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Khuram Ali Khan
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tion of Chebyshev functional with applications; Department of Mathematics, University of Sargodha. (February 16, 2018) - GHULAM ABBAS, Hermite-Hadamard-Fejér type... via generalized fractional integral operators; Department of Mathematics, University of Sargodha (May 03, 2019). - TASADUQ NIAZ, New Generalizations of Jen... ype Inequalities via Interpolating Polynomials; Department of Mathematics, University of Sargodha (July 09, 2020). - MUHAMMAD ADEEL, Levinson-type Inequalities via Interpolating Polynomials; Department of Mathematics, University of Sargodha (November 05, 2020). - Muhammad Yussouf, Hadamard and Fejer type
Exercise 2.6 (Solutions) @matric:9th_science:unit_02
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ac{\overline{z}}{\overline{w}}$ * (v) $\frac{1}{2}(z+\overline{z})$ is real part of z * (vi) $\frac{1}{2i}(z-\overline{z})$ is the imaginary part of z **Solution**\\ 6(i) $$\begin{array}{cl} z = 2+3i\\ w = 5-4i\\ * (i... &= \frac{1}{2}(4)\\ &= 2 \hbox{ (it is real part of } z). \end{array}$$ 6(vi) $$\begin{array}{cl} \frac{1}{2i}(z-\overline{z}) &= \frac{1}{2}(2+3i-(2-3i))\\
Question 7, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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n} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-2-p5|< Question 6]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-2-p7|Question 8, 9 >]]</btn></text>
MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
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lgebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The... nd of the page. ====MCQs==== - An equation $ax^2+bx+c=0$ is called - Linear - Quadratic ... - None of these - For a quadratic equation $ax^2+bx+c=0$ - $b \neq 0$ - $c \neq 0$ - $... her name for a quadratic equation in $x$ is - 2nd degree - Linear - Cubic - None of t
Unit 02: Differentiation @fsc:fsc_part_2_solutions
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===== Unit 02: Differentiation ====== {{ :fsc:fsc_part_2_solutions:fsc-2-unit-02-ptb.jpg?nolink|Unit 02: Differentiation}} Notes (Solutions) of Unit 02: ... ion, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You... er the derivative just take a print of [[FSc: FSc Part 2 Important Derivatives & Integrals|Important Deriv... ype="success" icon="fa fa-download"> * Exercise 2.1 | [[vfsc2>ch02:view&cp=01&p=07&ch=02&fp=Ex-2-1-FSC-part2-ver3-1|View Online]] | [[pdf>files/fsc/fsc_part2
PPSC Paper 2011 (Lecturer in Mathematics) @ppsc
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unction - guage function - neither - A particle moves along a curve \(F=(e^{-1},2\cos 3t,2\sin 3t)\), where \(t\) is time. The velocity at \... ily of hyperbola - a family of circles - A particular integral of the differential equation \((D^2+4)y=x\) is \\ - \(xc^{-2x}\) - \(x\cos2... $\dfrac{\pi}{6}$ - $\dfrac{\pi}{8}$ - If a particle in equilibrium is subjected to four forces \(F_1=2\hat i-5\hat j+6\hat k\), \(F_2=\hat i+3\hat j-7\hat k\), \(F_3=2\hat i-2\hat j-3\hat k\) and \(F_4\)
Atiq ur Rehman, PhD
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Rehman, PhD**\\ Associate Professor (Tenured)\\ Department of Mathematics\\ COMSATS University Islamabad... ps://mathscinet.ams.org/mathscinet/MRAuthorID/845724|mathscinet]] * See profile at [[http://www.sco... 7006197515|Scopus]] * See profile at [[http://ww2.comsats.edu.pk/faculty/FacultyDetails.aspx?Uid=18... ]] * See profile at [[https://orcid.org/0000-0002-7368-0700|ORCID Website]] <button collapse="arti
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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ons) ====== <lead>Notes (Solutions) of Exercise 1.2: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore.... estion 16(i) ** Separate into real and imaginary parts: $\dfrac{2-7i}{4+5i}$ (write into simple complex number) ... stion 16(ii) ** Separate into real and imaginary parts $\dfrac{{{\left( -2+3i \right)}^{2}}}{\left( 1+i \right)}$ (write into simple complex number) **Solutions** $\dfrac{{{\left( -2+3i \right)}^{2}}}{\left( 1+i \right)}=\dfrac{4+9{
Question 7, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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estion 7(i)===== Separate into real and imaginary parts $\dfrac{2+3i}{5-2i}$. ====Solution==== \begin{align}&\dfrac{2+3i}{... =&\dfrac{4}{29}+\dfrac{19}{29}i \end{align} Real part $=\dfrac{4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts $\dfrac{{{\left( 1+2i \right)}^{2}}}{1-3i}$. ====Solution==== \begin{align}&\dfrac
Question 7, Exercise 1.2 @math-11-kpk:sol:unit01
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estion 7(i)===== Separate into real and imaginary parts $\dfrac{2+3i}{5-2i}$. ====Solution==== \begin{align}&\dfrac{2+3i}{... =&\dfrac{4}{29}+\dfrac{19}{29}i \end{align} Real part $=\dfrac{4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts $\dfrac{{{\left( 1+2i \right)}^{2}}}{1-3i}$. ====Solution==== \begin{align}&\dfrac
PPSC Paper 2015 (Lecturer in Mathematics) @ppsc
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====== PPSC Paper 2015 (Lecturer in Mathematics) ====== {{ :ppsc:ppsc-maths-2015.jpg|PPSC Paper 2011 (Lecturer in Mathematics)}} On this page, we have given question from old (p... aper of Lecturer in Mathematics conducted in year 2011. This is a MCQs paper and answers are given at
MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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lgebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The... style{\frac{3}{10}})$ - $\displaystyle{\frac{3}{2+2i}}=$ - $1-i$ - $1+i$ - $-2i$ - $\displaystyle{\frac{3-3i}{4}}$ - $\overline{z_1+z_
Key to MCQs by Muhammad Imran Qureshi @fsc:fsc_part_1_mcqs:mcqs_by_muhammad_imran_qureshi
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shi======= This page include the key to [[fsc:fsc_part_1_mcqs:mcqs_by_muhammad_imran_qureshi]]. ==== Unit 02: Key ==== | 1- C | 2- A | 3- B | 4- C | 5- C | | 6- D | 7- A | 8- B | 9- C | 10-D | | 11-A | 12-B | 13-D | 14-A | 15-C | | 16-A | 17-C | 18-C | 1
Unit 03: Integration @fsc-part2-ptb:important-questions
