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- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- Punjab Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to **Muhammad Waqas Sulaima... contribution. Definitions by Mr. Aurang Zaib are given at [[:fsc-part1-ptb:definitions-aurang-zaib]] Definitions by Mr. [[people:Muzzammil-Subhan]] are given at [[:fsc-part1-ptb:definitions-Muzzammil-Subhan ... ruth Table:** A table to drives truth values of a given compound statement in terms of its component part
- Question 6(i-ix), Exercise 1.4 @math-11-nbf:sol:unit01
- bad, Pakistan. =====Question 6(i)===== Write a given complex number in the algebraic form: $\sqrt{2}\l... 1-i. \end{align} =====Question 6(ii)===== Write a given complex number in the algebraic form: $5\left(\co... }i \end{align*} =====Question 6(iii)===== Write a given complex number in the algebraic form: $2\left(\co... -2i \end{align*} =====Question 6(iv)===== Write a given complex number in the algebraic form: $4\left(\co
- PPSC Paper 2021 (Lecturer in Mathematics) @ppsc
- Lecturer in Mathematics)}} On this page, we have given question from old (past) paper of Lecturer in Mat... n year 2021. This is a MCQs paper and answers are given at the end of the paper. At the end of the PDF is also given to download. This paper is provided by Ms. [[:peo... hbb{R}\) - \(\mathbb{Q}\) - Not exist - Given \( \left(a_n\right)_{n\in \mathbb{N}}\), where \(
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- e inverse of 1? (iii) Is the set $G$, under the given operation a group? Abelian or non-abelian? **Solutions**\\ (i) From the given table we have $0+0=0$ and $0+1=1$. This show tha... (iii) It is clear from table that element of the given set satisfies closure law, associative law, identity law and inverse law thus given set is group under $\oplus$. Also it satisfies c
- Question 5, Exercise 1.3 @math-11-kpk:sol:unit01
- the equation ${{z}^{2}}+z+3=0$. ====Solution==== Given: $${{z}^{2}}+z+3=0.$$ According to the quadratic ... qrt{11}}{2}i\end{align} Thus the solutions of the given equation are $-\dfrac{1}{2}\pm\dfrac{\sqrt{11}}{2... the equation ${{z}^{2}}-1=z$.\\ ====Solution==== Given: $${{z}^{2}}-1=z$$ $$\implies {{z}^{2}}-z-1=0$$ A... sqrt{5}}{2}.\end{align} Thus the solutions of the given equations are $\dfrac{1\pm\sqrt{5}}{2}$. =====Que
- Question 1 and 2 Exercise 4.1 @math-11-kpk:sol:unit04
- == Find first four terms of the sequence with the given general terms: $a_n=\dfrac{n(n+1)}{2}$ ====Solution==== Given: $$a_n=\dfrac{n(n+1)}{2}$$ For first term, put $n... == Find first four terms of the sequence with the given general terms: $a_n=(-1)^{n-1} 2^{n+1}$ ====Solution==== Given: $$a_n=(-1)^{n-1} 2^{n+1}$$ For first term, put
- Question 2 Exercise 4.3 @math-11-kpk:sol:unit04
- of the components $a_1, a_n, n, d$ and $S_n$ are given. Find the one that is missing: $a_1=2, n=17, d=3$. GOOD ====Solution==== Given: $a_1=2, n=17, d=3$ \\ We need to find $a_{17}$ a... of the components $a_1, a_n, n, d$ and $S_n$ are given. Find the one that are missing $a_1=-40, S_{21}=210$. GOOD ====Solution==== Given: $a_1=-40$ and $S_{21}=210$.\\ So we have $n=21$
- Question 6(x-xvii), Exercise 1.4 @math-11-nbf:sol:unit01
- abad, Pakistan. =====Question 6(x)===== Write a given complex number in the algebraic form: $7 \sqrt{2}... revious parts.// =====Question 6(xi)===== Write a given complex number in the algebraic form: $10 \sqrt{2... vious parts.// =====Question 6(xii)===== Write a given complex number in the algebraic form: $2\left(\co... vious parts.// =====Question 6(xiii)===== Write a given complex number in the algebraic form: $\dfrac{1}{
- Question 5 Exercise 8.2 @math-11-nbf:sol:unit08
- s \theta$ and $\tan \theta$ using the information given: $\sin 2 \theta=\frac{24}{25}, 2 \theta$ in QII ** Solution. ** Given: $\sin 2\theta=\dfrac{24}{25}$, $2\theta$ in QII.... s \theta$ and $\tan \theta$ using the information given: $\cos 2 \theta=-\frac{7}{25}, 2 \theta$ in QIII ** Solution. ** Given: \(\cos 2\theta = -\dfrac{7}{25}\) and \(2\theta\
- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- , Punjab Text Book Board, Lahore. The answers are given at the end of the page. ====MCQs==== - A well ... $B\cup A$ - $\phi$ - $B$ - The set of a given set $S$ denoted by $P(S)$ containing all the poss... one of these - Logical form of $(A \cup B)'$ is given by - $p \vee q$ - $p \wedge q$ - $\si... (p \vee q)$ - Logical form of $(A \cap B)'$ is given by - $\sim (p \vee q)$ - $p \wedge q$
- About Us
- y putting some related keywords in the search box given in main menu. This site contains old papers, mo... l institute or board or university. The resources given on this site holds no official position in govern... e or board or university). The material/resources given on this site are open educational resources (OER)... ut type="info" icon="true"> While using resources given on this site you agree to a term that we (MathCit
- Mathematics 9 (Science Group) @matric
- formula to calculate distance between two points given in Cartesian plane. * use distance formula to find distance between two given points. * use distance formula to show that given three (or more) points are colinear. * Use distance formula to show that the given three non-collinear points for * and equilate
- Unit 03: Vectors (Solutions) @math-11-kpk:sol
- * Find a unit vector in the direction of another given vector. * Find the position vector of a point w... divides the line segment joining two points in a given ratio. * Use vectors to prove simple theorems o... e by a constant force in moving an object along a given vector. * Define cross or vector product of two... ween two vectors. * Find the vector moment of a given force about a given point. * Define scalar trip
- Question 5, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- \left( \alpha +\beta \right)$. ====Solution==== Given: $\tan\alpha =\dfrac{3}{4}$. As $\tan\alpha$ is... arrow \quad \sin\alpha &= \frac{3}{5}\end{align} Given: $\sec \beta =\dfrac{13}{5}.$ As \begin{align... \left( \alpha +\beta \right)$. ====Solution==== Given: $\tan\alpha =\dfrac{3}{4}$. As $\tan\alpha$ is... arrow \quad \sin\alpha &= \frac{3}{5}\end{align} Given: $\sec \beta =\dfrac{13}{5}.$ As \begin{align
- Question 2, Exercise 2.2 @math-11-kpk:sol:unit02
- & 2 & 0 \end{matrix}\right|=0$. ====Solution==== Given $$\left| \begin{matrix} 1 & 2 & 0 \\ 3 & 1... -1 & 3 \end{matrix} \right|=0$. ====Solution==== Given $$\left| \begin{matrix} 1 & 2 & 3 \\ -8 & ... 2 & 1 & 4 \end{matrix} \right|$. ====Solution==== Given $$\left| \begin{matrix} 1 & 3 & -2 \\ 3 & ... 2 & 4 & 2 \end{matrix} \right|$. ====Solution==== Given $$\left| \begin{matrix}3 & 2 & 0 \\1 & 1 & -3 \