics FSc part 2 Notes (Solutions) of Unit 05: Linear Inequalities and Linear Programming, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question

Unit 06: Conic Section: Mathematics FSc part 2

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Unit 06: Conic Section: Mathematics FSc part 2 Notes (Solutions) of Unit 06: Conic Section, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are nine exercises in this chapter. Please see the main page of this chapter for MCQs and important question

Unit 07: Vectors: Mathematics FSc part 2

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Unit 07: Vectors: Mathematics FSc part 2 Notes (Solutions) of Unit 07: Vectors, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question

ADS/BSc

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ADS/BSc One this page we have listed notes/resources widely used in BSc or in Associated Degree of Science (ADS). This includes notes of some famous books and other resources. Notes of Famous Books Notes of Calculus with Analytic Geometry Notes of Calculus with Analytic Geometry Notes of Mathematical Method Notes of Mathematical Method Introduction to Mechanics Introduction to Mechanics Other notes Notes of Mechanics Notes of Mechanics written by different authors for BSc or BS…

MTH322: Real Analysis II (Fall 2018)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:11 +0000

MTH322: Real Analysis II (Fall 2018) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in

MTH211: Discrete Mathematics (Fall 2020)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:14 +0000

MTH211: Discrete Mathematics (Fall 2020) Course Objectives: Discrete Mathematics is branch of Mathematics which deals with discrete structures like logic. sequences, graphs, relations in contrast to Calculus. where we enjoy the continuity of functions and the set of real numbers. This course is introduction to discrete structures which are not the part of main stream courses. Discrete Mathematics has applications in Computer Science. Economics and Decision Making etc. This course will help t…

MTH322: Real Analysis II (Spring 2017)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:35 +0000

~~DISCUSSION:closed~~ MTH322: Real Analysis II (Spring 2017) Do you have questions or comments? Please use Discussion at the end of this page. This course is offered to MSc, Semester III at Department of Mathematics, COMSATS Institute of Information Technology, Attock campus. The is course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in

MTH211: Discrete Mathematics (Fall 2020)

anonymous@undisclosed.example.com (Anonymous) — Thu, 10 Jun 2021 09:02:12 +0000

MTH211: Discrete Mathematics (Spring 2022)

anonymous@undisclosed.example.com (Anonymous) — Mon, 12 Sep 2022 04:56:59 +0000

MTH211: Discrete Mathematics (Spring 2022) Course Objectives: Discrete Mathematics is branch of Mathematics which deals with discrete structures like logic. sequences, graphs, relations in contrast to Calculus. where we enjoy the continuity of functions and the set of real numbers. This course is introduction to discrete structures which are not the part of main stream courses. Discrete Mathematics has applications in Computer Science. Economics and Decision Making etc. This course will help…

Definitions: FSc Part1 KPK

anonymous@undisclosed.example.com (Anonymous) — Mon, 28 Aug 2023 16:59:59 +0000

Definitions: FSc Part1 KPK A Textbook of Mathematics for Class XI is published by Khybar Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. The book has total of twelve (12) chapters. Definition of the book provide the quick overview of the book.$360^\circ$$\theta$$90^{\circ} \pm \theta, 180^{\circ} \pm \theta, 270^{\circ} \pm \theta, 360^{\circ} \pm \theta$$16^\circ 13' 9''$$sin(\alpha+2\pi)=sin\alpha$$sin x=\frac{2}{7}$$cos x-tan x=0$

Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib

anonymous@undisclosed.example.com (Anonymous) — Sat, 30 Mar 2024 16:48:20 +0000

Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib Definitions from Textbook of Algebra and Trigonometry Class XI, published by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to Aurang Zaib for his valuable contribution. Chapter 01: Number System $ \dfrac{p}{q} $$ p, q \in \mathbb{Z} $$ q \neq 0 $$ \dfrac{3}{4} $$ \dfrac{7}{2} $$ \sqrt{2} $$ \pi $$ \mathbb{R} $$ 0.25 $$ 3.75 $$ 0.3333... $$ 1.234234... $$ \pi $$ 3.1415... $$ \sqrt{2} $\(…

MCQs Bank: FSc-I

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:43:02 +0000

MCQs Bank: FSc-I Lot of high quality MCQs covering Textbook of Algebra and Trigonometry Class XI are available here. There are fourteen (14) chapters in this book, therefore MCQs of each chapters are given on separate page. This book was published by Punjab Textbook Board (PTB) Lahore, Pakistan. These MCQs are not only helpful for this book but can be considered for students of Higher Secondary Schools. Answer are also given on the same page.

Multiple Choice Questions (MCQs)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:43:03 +0000

Multiple Choice Questions (MCQs) Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters. Our plan is to give lot of Multiple Choice Questions (MCQs) for the above mentioned book. MCQs are very important because most of entry tests, admission tests and job tests consists of only MCQs.$\sqrt{3}$$n$$\sqrt{n}$$\forall a, b, c \in R$$a0\Rightarrow ac\geq bc$$a0\Rightarrow ac> bc$$a

FSc Part 1 Mathematics Notes/Solutions

anonymous@undisclosed.example.com (Anonymous) — Tue, 08 Aug 2023 17:59:03 +0000
FSc Part 1 Mathematics Notes/Solutions [FSc Part1 PTB Book Cover] Notes (Solutions) of Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. There are fourteen chapters in this book and we have work hard to make easy and suitable solution for students and teachers so that it help them learn things quickly and easily. Please click on a desire chapter to view the solution of any particular exercise. This work is licensed under a Cre…

Important Trigonometric Formulae

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:38 +0000
Important Trigonometric Formulae These two pages contains all the important trigonometric formulae used in Chapter 09 to Chapter 14. These notes are provide by Ali Nawaz Bajwa (MS(Math), M.Ed.). It is necessary for student to remembers these values by heart.

FSc Part 1 Mathematics Notes/Solutions

anonymous@undisclosed.example.com (Anonymous) — Sun, 20 Jul 2025 09:10:04 +0000
FSc Part 1 Mathematics Notes/Solutions This is an old book. Notes of new book are available at following link: [FSc Part1 PTB Book Cover] Notes (Solutions) of Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore.

Chap 04: Formulas Introduction to Analytics Geometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:43 +0000
Chap 04: Formulas Introduction to Analytics Geometry On these four pages, one can find all the formulas used in Chapter 04: Formulas Introduction to Analytics Geometry of FSc Part 2. There are five exercises in chapter 04 with lot of questions. These basic things help to solve the questions easily without going to the depth of each concept.

