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- Question 1, Exercise 8.1 @math-11-nbf:sol:unit08
- on 1(i)===== Find the value of $\cos (\alpha \pm \beta), \sin (\alpha \pm \beta)$ and $\tan (\alpha \pm \beta)$ for the pair of angles. $\alpha=180^{\circ}, \beta=60^{\circ}$ ** Solution. ** Given: $\alpha=18
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- itions-Muzzammil-Subhan ]] ===== Chapter 01: Number system ===== * **Rational number:** A number which can be written in the form of $\frac{p}{q}$, where $p,q \in \mathbb{Z}$, $q\neq 0$, is called
- Question 11, Exercise 8.1 @math-11-nbf:sol:unit08
- 270^{\circ}-\lambda\right)}=1$ ** Solution. ** \begin{align*} L.H.S & = \dfrac{\sin \left(180^{\circ... (90^{\circ}+\alpha\right)}=-1$ ** Solution. ** \begin{align*} L.H.S & = \frac{\sin \left(90^{\circ}+... estion 11(iii)===== Show that: $\tan \alpha+\tan \beta=\dfrac{\sin (\alpha+\beta)}{\cos \alpha \cos \beta}$ ** Solution. ** \begin{align*} L.H.S & = \ta
- Question 5, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... 5(i)===== If $\tan \alpha =\dfrac{3}{4}$, $\sec \beta =\dfrac{13}{5}$ and neither the terminal side of the angle of measure $\alpha$ nor $\beta$ in the first Quadrant, then find: $\sin \left( \alpha +\beta \right)$. ====Solution==== Given: $\tan\alpha
- Question 5, Exercise 10.1 @math-11-kpk:sol:unit10
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... 5(i)===== If $\tan \alpha =\dfrac{3}{4}$, $\sec \beta =\dfrac{13}{5}$ and neither the terminal side of the angle of measure $\alpha$ nor $\beta$ in the first Quadrant, then find: $\sin \left( \alpha +\beta \right)$. ====Solution==== Given: $\tan\alpha
- Question 2, Exercise 2.3 @math-11-kpk:sol:unit02
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... the matrix by using elementary row operation. $$\begin{bmatrix}4 & -2 & 5 \\ 2 & 1 & 0 \\ -1 & 2 & 3 \end{bmatrix}$$ ====Solution==== Let $$A=\begin{bmatrix} 4 & -2 & 5 \\ 2 & 1 & 0 \\ -1 & 2 & 3 \end{bmatrix}.$$ Then \begin{align}|A|&=\begin{vmatrix}4 & -2 & 5 \\ 2 & 1
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- r his valuable contribution. =====Chapter 01: Number System===== ====Rational Number==== A number which can be expressed in the form \( \dfrac{p}{q} \), where \( p, q \in \mathbb{Z} \) and \( q \neq
- Question 3, Exercise 2.1 @math-11-kpk:sol:unit02
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(i)===== If $A=\begin{bmatrix}x & y & z\end{bmatrix}$, $B=\begin{bmatrix}a & h & g\\h & b & f\\g & f & c\end{bmatrix}$ and $C=\begin{bmatrix}x\\y\\z\end{bmatrix}$. Verify that $\l
- Khuram Ali Khan
- al. Appl., Vol. 2010, 16 pages, (Published on October 18, 2010), Impact Factor 0.879. ([[http://www.jo... ek Fawzi Abdelhamid Ibrahim, and Khuram Ali Khan, Behavior of a competitive system of second-order dif... Vol 4, No 6 (2014), 1091-1113 (Published in December 2014). ([[http://scik.org/index.php/jmcs/article... Ali Khan and Josip Pečarić, Cyclic Refinement of Beck’s Inequalities, Proc. A. Razmadze Math. Inst.,
- Question 4 Exercise 8.2 @math-11-nbf:sol:unit08
- \theta$ lies in QI, $\sin$ is positive in QI, so \begin{align*} \sin\theta & = \sqrt{1-\left(\frac{3}... = \frac{4}{5} \end{align*} (a) $\sin 2 \theta$ \begin{align*} \sin 2\theta & = 2 \sin\theta \cos\the... \right) \left(\frac{3}{5} \right)\\ \end{align*} \begin{align*} \implies \boxed{\sin 2\theta = \frac{24}{25}}. \end{align*} (b) $\cos 2 \theta$ \begin{align*} \cos 2\theta & = 1-2\sin^2\theta \\ &
- Question 5 and 6, Exercise 8.1 @math-11-nbf:sol:unit08