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frac{dy}{dx})=2(y^2+\frac{dy}{dx})$--- // BSIC Sargodha(2017)// </list-group> {{tag>FSc FSc_Part2 Important_Questions_FSc_2}}
Unit 06: Conic section @fsc-part2-ptb:important-questions
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f the conic $y=1+x^2$ and $y=1+4x-x^2$.--- // BSIC Sargodha(2017)// </list-group> {{tag>FSc FSc_Part2 Important_Questions_FSc_2}}
Question 6, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Chapter 04: Quadratic Equations @fsc:fsc_part_1_solutions
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Unit 03: Integration @fsc:fsc_part_2_solutions
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MTH322: Real Analysis II (Fall 2021) @atiq
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MTH322: Real Analysis II (Fall 2020) @atiq
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Question 3 & 4, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Unit 06: Conic Section @fsc:fsc_part_2_solutions
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Question 6, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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MTH322: Real Analysis II (Spring 2023) @atiq
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Question 5, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Question 8 and 9, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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Question 2, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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MTH211: Discrete Mathematics (Spring 2022) @atiq
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PPSC Paper 2021 (Lecturer in Mathematics) @ppsc
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MCQs by Nauman Idrees @fsc:fsc_part_1_mcqs
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Unit 01: Functions and Limits @fsc:fsc_part_2_solutions
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Question 13, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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MCQs by Nauman Idrees @fsc:fsc_part_2_mcqs
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Question 6, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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MTH321: Real Analysis I (Spring 2023) @atiq
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MCQs by Muhammad Imran Qureshi @fsc:fsc_part_2_mcqs
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Question 5, Exercise 10.3 @fsc-part1-kpk:sol:unit10
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Question 3, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Question 2, Exercise 10.3 @fsc-part1-kpk:sol:unit10
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MCQs by Muhammad Imran Qureshi @fsc:fsc_part_1_mcqs
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Question 2, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 1 Exercise 4.5 @math-11-kpk:sol:unit04
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MTH322: Real Analysis II (Spring 2019) @atiq
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Unit 07: Vectors @fsc:fsc_part_2_solutions
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Question 5, Exercise 10.3 @fsc-part1-kpk:sol:unit10
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Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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MTH322: Real Analysis II (Fall 2016) @atiq
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Trigonometric Formulas @fsc-part1-ptb
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Unit 07: Vectors @fsc-part2-ptb:important-questions
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MTH211: Discrete Mathematics (Fall 2020) @atiq
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MTH322: Real Analysis II (Spring 2022) @atiq
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Question 1 Exercise 5.3 @math-11-kpk:sol:unit05
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Question 6, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Solution and Area of Oblique Triangle @fsc-part1-ptb
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Old Papers of M.Phil. Quaid-e-Azam University. @papers
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Formatting Syntax @wiki
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Question11 and 12, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Question 2, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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Question 7 & 8 Exercise 4.5 @math-11-kpk:sol:unit04
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MTH322: Real Analysis II (Fall 2018) @atiq
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Question 2, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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MTH322: Real Analysis II (Fall 2017) @atiq
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FSc Part 2 (KPK Boards) @fsc
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Question, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Exercise 2.1 (Solutions) @matric:9th_science:unit_02
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MATH-505: Complex Analysis @atiq
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Question 5, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 12, 13 & 14, Exercise 3.2 @math-11-kpk:sol:unit03
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MTH322: Real Analysis II (Spring 2017) @atiq
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Question 5 & 6 Exercise 4.5 @math-11-kpk:sol:unit04
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MathCraft: PDF to LaTeX file: Sample-01 @mathcraft
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Question 7, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Amir Shehzad @people
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Short Questions by Mr. Akhtar Abbas @fsc:fsc_part_1_mcqs
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Question 1, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 5, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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FSc Part 2 Model Papers @fsc