Definitions: FSc Part1 KPK

anonymous@undisclosed.example.com (Anonymous) — Tue, 05 Dec 2023 02:44:42 +0000
Definitions: FSc Part1 KPK A Textbook of Mathematics for Class XI is published by Khybar Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. The book has total of twelve (12) chapters. Definition of the book provide the quick overview of the book.$360^\circ$$\theta$$90^{\circ} \pm \theta, 180^{\circ} \pm \theta, 270^{\circ} \pm \theta, 360^{\circ} \pm \theta$$16^\circ 13' 9''$$sin(\alpha+2\pi)=sin\alpha$$sin x=\frac{2}{7}$$cos x-tan x=0$

Definitions: Mathematics 11 NBF

anonymous@undisclosed.example.com (Anonymous) — Wed, 10 Jul 2024 18:51:53 +0000
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…

General Mathematics 9

anonymous@undisclosed.example.com (Anonymous) — Mon, 15 Dec 2025 16:49:07 +0000
General Mathematics 9 [General Mathematics 9th Class] There are ten chapters in General Mathematics 9 for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. One can download the PDF file of the notes. Please remember that, to view these notes one must have PDF reader installed in their system. We will try our best to add online view of the notes very soon.

Chapter 02: The Derivative

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:28 +0000
Chapter 02: The Derivative [Chapter 02: The Derivative BSc Calculus] Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Here are few online resource, which are very helpful to find derivative.

Chapter 01: Complex Numbers

anonymous@undisclosed.example.com (Anonymous) — Mon, 11 Dec 2023 12:59:57 +0000
Chapter 01: Complex Numbers [Chapter 01 Complex Numbers Methods] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. A complex number is an element $(x,y)$ of the set $$ \mathbb{R}^2=\{(x,y): x,y \in \mathbb{R}\} $$ obeying the following rules of addition and multiplication.$z_1=(x_1,y_1)$$z_2=(x_2,y_2)$$z_1+z_2= (x_1+x_2, y_1+y_2)$$z_1 z_2 = (x_1 x_2 - y_1 y_2, x_1 y_2+y_1 x_2)$$\mathbb{R}^2$$\mathbb{C}$

Chapter 02: Groups

anonymous@undisclosed.example.com (Anonymous) — Mon, 11 Dec 2023 13:00:23 +0000
Chapter 02: Groups [Chapter 02: Groups] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Definition (axioms of group) * Definition ( commutative group ) *

Chapter 06: Vector Spaces

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:47 +0000
Chapter 06: Vector Spaces Notes of Chapter 06 Vector Spaces of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Subspaces * Linear combinations and spanning sets

Introduction to Mechanics

anonymous@undisclosed.example.com (Anonymous) — Sat, 13 Jan 2024 10:50:44 +0000
Introduction to Mechanics [Introduction to Mechanics by Q.K Ghori] Notes of Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. There are thirteen chapters in this book. We don't have all the notes of this book but the notes which we have are listed below. Please choose your require chapter to see the notes.

MCQs with Answers (FSc/ICS Part 1)

anonymous@undisclosed.example.com (Anonymous) — Thu, 02 May 2024 17:03:11 +0000
MCQs with Answers (FSc/ICS Part 1) [MCQs Choice] In this one PDF, MCQs of all chapters of FSc/ICS Part1 are given. There are seven chapters. Answers of MCQs is starting from page 71. SAMPLE MCQs * $i^{13}=$............. * (A) $i$ * (B) 1 * (C) -1 * (D) 2 * $S$$1, \omega, \omega^2$$-1, \omega, \omega^2$$-1, -\omega, -\omega^2$$1, -1, 2$$ax^2+bx+c=0$$a=0, b\neq 0$$a\neq 0$$a=b=0$$b=$$ax^2+bx+c=0$$a=0, b\neq 0$$a\neq 0$$a=b=0$$b=$$n!=n(n-1)(n-2)...3\cdot 2\cdot 1$$n$

MCQs with key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:44 +0000
MCQs with key [MCQs Choice] In this one PDF, MCQs of all chapters of FSc Part2 are given. There are seven chapters. Keys of MCQs is starting from page 51. SAMPLE MCQs * A function $I(x)=x$ is called * (A) A linear function * (B) An identity function * (C) A quadratic function$\frac{d}{dx} \tan 3x =$$3\sec^2 3x$$\frac{1}{3}\sec^2 3x$$\cot 3x$$\sec^2 x$$y=f(x)$$y$$dy=f'(x)$$dy=f'(x) dx$$dy=f(x)$$\frac{dy}{dx}$$x<0$$y<0$$P(x,y)$$ax+by

Assessment Scheme

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:51 +0000
Assessment Scheme Chapter wise marks distribution is given below. Mathematics Class 12 Time: 3 Hours Marks: 100 Ch # Chapter name Weightage % Distribution of marks 1 Functions and limits 7% 11 2 Differentiation 21% 30

Unit 01: Functions and Limits

anonymous@undisclosed.example.com (Anonymous) — Sat, 03 Jun 2023 16:30:56 +0000
Unit 01: Functions and Limits [Unit 01: Functions and Limits] Notes (Solutions) of Unit 01: Functions and Limits, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are five exercises in this chapter. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from $\lim_{x\to a}\frac{x^n-a^n}{x-a} = na^{n-1}$$\lim_{x\to0}\frac{\sqrt{x+a} - \sqrt{a}}{x} = \frac{…

Unit 02: Differentiation

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:05 +0000
Unit 02: Differentiation [Unit 02: Differentiation] Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$f'(x)$$x^n$$n \in \mathbb{Z}$$\frac{x+1}{x-1}$$x$$$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \frac{(x-1)\frac{d}{dx}(x…

Chapter 01: Complex Numbers

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:20 +0000
Chapter 01: Complex Numbers Notes of Chapter 01: Complex Numbers of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources. [Download PDF ~ ch01-complex-numbers-fsc1-kpk.pdf] fsc kpk_fsc_part1

Chapter 02: Matrices and Determinants

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:20 +0000
Chapter 02: Matrices and Determinants Notes of Chapter 02: Matrices and Determinants of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.

Chapter 03: Vectors

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:21 +0000
Chapter 03: Vectors Notes of Chapter 03: Vectors of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources. [Download PDF ~ ch03-vectors-fsc1-kpk.pdf] fsc kpk_fsc_part1

Chapter 04: Sequences

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:21 +0000
Chapter 04: Sequences Notes of Chapter 04: Sequences of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources. [Download PDF ~ ch04-sequences-fsc1-kpk.pdf] fsc kpk_fsc_part1

Chapter 05: Miscellaneous Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:22 +0000
Chapter 05: Miscellaneous Series Notes of Chapter 05: Miscellaneous Series of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources. [Download PDF ~ ch05-miscellaneous-series-fsc1-kpk.pdf] fsc kpk_fsc_part1

Chapter 06: Permutation, Combination and Probability

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:22 +0000
Chapter 06: Permutation, Combination and Probability Notes of Chapter 06: Permutation, Combination and Probability of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.

Chapter 07: Mathematical Induction and Binomial Theorem

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:23 +0000
Chapter 07: Mathematical Induction and Binomial Theorem Notes of Chapter 07: Mathematical Induction and Binomial Theorem of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.