- stion 5===== For $\sin \alpha=\dfrac{4}{5}, \tan \beta=-\dfrac{5}{12}$ with terminal side of an angles in QII, find $\cos (\alpha+\beta)$ and $\cos (\alpha-\beta)$. ** Solution. ** Given: $\sin \alpha=\dfrac{4}{5}$, $\alpha$ is in QII and $\tan \beta=-\dfrac{5}{12}$, $\beta$ is in QII. We have an
- PPSC Paper 2011 (Lecturer in Mathematics) @ppsc
- - $x^2=1$ - The group of Quaterminons is a non-abelian group of order --------- \\ - $6$ - $... very group of prime order is ------- \\ - an abelian but not cyclic - an abelian group - a non-abelian group - a cyclic group - Any two conjugate subgroup of a group $G
- Exercise 6.1 @matric:9th_science
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... 3-2x^2)$, $54(27x^4-x)$ **Solution:**\\ (i) $\begin{align} x^2+5x+6&=x^2+3x+2x+6,\\ &=x(x+3)+2(x+3)\\ &=(x+3)(x+2) \end{align}$ $\begin{align} x^2-4x-12&=x^2-6x+2x-12,\\ &=x(x-6)+2(x... &=(x-6)(x+2) \end{align}$ H.C.F= $x+2$ (ii) $\begin{align} x^3-27 &=x^3-3^3,\\ &=(x-3)(x^2+3x+9)\e
- Question 13 Exercise 6.2 @math-11-kpk:sol:unit06
- ok of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Pesha... , Pakistan. =====Question 13(i)===== Find the number of permutation of word "Excellence." How many of these permutations begin with $\mathrm{E}$ ? ====Solution==== The total number of letters in 'Excellence' are: $n=10$, out of w
- MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
- ====== MCQs: Ch 01 Number Systems ====== High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry ... - $-2i$ - $2$ - $\sqrt{2}$ is ------- number. - natural - complex - irrational ... displaystyle{\frac{p}{q}}$ form - A rational number is a number which can be expressed in the form -
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university
- Chapter 01: Viewer @bsc:notes_of_calculus_with_analytic_geometry:ch01_real_numbers_limits_and_continuity
- 1st SIBAU-NU International Workshop on Matrix Analysis and Linear Algebra (15-17 October 2021) @events
- How to prepare admission test (A short guide) @papers:old_admission_test_of_assms_for_ph.d._mathematics
- International Conference on Mathematics and Its Applications GCU Lahore, Pakistan (November 13-15, 2017) @conferences
- Second Conference on Mathematical Sciences (SCMS-2013), International Islamic University, Islamabad, Pakistan (1-2 November 2013) @conferences
- 5th UMT International Conference on Pure and Applied Mathematics, Lahore (March 29th to 31st, 2019) @conferences
- Recent Advances in Mathematical Methods, Models & Applications, LSC Lahore, Pakistan (April 13-14, 2019) @conferences
- 3rd International Conference on Pure and Applied Mathematics UoS Sargodha (November 10-11, 2017) @conferences
- International Conference on Computing and Mathematical Sciences, IBA Sukkur (February 25-26, 2017) @conferences
- 2nd International Conference on Pure and Applied Mathematics UoS Sargodha (November 26-27, 2016) @conferences
- International Conference on Recent Advances in Applied Mathematics, CIIT, Lahore (Dec 17-18, 2015) @conferences
- 5th World Conference on 21st Century Mathematics 2011, ASSMS, Lahore (9-13 February 2011) @conferences
- 22nd International Pure Mathematics Conference on Algebra, Analysis and Geometry (23 to 25 August 2021) @events
- Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations @fsc:kpk_fsc_part_1
- Chapter 10: Viewer @bsc:notes_of_mathematical_method:ch10_higher_order_linear_differential_equations
- View Online: BSc Mathematics (Old Papers) @papers:old_papers_for_bsc_mathematics:sargodha_university