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Mathematics 10 (Science Group) @matric
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Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
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Question 3 & 4, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 4 and 5, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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MTH231: Linear Algebra @atiq
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Question 1, Exercise 10.3 @fsc-part1-kpk:sol:unit10
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Question 1, Exercise 10.3 @math-11-kpk:sol:unit10
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FSc Part 1 (KPK Boards) @fsc
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Question 1, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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Chapter 01: Number System @fsc:fsc_part_1_solutions
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Question 3, Exercise 10.3 @fsc-part1-kpk:sol:unit10
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Question 1, Exercise 10.2 @math-11-kpk:sol:unit10
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MTH322: Real Analysis II (Fall 2019) @atiq
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MTH211: Discrete Mathematics (Fall 2020) @atiq
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FSc/ICS Part 2 Solutions @fsc
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Question 2 Exercise 4.5 @math-11-kpk:sol:unit04
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Question 4 Review Exercise @math-11-kpk:sol:unit05
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FSc
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Question 2 & 3, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
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Chapter 05: Partial Fractions @fsc:fsc_part_1_solutions
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Question 8, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Exercise 2.5 (Solutions) @matric:9th_science:unit_02
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Papers (Old/Past/Model): BISE @fsc-part1-ptb:bise-papers
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Question 1, Review Exercise 1 @fsc-part1-kpk:sol:unit01
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Question 2 & 3 Exercise 5.4 @math-11-kpk:sol:unit05
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FSc/ICS Part 2 (Mathematics): PTB
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Home
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Old Papers (FSc Part 2) @fsc
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Question 9 & 10, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Question 8, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Ch 10: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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FSc Part 1 Model Papers @fsc
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Quotes for the April @quote-of-the-day
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Short Questions by Mr. Akhtar Abbas @fsc:fsc_part_2_mcqs
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Syllabus for UoS (Private only) @msc:syllabus
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Question 8, Exercise 1.2 @math-11-kpk:sol:unit01
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MATH-300: Basic Mathematics for Chemist @atiq
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Question 11, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Question 6 Exercise 3.4 @math-11-kpk:sol:unit03
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Question 3, Exercise 10.2 @fsc-part1-kpk:sol:unit10
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Question 1, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Question 1, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Question 7, Exercise 3.2 @math-11-kpk:sol:unit03
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MTH211: Discrete Mathematics (Spring 2020) @atiq
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FSc Part 1 Mathematics Notes/Solutions @fsc-part1-ptb
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FSc Part 1 Mathematics Notes/Solutions @fsc
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Question 1, Review Exercise 10 @fsc-part1-kpk:sol:unit10
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Question 4 Exercise 4.5 @math-11-kpk:sol:unit04
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Question 1, Exercise 10.1 @math-11-kpk:sol:unit10
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Question 3, Exercise 10.2 @math-11-kpk:sol:unit10
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Quotes for the February @quote-of-the-day
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Unit 06: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Question 3 Exercise 4.5 @math-11-kpk:sol:unit04
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Ch 01: Number Systems @fsc-part1-ptb:important-questions
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Question 5, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Unit 03: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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MCQs/Objective: HSSC-II @fsc
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Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
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Question 1, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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CHEM-501: Basic Mathematics for Chemist @atiq
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MCQs with Answers (FSc/ICS Part 1) @fsc:fsc_part_1_mcqs
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Ch 02: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 12: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Important Questions: HSSC-I @fsc-part1-ptb
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Muhammad Fiaz Hussain @people
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Quotes for the May @quote-of-the-day
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Question 4, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Ch 09: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Question 5 & 6 Review Exercise @math-11-kpk:sol:unit05