Chapter 08: Function and Graphs

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:23 +0000
Chapter 08: Function and Graphs Notes of Chapter 08: Function and Graphs of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources. [Download PDF ~ ch08-functions-and-graphs-fsc1-kpk.pdf] fsc kpk_fsc_part1

Chapter 09: Linear Programming

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:24 +0000
Chapter 09: Linear Programming Notes of Chapter 09: Linear Programming of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources. [Download PDF ~ ch09-linear-programming-fsc1-kpk.pdf] fsc kpk_fsc_part1

Chapter 10: Trigonometric Identities of Sum and Difference of Angles

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:25 +0000
Chapter 10: Trigonometric Identities of Sum and Difference of Angles Notes of Chapter 10: Trigonometric Identities of Sum and Difference of Angles of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.

Chapter 11: Application of Trigonometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:26 +0000
Chapter 11: Application of Trigonometry Notes of Chapter 11: Application of Trigonometry of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.

Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of ...

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:26 +0000
Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations Notes of Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations of “A Textbook of Mathematics for Class XI

Open MCQs of Mathematics 11

anonymous@undisclosed.example.com (Anonymous) — Thu, 26 Feb 2026 17:44:37 +0000
Open MCQs of Mathematics 11 [Open MCQs of Mathematics 11] This is an initial release of the MCQs. The beautiful thing for these notes is that you can edit this booklet. Our aim is to make a database for the high quality MCQs available for all. Please remember these MCQs are related to the book

Theoretical Mechanics by Khalid Latif Mir (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Feb 2021 08:58:47 +0000
Theoretical Mechanics by Khalid Latif Mir (Solutions) [Theoretical Mechanics by Khalid Latif Mir (Solutions)] We are very thankful to Prof. Fazal Abbas Sajid for sharing these solutions. An Intermediate Course in Theoretical Mechanics By Khalid Latif Mir is a famous book taught in different universities of the Pakistan. On this page, we have added the solutions of the exercises of the book.

University of the Punjab, Lahore (Old Papers)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:34 +0000
University of the Punjab, Lahore (Old Papers) [Old paper PU] Old papers for BSc (Mathematics), University of the Punjab, Lahore. From 2016, BSc has been split in to two parts. There will be exam after each year. Syllabus and chapter-wise paper pattern for Mathematics A & B courses is available

Chapter 04: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:52:02 +0000
Chapter 04: Viewer These notes are written by Prof. Muhammad Farooq. We are very thankful to him for providing these notes. List of all exercises of chapter 04 * Solution of Exercise 4.1 * Solution of Exercise 4.2 * Solution of Exercise 4.3 * Solution of Exercise 4.4 * Solution of Exercise 4.5 * Solution of Exercise 4.6

Viewer: Ch 01 Complex Numbers

anonymous@undisclosed.example.com (Anonymous) — Wed, 09 Mar 2022 19:08:50 +0000
Viewer: Ch 01 Complex Numbers Notes of Chapter 01: Complex Numbers of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page.

Chapter 04: Centres of Mass and Gravity

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:04 +0000
Chapter 04: Centres of Mass and Gravity Notes of Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. These notes are written by Prof. Muhammad Tanveer. Following are the main topics of this chapter. * Linear Moment

Chapter 05: Friction

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:06 +0000
Chapter 05: Friction Notes of Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. These notes are written by Prof. Muhammad Tanveer. Following are the main topics of this chapter. * Friction * Laws of friction

Chapter 08: Rectilinear Motion

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:09 +0000
Chapter 08: Rectilinear Motion Notes of Chapter 08: Rectilinear Motion: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Thanks to Mr. Tahir Aziz and Atiq ur Rehman for sending these notes. * Motion with constant acceleration

Chapter 10: Motion of a Projectile

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:09 +0000
Chapter 10: Motion of a Projectile Notes of Chapter 10: Motion of a Projectile: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. These notes are written by Prof. Shariq Mehtab Syed * Trajectory of a Projectile

Chapter 12: Orbital Motion

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:09 +0000
Chapter 12: Orbital Motion Notes of Chapter 12: Orbital Motion: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. * Motion under the Central * Elliptic Orbit under a central Force * Polar form of the Orbit

View Online (Solutions of Chapter 01)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:24 +0000
View Online (Solutions of Chapter 01) Here is the list of all exercises of Chapter 01 * Exercise 1.1 (Handwritten) * Exercise 1.2 (Handwritten) * Exercise 1.3 (Handwritten)

View Online (Solutions of Chapter 02)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:28 +0000
View Online (Solutions of Chapter 02) Here is the list of all exercises of Chapter 02 * Exercise 2.1 * Exercise 2.2 (Handwritten) * Exercise 2.3 (Handwritten) * Exercise 2.4 * Exercise 2.5 * Exercise 2.6 (Handwritten) * Exercise 2.7 (Handwritten) * Exercise 2.8

View Online (Solutions of Chapter 03)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:34 +0000
View Online (Solutions of Chapter 03) Here is the list of all exercises of Chapter 03 * Exercise 3.1 * Exercise 3.2 * Exercise 3.3 (Handwritten) * Exercise 3.4 (Handwritten) * Exercise 3.5 * Exercise 3.5 by Prof. Tahir Nazir * Exercise 3.5 by Prof. Shatriq Mahataab

View Online (Solutions of Chapter 03)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:34 +0000
View Online (Solutions of Chapter 03) Here is the list of all exercises of Chapter 03 * Exercise 3.1 * Exercise 3.2 * Exercise 3.3 (Handwritten) * Exercise 3.4 (Handwritten) * Exercise 3.5 * Exercise 3.5 by Prof. Tahir Nazir * Exercise 3.5 by Prof. Shatriq Mahataab

View Online (Solutions of Chapter 04)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:41 +0000
View Online (Solutions of Chapter 04) Here is the list of all exercises of Chapter 04 * Exercise 4.1 (Handwritten) * Exercise 4.2 (Handwritten) * Exercise 4.3 (Handwritten) * Exercise 4.4 * Exercise 4.5 (Handwritten) * Exercise 4.6 (Handwritten) * Exercise 4.7 * Exercise 4.8 (Handwritten) * Exercise 4.9 (Handwritten) * Exercise 4.10 (Handwritten)

View Online (Solutions of Chapter 05)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:45 +0000
View Online (Solutions of Chapter 05) Here is the list of all exercises of Chapter 05 * Exercise 5.1 * Exercise 5.2 (Handwritten) * Exercise 5.3 * Exercise 5.4 (Handwritten)

View Online (Solutions of Chapter 08)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:58:08 +0000
View Online (Solutions of Chapter 08) Here is the list of all exercises of Chapter 08 * Exercise 8.1 * Exercise 8.2 * Exercise 8.3

View Online (Solutions of Chapter 09)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:58:19 +0000
View Online (Solutions of Chapter 09) Here is the list of all exercises of Chapter 09 * Exercise 9.1 * Exercise 9.2 * Exercise 9.3 * Exercise 9.4 (Handwritten)

Report Error

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:39:27 +0000
Report Error Thank you very much for coming on this page as we understand that you come to this page for helping us and community of mathematics. We really appreciate your effort to give us your quality time. In case of “Broken Link”, please provide us the link by copying the link from address bar and paste it in comments box.

Report Error

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Report Error Thank you very much for coming on this page as we understand that you come to this page for helping us and community of mathematics who are using this website. We really appreciate your effort to give us your quality time.

FSc Part 1 (Mathematics): KPK

anonymous@undisclosed.example.com (Anonymous) — Tue, 12 Dec 2023 17:09:07 +0000
FSc Part 1 (Mathematics): KPK [A Textbook of Mathematics for Class XI] A Textbook of Mathematics for Class XI is published by Khybar Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. The book has total of twelve (12) chapters. This book is written by Prof. Dr. Gulzar Ali Khan, Prof. Dr. Islam Noor and Prof. Dr. Muhammad Shah.

FSc/ICS Part 1 (Mathematics): PTB

anonymous@undisclosed.example.com (Anonymous) — Sat, 19 Jul 2025 17:19:20 +0000
FSc/ICS Part 1 (Mathematics): PTB This is an old book. Notes of new book are available at following URL: [Textbook of Algebra and Trigonometry Class XI] Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters.

Home

anonymous@undisclosed.example.com (Anonymous) — Tue, 24 Mar 2026 18:10:06 +0000
Home Welcome to MathCity.org. Please browse the website by using navigation bar or search the website. More Quotes :---: MathCity.org Updates * | FSc (PECTAA) | Solutions of the many exercises of Mathematics 11 (by PECTAA) has been add. read more for download NEW * | Notes | Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad has been added in the notes section.

Mathematics 9th for Matric (PCTB)

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 May 2026 16:19:23 +0000
Mathematics 9th for Matric (PCTB) [Mathematics 9th for Matric (PCTB)] Mathematics 9 is published by Punjab Curriculum and Textbook Board (PCTB), Lahore, Pakistan. This is a textbook for all the boards of Punjab for matriculation. The book has total of thirteen (13) chapters. The book is written by Muhammad Akhtar Shirani (Senior Subject Specialist, Mathematics), Madiha Mehmood, (Subject Specialist, Statistics) and Ghulam Murtaza (Subject Specialist, Mathematics).

FSc/ICS Part 1 (Mathematics): KPK

anonymous@undisclosed.example.com (Anonymous) — Tue, 06 Feb 2024 13:20:19 +0000
FSc/ICS Part 1 (Mathematics): KPK [A Textbook of Mathematics for Class XI] A Textbook of Mathematics for Class XI is published by Khybar Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. The book has total of twelve (12) chapters. This book is written by Prof. Dr. Gulzar Ali Khan, Prof. Dr. Islam Noor and Prof. Dr. Muhammad Shah.

Mathematics 11 for FSc ICS (NBF)

anonymous@undisclosed.example.com (Anonymous) — Sat, 14 Feb 2026 14:30:09 +0000
Mathematics 11 for FSc ICS (NBF) [A Textbook of Mathematics for Class XI] 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. This book is written by Dr. Khalid Mahmood, Dr. Saleem Ullah Satti, M Dabeer Mughal, Dr. Naveed Akmal and Dr. Shahzad Ahmad.

Mathematics 11 (PECTAA)

anonymous@undisclosed.example.com (Anonymous) — Sun, 20 Jul 2025 06:50:20 +0000
Mathematics 11 (PECTAA) [Mathematics 11 for FSc and ICS (PECTAA)] Mathematics 11 is is based on Updated/Revised National Curriculum of Pakistan 2023 and has been approved by the Punjab Education, Curriculum, Training and Assessment Authority (PECTAA) previously known as Punjab Textbook Board (PTB). This is a textbook for all the boards of Punjab for 11th class (FSc or ICS Part 1 or HSSC-I). The book has total of fourteen (14) units.

Mathematics 12 for FSc ICS (NBF)

anonymous@undisclosed.example.com (Anonymous) — Mon, 16 Feb 2026 07:08:57 +0000
Mathematics 12 for FSc ICS (NBF) [Textbook of Mathematics for Class 12] Textbook of Mathematics for Class XII is published by National Book Foundation (NBF), Islamabad, Pakistan. NBF can be considered as Federal Textbook Board Islamabad. The book has total of ten (10) chapters. Dr, Khalid Mahmood is the Managing Author. Saleem Ullah Satti, Muhammad Dabeer Mughal, Dr. Naveed Akmal and Muhammad Anwar ul Haq are the co-authors of the book.

MTH604: Fixed Point Theory and Applications

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:08 +0000
MTH604: Fixed Point Theory and Applications Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also ed…

MTH322: Real Analysis II (Fall 2019)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:12 +0000
MTH322: Real Analysis II (Fall 2019) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers. these notions included in

MTH604: Fixed Point Theory and Applications (Fall 2022)

anonymous@undisclosed.example.com (Anonymous) — Fri, 06 Jan 2023 04:37:11 +0000
~~DISCUSSION~~ MTH604: Fixed Point Theory and Applications (Fall 2022) [FPTA] Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem f…

MATH-510: Topology

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:25 +0000
MATH-510: Topology Topology is an important branch of mathematics that studies all the “qualitative” or “discrete” properties of continuous objects such as manifolds, i.e. all the properties that aren't changed by any continuous transformations except for the singular (infinitely extreme) ones.$(T_0, T_1, T_2)$$\mathbb{R}$$X=\{a\}$$X$$X$$X$$\tau$$\mathbb{N}$$\tau$$(\mathbb{Z}, \tau)$$\mathbb{N}$$\tau$$A=\{\pm 100,\pm 101, \pm 102, ... \}$$\tau$$E=\{0,\pm 2,\pm 4,...\}$$\tau$$\tau$$B=\{1,2,3,...…

MATH-510: Topology

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:24 +0000
MATH-510: Topology Objectives of the course This is an introductory course in topology, giving the basics of the theory. Course contents Topological spaces, bases and sub-bases, first and second axiom of countability, separability, continuous functions and homeomorphism, finite product space. Separation axioms $(T_0, T_1, T_2)$

MATH-608: Research Methodology

anonymous@undisclosed.example.com (Anonymous) — Wed, 29 Sep 2021 16:16:53 +0000
MATH-608: Research Methodology Objectives of the course Introduction to the students will be given that research in mathematics is conducted covering every fact of the research process, finding and defending suitable problems, performing literature survey.

MTH604: Fixed Point Theory and Applications

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:39 +0000
MTH604: Fixed Point Theory and Applications Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also ed…

MTH604: Fixed Point Theory and Applications (Spring 2020)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:41 +0000
~~DISCUSSION~~ MTH604: Fixed Point Theory and Applications (Spring 2020) Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for mul…

MTH604: Fixed Point Theory and Applications (Spring 2021)

anonymous@undisclosed.example.com (Anonymous) — Mon, 22 Feb 2021 15:12:31 +0000
~~DISCUSSION~~ MTH604: Fixed Point Theory and Applications (Spring 2021) Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for mul…

Definitions and Review

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:56 +0000
Definitions and Review Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters. On this page, we have posted material related to definitions, reviews and quick reviews.