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Mathematics CUI: LaTeX Resources
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Examples for the Wrap Plugin @wiki
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Question 8, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Unit 02: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Short Term Preparation FSc 2 @fsc-part2-ptb
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Akhtar Abbas @people
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Important Questions: HSSC-II @fsc-part2-ptb
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Fill in the blanks by Rauf & Nabeel @fsc:fsc_part_1_mcqs
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FBISE Annual 2009 @fsc:fsc_part_1_old_papers
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FBISE Annual 2011 @fsc:fsc_part_1_old_papers
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FBISE Annual 2012 @fsc:fsc_part_1_old_papers
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FSc-I Mathematics KPK: View Online @fsc:kpk-fsc-part1-km
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Syllabus for PU @msc:syllabus
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MATH-301: Complex Analysis @atiq
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Unit 05: Miscellaneous Series (Solutions) @math-11-kpk:sol
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Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 14 and 15 Exercise 6.2 @math-11-kpk:sol:unit06
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FSc/ICS Part 1 (Mathematics): PTB
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PPSC General Information, Syllabus, Paper Pattern
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Unit 05: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Question 9 & 10 Review Exercise 6 @math-11-kpk:sol:unit06
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Ch 01: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 11: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 13: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Unit 01: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Unit 04: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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MTH480: Introductory Quantum Mechanics @atiq
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Question 6, Exercise 1.1 @fsc-part1-kpk:sol:unit01
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Ch 04: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 06: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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MCQs with key @fsc:fsc_part_2_mcqs
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Question 9 and 10, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Question 9 & 10 Exercise 4.5 @math-11-kpk:sol:unit04
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Papers
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MTH604: Fixed Point Theory and Applications @atiq
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Are the functions are same? @dyk
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MCQs/Objective: HSSC-I @fsc
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Partial Differential Equations by M Usman Hamid @notes
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Partial Differential Equations by Muzammil Tanveer @notes
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Ch 07: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Question 9, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Ch 14: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Preparation Guide @msc:syllabus:uos
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Important Derivatives & Integrals @fsc
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FSc Part 1 (Mathematics): KPK
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Dr. Muhammad Imran Qurshi
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Definitions: FSc Part1 KPK @fsc-part1-kpk
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Definitions: FSc Part1 KPK @math-11-kpk
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Complex Analysis by M Usman Hamid @notes
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Metric Spaces (Notes) @notes
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Question 4 Exercise 5.4 @math-11-kpk:sol:unit05
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Question 3 and 4 Exercise 6.2 @math-11-kpk:sol:unit06
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FSc/ICS Part 1 (Mathematics): KPK
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Notes of Mathematics
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MTH611: Integral Inequalities (Fall 2019) @atiq
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Vector Analysis by Hameed Ullah: Notes @bsc
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Short Term Preparation FSc/ICS 1 @fsc-part1-ptb
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FSc (Kyber Pakhtunkhwa (KPK) Boards) @fsc
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Measure Theory by M Usman Hamid & Saima Akram @notes
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Unit 07: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Notes of Vector Analysis @bsc
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Fluid Mechanics by Ali Raza @notes
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Handwritten Notes of Real Analysis by Asim Marwat @notes
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Real Analysis Notes by Prof Syed Gul Shah @notes
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MCQs Bank: FSc-I @fsc-part1-ptb
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Solutions: Math 11 KPK @math-11-kpk
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Advance Analysis by Ms. Iqra Liaqat @notes
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Functional Analysis by Mr. Tahir Hussain Jaffery @notes
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Chapter 03: Matrices @bsc:notes_of_mathematical_method
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