Old Question Papers/Model Papers HSSC-I (FSc-I): FBISE

anonymous@undisclosed.example.com (Anonymous) — Mon, 11 Dec 2023 13:01:04 +0000
Old Question Papers/Model Papers HSSC-I (FSc-I): FBISE [FBISE Paper Papers HSSC-I] Old (past) question papers and model papers of mathematics for HSSC-I (FSc Part 1) conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad. Paper Pattern The recommended book for the mathematics paper is

Solution and Area of Oblique Triangle

anonymous@undisclosed.example.com (Anonymous) — Mon, 25 Sep 2023 15:48:59 +0000
Solution and Area of Oblique Triangle These are the common formulas used in Chapter 12 of Textbook of Algebra and Trigonometry Class XI, Punjab Textbook Board Lahore. This handout is very helpful to remember the formulas. All these formulas are given for real valued and defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word file is also given if you wish to modify the contents or credit as you need.$a^2=b^2+c^2-2bc\cos \alpha$$b^2=c^2+a^2-2ca\cos \bet…

Trigonometric Formulas (New Edition)

anonymous@undisclosed.example.com (Anonymous) — Sun, 22 Sep 2024 09:02:18 +0000
fsc fsc_part1 formula_pages muzzammil_subhan Trigonometric Formulas (New Edition) This page contains all the important trigonometric formulas used in chapter 9 to 14 of FSc Part 1. This page was sent by Muzzammil Subhan. [Download PDF]

Trigonometric Formulas

anonymous@undisclosed.example.com (Anonymous) — Thu, 25 May 2023 02:59:50 +0000
Trigonometric Formulas These are the common formulas used in Chapter 9 to 14 of Textbook of Algebra and Trigonometry Class XI, Punjab Textbook Board Lahore. This handout is very helpful to remember the formulas. All these formulas are given for real valued and defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word file is also given if you wish to modify the contents or credit as you need.${{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1$$1+{{\tan }^{2}}\t…

Derivatives, Integration Formulas & Rules

anonymous@undisclosed.example.com (Anonymous) — Sun, 22 Sep 2024 17:07:06 +0000
math_12 formula_pages muzzammil_subhan Derivatives, Integration Formulas & Rules This page contains all the important derivative and integration formulas & rules used in chapter 2 and 3 of FSc Part 2. This page is send by Muzzammil Subhan. [Download PDF]

Subjective Mathematics 12th by Muhammad Shahbaz

anonymous@undisclosed.example.com (Anonymous) — Tue, 23 Sep 2025 19:59:04 +0000
Subjective Mathematics 12th by Muhammad Shahbaz [Subjective Mathematics 12th by Muhammad Shahbaz] These handwritten notes are sent by Muhammad Shahbaz. We are very thankful to him for sending these notes. These notes are based on the book “Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan.'' There are total seven (7) units in this book.

MCQs/Objective: HSSC-I

anonymous@undisclosed.example.com (Anonymous) — Thu, 02 May 2024 17:05:13 +0000
MCQs/Objective: HSSC-I Short Questions by Mr. Akhtar Abbas NEW Short Questions without answers by Mr. Akhtar Abbas for FSc Part 1. MCQs-Short Questions by Mr Parvez Khan MCQs and Short Question by Mr. Parvez Khan composed by Momin Ali: Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) MCQs by Nauman Idrees

Solution & Area of Oblique Triangle

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:41 +0000
Solution & Area of Oblique Triangle Here is the list of all the formulas used in Chapter 12 of FSc Part 1. If there is difficulty to remember these formulas then take a print of this page and see formula from this page while solving the question. After a while you will learn all formulas by heart. To download the PDF of this page see below.

Trigonometric Review

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:42 +0000
Trigonometric Review Here the review of the formulas are given, which are used in Chapter 9 to 14 of Text Book of Algebra and Trigonometry Class XI, Punjab Text Book Board Lahore. This handout is very helpful to remember the formulas. All these formulas are given for real valued and defined trigonometric functions. A PDF file can be downloaded for high quality printing. We are very thankful to

Important Formulas Derivatives

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:45 +0000
Important Formulas Derivatives This page contains all the important derivatives used in chapter 2 and 3 of FSc Part 2. This page is send by Ali Nawaz Bajwa (MS(Math), M.Ed.). It is very helpful to remember thes formulas. [Download PDF]

Important Formulas Integration

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:46 +0000
Important Formulas Integration This page contains all the important integration used in chapter 3 of FSc Part 2. This page is send by Ali Nawaz Bajwa (MS(Math), M.Ed.). This page helps to remember important formulas of integration. [Download PDF]

MCQs/Objective: HSSC-II

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Mar 2025 15:21:10 +0000
MCQs/Objective: HSSC-II On this page, MCQ/Objective for FSc-II (HSSC-II) or FSc Part 2 are given. * Objective Mathematics 12th by Muhammad Shahbaz NEW * Short Questions without answers by Mr. Akhtar Abbas for FSc Part 2. * Short Questions by Mr. Akhtar Abbas * Short Questions without answers by Mr. Akhtar Abbas for FSc Part 2.

FSc Part 2 Model Papers

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:48 +0000
FSc Part 2 Model Papers Federal Board of Intermediate & Secondary Education, Islamabad ARW 1st Model Paper 2009 View Online Download PDF (84KB) ARW Official Model Paper (with solution) Download PDF (233KB) Board of Intermediate & Secondary Education. All the boards in Punjab expect Federal Board have the same paper pattern.

FSc Part 2 (KPK Boards)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:52 +0000
FSc Part 2 (KPK Boards) [A Textbook of Mathematics For Class XII] Notes of FSc Part 2 of “A Textbook of Mathematics For Class XII” published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated.$y=x^n$$y=(ax+b)^n$

MCQS of Mathematics 9 (PCTB)

anonymous@undisclosed.example.com (Anonymous) — Tue, 18 Nov 2025 17:29:59 +0000
MCQS of Mathematics 9 (PCTB) Mathematics 9 is published by Punjab Curriculum and Textbook Board (PCTB), Lahore, Pakistan. This is a textbook for all the boards of Punjab for matriculation. The book has total of thirteen (13) chapters. The book is written by Muhammad Akhtar Shirani (Senior Subject Specialist, Mathematics), Madiha Mehmood, (Subject Specialist, Statistics) and Ghulam Murtaza (Subject Specialist, Mathematics).

Solutions: Math 11 KPK

anonymous@undisclosed.example.com (Anonymous) — Thu, 01 Feb 2024 02:36:03 +0000
Solutions: Math 11 KPK [Solutions of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa] Solutions of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been introduced Students Learning Outcomes (SLOs) Based Examination. Its complete scheme of studies is available on the FBISE website

Solutions: Math 11 NBF

anonymous@undisclosed.example.com (Anonymous) — Sat, 01 Feb 2025 19:18:00 +0000
Solutions: Math 11 NBF [Solutions of Model Textbook of Mathematics for Class XI] Solutions of 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. Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been introduced Students Learning Outcomes (SLOs) Based Examination. Its complete scheme of studies is available on the FBISE website

Mathematical Method by Sir Muhammad Awais Aun

anonymous@undisclosed.example.com (Anonymous) — Mon, 17 Apr 2023 09:02:35 +0000
Mathematical Method by Sir Muhammad Awais Aun [Mathematical Method by Muzammil Tanveer] Mathematical methods are the approaches employed by mathematicians to address issues in mathematics and science. Algebra, functions, relations and associated graphs, calculus, and statistics are examples of mathematical techniques. Through their usage in resolving practical issues, they are applied to modelling.

Amir Shehzad

anonymous@undisclosed.example.com (Anonymous) — Tue, 07 Sep 2021 09:25:23 +0000
Amir Shehzad We are very thankful to Mr. Amir Shehzad for his contribution to the website. [Mr. Amir Shehzad] * Email: * Cell: +92-343-4443214 * YouTube Chanel: Contribution: 9th (Science) (PTB) * Unit 04 (10th Science PTB) | VIEW View Online | [Download PDF] * [MCQs of Full Book, Matric 9th (Science) PTB] * [Definitions] for 9th Class Science

Muhammad Fiaz Hussain

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:44:41 +0000
Muhammad Fiaz Hussain We are very thankful to Muhammad Fiaz Hussain for contributing to our website. * M.Sc, M.Phil. in Applied & Analytic Mathematics (COMSATS Institute of Information Technology Islamabad) * Email: * Cell: +92-333-6639466; +92-300-504117

Chapter 04: Techniques of Integration

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:29 +0000
Chapter 04: Techniques of Integration These notes are written by Mr. Aqeel Nawaz. We are very thankful to him for providing these notes. * Anti-derivative * Table of integrals * Integration by substitution * Integration by parts * Column (or tabular) integration

Chapter 04: Techniques of Integration

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:30 +0000
Chapter 04: Techniques of Integration These notes are written by Prof. Muhammad Farooq. We are very thankful to him for providing these notes. * Anti-derivative * Table of integrals * Integration by substitution * Integration by parts * Column (or tabular) integration

Chapter 05: The Definite Integral

anonymous@undisclosed.example.com (Anonymous) — Tue, 05 Dec 2023 03:01:56 +0000
Chapter 05: The Definite Integral These notes are written by Mr. Abrar Mustafa. We are very thankful to him for providing these notes. * The definite integral as limit of a sum * Evaluation of limit of a sum * Evaluation of definite integral

Chapter 06: Plane Curves I

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:31 +0000
Chapter 06: Plane Curves I Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Conic section] Contents and summary * Conic sections * The parabola * The ellipse

Chapter 07: Plane Curves II

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:32 +0000
Chapter 07: Plane Curves II Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Asymptote] Contents and summary * Asymptotes: A straight line $l$ is called an asymptote for a curve $C$$l$$C$$l$$l$

Chapter 08: Analytic Geometry of Three Dimensions

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:33 +0000
Chapter 08: Analytic Geometry of Three Dimensions Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents & Summary * Distance between two points$\mathbb{R}^3$

Chapter 09: Functions of Several Variables

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:33 +0000
Chapter 09: Functions of Several Variables * Homogeneous Functions * Differentials * Change of variables, the chain rule * Implicit functions * Directional derivative * Tangent planes and normal lines * Extrema of functions of two variables

Chapter 05: Determinants

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:47 +0000
Chapter 05: Determinants * Determinant of a square matrix * Axiomatic definition of a determinant * Determinant as sum of products of elements * Determinant of the transpose * An algorithm to evaluate Det A * Determinants and inverse of matrices

Chapter 07: Inner Product Spaces

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:48 +0000
Chapter 07: Inner Product Spaces Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Inner product spaces form and important topic of Functional Analysis. These are simply vector space over the field of real or complex numbers and with an inner product defined on them.

Chapter 08: Infinite Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:49 +0000
Chapter 08: Infinite Series Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Infinite series are of great importance in both pure and applied mathematics. They play a significant role in Physics and engineering. In fact many functions can be represented by infinite series. The theory of infinite series is developed through the use of special kind of function called sequence.

Chapter 09: First Order Differential Equations

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:50 +0000
Chapter 09: First Order Differential Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * D.E and their classification * Formation of differential equation

Chapter 10: Higher Order Linear Differential Equations

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:51 +0000
Chapter 10: Higher Order Linear Differential Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Higher order linear differential equations

Notes of Mechanics by Tariq Mahmood Qadri

anonymous@undisclosed.example.com (Anonymous) — Thu, 25 Feb 2021 13:08:49 +0000
Notes of Mechanics by Tariq Mahmood Qadri [Notes of Mechanics by Tariq Mahmood Qadri] We are very thankful to Tariq Mahmood Qadri for providing these notes. These notes are helpful at BSc or BS level of Mathematics. Vector and Mechanics is essential part of the B Course of Mathematics in BSc or in Associate Degree of Science (ADS).

Ch 02: Functions and Groups

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:39 +0000
Ch 02: Functions and Groups The important questions of Chapter 2 of Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan has been given on this page. These questions are selected from old papers.$(2,4)$$\{a,\{b,c\}\}$$A-B=A \cup B^c$$p \longrightarrow q$$\{(1,2),(2,5),(3,7),(4,9),(5,11)\}$$\{a,b \}$$\{\{a,b\}\}$$~(p \longrightarrow q) \longrightarrow p$$A \cap(B \cup C)=(A \cap B)\cup(A \cap C)$$A=\{1,2,3,4\}$$B=\{3,4,5,6,7,8\}$$C=\{5,6,7,9,…

MCQs: Ch 01 Number Systems

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:49 +0000
MCQs: Ch 01 Number Systems High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. MCQs * If $*$$A$$a, b \in A$$a+b \in A$$a-b \in A$$a \times b \in A$$a * b \in A$$z=(1,3)$$z^{-1}= $$(\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$$(-\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$$(\displaystyle{\frac{1}{10}},-\display…

MCQs: Ch 02 Sets, Functions and Groups

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:49 +0000
MCQs: Ch 02 Sets, Functions and Groups High quality MCQs of Chapter 02 Sets, Functions and Groups of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page.$\forall$$\wedge$$<$$\in$$A$$B$$A\cap B=\phi$$A=B$$B\subseteq A$$A \subseteq B$$A$$B$$A-B \neq \phi$$A=B$$A \subseteq B$$B\subseteq A$$A$$B$$A\cap B=A$$B \subseteq A$$A\cap B=\phi$$A\subseteq B$$B\subseteq A$$A=\phi$$A \cup B=A$$A \cap B=…

MCQs: Ch 04 Quadratic Equations

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:50 +0000
MCQs: Ch 04 Quadratic Equations High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. MCQs $ax^2+bx+c=0$$ax^2+bx+c=0$$b \neq 0$$c \neq 0$$a \neq 0$$x$$ax^2+bx+c$$ax^2+bx+c=0$$\{a,b\}$$ax^2+bx+c=0$$a\neq 0$$x= \frac{b \pm \sqrt{b^2-4ac}}{a}$$x= \frac{-b \pm \sqrt{b^2+4ac}}{2a}$$x= \frac{-b \pm \sqrt{4ac-b^2}}{2a}$$x= \frac{-b \pm \sqrt{b^2-…

MCQs Made by Nauman Idrees

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:08 +0000
MCQs Made by Nauman Idrees Chapter 01 View Online Download PDF (43KB) * Online View

MCQs-Short Questions by Mr Parvez Khan

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:05 +0000
MCQs-Short Questions by Mr Parvez Khan * MCQs and Short Question written by Mr. Parvez Khan, composed by Mr. Momin Ali from Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) * Key to the MCQs is given at page 57. Erratum $180^{\circ}$

Unit 03: Integration

anonymous@undisclosed.example.com (Anonymous) — Sat, 03 Jun 2023 17:25:33 +0000
Unit 03: Integration [Unit 03: Integration] Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$dy$$\delta{y}$$[f(x)]^n f'(x)$$[f(x)]^{-1}f'(x)$

Unit 04: Introduction to Analytic Geometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:07 +0000
Unit 04: Introduction to Analytic Geometry [Unit 01: Functions and Limits] Notes (Solutions) of Unit 04: Introduction to Analytic Geometry, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$ax^2+ 2hxy+by^2=0$

Unit 05: Linear Inequalities and Linear Programming

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:08 +0000
Unit 05: Linear Inequalities and Linear Programming [Unit 05: Linear Inequalities and Linear Programming] Notes (Solutions) of Unit 05: Linear Inequalities and Linear Programming, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.

Unit 06: Conic Section

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:08 +0000
Unit 06: Conic Section [Unit 06: Conic Section] Notes (Solutions) of Unit 06: Conic Section, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.

Unit 07: Vectors

anonymous@undisclosed.example.com (Anonymous) — Thu, 25 Mar 2021 17:27:32 +0000
Unit 07: Vectors [Unit 07: Vectors] Notes (Solutions) of Unit 07: Vectors, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$u\cdot v$$u\times v$$u\cdot(v\times w)$

Chapter 01

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:33 +0000
Chapter 01 Under construction

Unit 06: Permutation and Combination

anonymous@undisclosed.example.com (Anonymous) — Sun, 09 Mar 2025 10:56:17 +0000
Unit 06: Permutation and Combination This is a sixth unit of the book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. On this page we have provided the solutions of the questions.$n$$n!$$n$$r$$n$$r$

Matric 9th (General): Online View

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:48:06 +0000
Matric 9th (General): Online View List of all chapters * VIEW Unit 01: Percentage Ratio and Proportion * VIEW Unit 02: Zakat, Ushr and Inheritance * VIEW Unit 03: Business Mathematics * VIEW Unit 04: Financial Mathematics * VIEW Unit 05: Consumer Mathematics * VIEW Unit 06: Exponents and Logarithms * VIEW Unit 07: Arithmatic and Geometric Sequence * VIEW Unit 08: Sets and Functions * VIEW Unit 09: Linear Graphs * VIEW Unit 10: Basic Statistic matric 9th_general

Chapter 04 - Differentiation

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:57 +0000
Chapter 04 - Differentiation * Derivative of a function * Theorem: Let f be defined on [a,b], if f is differentiable at a point $x\in [a,b]$, then f is continuous at x. (Differentiability implies continuity) * Theorem (derivative of sum, product and quotient of two functions)$x\in [a,b]$$f'(x)$$f'(x)=0$$\mathbb{R}^k$$\underline{f}$$x\in (a,b)$$\left|\underline{f}(b)-\underline{f}(a)\right|\le (b-a)\left|\underline{f'}(x)\right|$

Chapter 03 - Limits and Continuity

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:57 +0000
Chapter 03 - Limits and Continuity * Limit of the function, examples and definition * Theorem: Suppose (i) $(X,{d_x})$ and $(Y,{d_y})$ be two metric spaces (ii) $E\subset X$ (iii) $f:E\to Y$ i.e. f maps E into X (iv) p is the limit point of E. Then $\lim_{x\to p} f(x)=q$ iff $\lim_{n\to\infty}f(p_n)=q$ for every sequence {$p_n$} in E such that ${p_n}\ne p$$\lim_{n\to\infty}{p_n}=p$$\lim_{x\to c}f(x)$$c\in G$$\lim_{x\to c}f(x)=l$$\varepsilon$$\delta>0$$|f(t)-f(s)|<\varepsilon$$\left\{x:|x-c|…

Chapter 01 - Real Number System

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:59 +0000
Chapter 01 - Real Number System Contents & Summary * Theorem: There is no rational p such that $p^2=2$. * Theorem: Let A be the set of all positive rationals p such that $p^2>2$ and let B consist of all positive rationals p such that $p^2<2$ then A contain no largest member and $x0$$n>0$$y^n=x$$\underline x,\underline y\in \mathbb{R}^n$$\|\underline x^2\|=\underline x\cdot \underline x$$\|\underline x\cdot \underline y\|=\|\underline x\| \|\underline y\|$$\underline …

Chapter 02 - Sequence and Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:59 +0000
Chapter 02 - Sequence and Series Contents * Sequence, Subsequence, Increasing Sequence, Decreasing Sequence, Monotonic Sequence, Strictly Increasing or Decreasing * Bernoulli’s Inequality * Bounded Sequence * Convergence of the Sequence$s_n\frac{1}{2}s$$\{s_n\}$$\{t_n\}$$\left\{a{s_n}+b{t_n}\right\}$$as+bt$$\left\{{s_n}{t_n}\right\}$$\left\{\frac{{{s_n}}}{{{t_n}}} \right\}$$\frac{s}{t}$${t_n}\ne…

Paper Pattern for General Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:17 +0000
Paper Pattern for General Mathematics Paper pattern for General Mathematics chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. This pattern is made by Prof. Muhammad Farooq.

Paper Pattern for A-Course of Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:23 +0000
Paper Pattern for A-Course of Mathematics Paper pattern for A-Course of Mathematics, chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. * Download PDF ~ BSC_maths_paper_pattern_farooq.pdf bsc punjab_university paper_pattern syllabus

Paper Pattern for B-Course of Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:29 +0000
Paper Pattern for B-Course of Mathematics Paper pattern for B-Course of Mathematics chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. This pattern is made by Prof. Muhammad Farooq.

Ch 01: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:40 +0000
Ch 01: Key This page include the key to MCQs by Nauman Idrees of Chapter 01. 1- A 2- A 3- A 4- B 5- C 6- D 6- A 7- D 8- A 9- D 10- C 11- B 12- B 13- C 14- A 15- B 16- A 17- A 18- A 19- A 20- B 21- C 22- D 23- B 24- C 25- A 26- B 27- C 28- B

Ch 02: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:39 +0000
Ch 02: Key This page include the key to MCQs by Nauman Idrees of Chapter 02. 1- D 2- A 3- B 4- B 5-A 6- C 7- A 8- B 9- D 10- A 11- B 12- D 13- A 14- B 15- D 16- A 17- D 18- D 19- A 20- A 21- B 22- C 23- B 24- A 25- D 26- B 27- D 28- C 29- A

Ch 03: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:42 +0000
Ch 03: Key This page include the key to MCQs by Nauman Idrees of Chapter 03. 1- B 2- A 3- C 4- A 5- C 6- C 7- D 8- B 9- B 10-C 11-C 12-C 13-B 14-C 15-A 16-A 17-D

Ch 04: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:45 +0000
Ch 04: Key This page include the key to MCQs by Nauman Idrees of Chapter 04. 1 -A 2 -B 3 -A 4 -C 5-C 6 -C 7 -C 8 -D 9 -D 10-A 11-C 12-A 13-A 14-A 15-D 16-D 17-B 18-B 19-D 20-A 21-D 22-C 23-B 24-B 25-A 26-C 27-C 28-B 29-D 30-D

Ch 05: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:50 +0000
Ch 05: Key This page include the key to MCQs by Nauman Idrees of Chapter 01. 1- A 2- C 3- A 4- B 5- B 6- B 7- C 8- D 9- A 10-C 11-D 12-D

Ch 06: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:56:51 +0000
Ch 06: Key This page include the key to MCQs by Nauman Idrees of Chapter 06. 1- A 2- C 3- C 4- C 5- C 6- D 7- A 8- A 9- A 10- C 11- A 12- A 13- A 14- C 15- C 16- C 17- B 18- C 19- NO OPTION 20- A 21- B 22- B 23- A 24- A 25- ERROR 26- D 27- C

Ch 07: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:03 +0000
Ch 07: Key This page include the key to MCQs by Nauman Idrees of Chapter 07. 1- B 2- B 3- B 4- C 5- C 6- A 7- D 8- A 9- D 10- A 11- D 12- A 13- A 14- D 15- C 16- A 17- D 18- B 19- B 20- B 21- C 22- B 23- B 24- C 25- A 26- B

Ch 08: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:03 +0000
Ch 08: Key This page include the key to MCQs by Nauman Idrees of Chapter 08. 1- B 2- A 3- B 4- D 5- D 6- A 7- D 8- D 9- A 10- A 11- D 12- A 13- A 14- A 15- A 16- B 17- B 18- A 19- C

Ch 09: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:09 +0000
Ch 09: Key This page include the key to MCQs by Nauman Idrees of Chapter 09. 1- B 2- B 3- A 4- D 5- A 6- D 7- B 8- A 9- A 10- A 11- C 12- E 13- A 14- A 15- C 16- E 17- C 18- C 19- B 20- E 21- A 22- D 23- A 24- D 25- C 26- A 27- B 28- B 29- A $\pi/6$

Ch 10: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:09 +0000
Ch 10: Key This page include the key to MCQs by Nauman Idrees of Chapter 10. 1- B 2- B 3- B 4- B 5- A 6- C 7- D 8- E 9- B 10- D 11- A 12- C 13- D 14- B 15- E 16- A 17- B 18- D 19- D 20- A 21- A 22- C 23- B 24- E 25- B 26- B 27- A 28- E 29- B

Ch 11: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:12 +0000
Ch 11: Key This page include the key to MCQs by Nauman Idrees of Chapter 11. 1- B 2- A 3- B 4- A 5- C 6- D 7- C 8- D 9- A 10- A 11- B 12- B 13- E 14- E 15- B 16- A 17- E 18- E 19- D 20- D 21- E 22- E 23- D 24- D 25- B 26- B 27- D 28- D 29- C

Ch 12: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:12 +0000
Ch 12: Key This page include the key to MCQs by Nauman Idrees of Chapter 12. 1- B 2- B 3- A 4- B 5- B 6- A 7- A 8- B 9- A 10- E 11- C 12- B 13- ? 14- ? 15- C 16- B 17- A 18- A 19- A 20- B 21- C 22- E 23- C 24- B 25- B 26- C 27- E 28- A 29- A

Ch 13: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:13 +0000
Ch 13: Key This page include the key to MCQs by Nauman Idrees of Chapter 13. 1- A 2- E 3- ? 4- A 5- D 6- E 7- C 8- E 9- D 10- A 11- B 12- E 13- ? 14- C 15- B 16- B 17- A 18- ? 19- B 20- B 21- E 22- E 23- D 24- D 25- D 26- E 27- D 28- B 29- ?

Ch 14: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:13 +0000
Ch 14: Key This page include the key to MCQs by Nauman Idrees of Chapter 14. 1- C 2- A 3- C 4- B 5- E 6- B 7- D 8- B 9- A 10- C 11- A 12- C 13- B 14- A 15- C 16- C 17- C 18- A 19- C 20- C 21- D 22- C 23- B 24- D 25- B

View Online (Solutions of Chapter 06)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:57:48 +0000
View Online (Solutions of Chapter 06)

Unit 07: Key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:59:39 +0000
Unit 07: Key This page include the key to MCQs by Nauman Idrees of Chapter 07. 1- C 2- B 3- C 4- B 5- B 6- C 7- C 8- C 9- B 10- A 11- D 12-C 13- D 14-C 15- D PRODUCT OF VECTOR 1- D 2- D 3- A 4- C 5- C 6- D 7- A 8- D 9- B 10- C 11- ERROR

View Online (Solutions of Unit 03)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:14 +0000
View Online (Solutions of Unit 03) Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. In this chapter, integration is defined and basic techniques of integration are given.

View Online (Solutions of Unit 04)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:17 +0000
View Online (Solutions of Unit 04) Notes (Solutions) of Unit 04: Introduction to Analytic Geometry, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. This chapter have only five exercises but it covers lot of topics of analytic geometry in the plane.

Review Exercise 2 (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Sun, 08 Feb 2026 16:57:09 +0000
Review Exercise 2 (Solutions) The solutions of the Review Exercise 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 MCQs and question all topics included in this chapter.$A$$m \times n$$B$$n \times p$$A B$$n \times p$$m \times p$$p \times m$$n \times n$$A$$1 \times n$$A^{t} A$$1 \times n$$n \times 1$$1 \times 1$$n \times n$$a_{i j}$$A$$a_{i j}=(-…