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- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- alent if there exists a one-to-one correspondence between their elements. ===Example:=== \( A = \{2, 4, 6,... thers. ====Function==== A function is a relation between two non-empty sets \( A \) and \( B \), where eac
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- t if one to one correspondence can be established between them.\\ e.g. $A=\{2,4,6,8\}$, $B=\{a,b,c,d\}$ ... etic Mean:** A number $A$ is said to be the $A.M$ between the two numbers $a$ and $b$. If $a,A,b$ are in $A... ic Mean:** A number is said to be geometric means between two numbers $a$ and $b$. If $a,G,b$ are in $G.P$.... mber $H$ is said to be the harmonic means ($H.M$) between two numbers $a$ and $b$, if $a, H, b$ are in $H.P
- Mathematics CUI: LaTeX Resources
- $ $ (dollar) sign to write equation or symbols in between statements or sentences, e.g.\\ Let $I$ be an int
- MathCraft: PDF to LaTeX file: Sample-02 @mathcraft
- eq f(x) \leq s(x)$$ Integrating both inequalities between $a$ and $b$ \begin{equation*} \int_{a}^{b} r(x)
- MTH480: Introductory Quantum Mechanics @atiq
- underlying physical principles. The relationship between classical and quantum mechanics is explored to il
- Question 14 Exercise 4.2 @math-11-kpk:sol:unit04
- Question 14(i)===== Insert three arithmetic means between 6 and 41. GOOD ====Solution==== Let $A_1, A_2, A_3$ be three arithmetic means between 6 and 41. Then $6, A_1, A_2, A_3, 41$ are in A.P.... ac{1}{4}.\end{align} Hence three arithmetic means between 6 and 41 are $$14\dfrac{3}{4},23\dfrac{1}{2},32\d... Question 14(ii)===== Insert four arithmetic means between 17 and 32. GOOD ====Solution==== Let $A_1, A_2, A
- Question 17 Exercise 4.2 @math-11-kpk:sol:unit04
- ==Question 17===== There are $n$ arithmetic means between 5 and 32 such that the ratio of the 3rd and 7th m... 1, A_2, A_3, \ldots, A_n$ be $n$ arithmetic means between 5 and 32. Then $5, A_1, A_2, A_3, \ldots, A_n, 32
- Question 16 Exercise 4.2 @math-11-kpk:sol:unit04
- ====Question 16===== Insert five arithmetic means between $5$ and $8$ and show that their sum is five times the arithmetic mean between $5$ and $8$. GOOD ====Solution==== Let $A_1, A_2, A_3, A_4, A_5$ be five arithmetic means between $5$ and $8$. Then $5, A_1, A_2, A_3, A_4, A_5, 8$... },6,\dfrac{13}{2},7, \dfrac{15}{2}$ are five A.Ms between $5$ & $8$. Now \begin{align}A_1&+A_2+A_3+A_4+A_5
- Question 15 Exercise 4.2 @math-11-kpk:sol:unit04
- a^{n+1}+b^{n+1}}{a^n+b^n}$ is the arithmetic mean between $a$ and $b$. Where $a$ and $b$ are not zero simul... on==== Suppose $A$ represents the arithmetic mean between $a$ and $b$, then $$ A=\dfrac{a+b}{2}. --- (1) $$
- Question 12 & 13 Exercise 4.2 @math-11-kpk:sol:unit04
- =====Question 13(i)===== Find the arithmetic mean between $12$ and $18$. GOOD ====Solution==== Here $a=12, ... }\\&=\dfrac{30}{2}=15.\end{align} Hence 15 is A.M between 12 and 18. GOOD =====Question 13(ii)===== Find the arithmetic mean between $\dfrac{1}{3}$ and $\dfrac{1}{4}$. ====Solution==... ===Question 13(iii)===== Find the arithmetic mean between $-6,-216$. GOOD ====Solution==== Here $a=-6, b=-2
- Question 5 and 6 Exercise 6.3 @math-11-kpk:sol:unit06
- total number lines. We know one line can be drawn between each two points, so total number of lines are: $$
- Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
- =====Question 11===== How many numbers each lying between $10$ and $1000$ can be formed with digits $2.3,4,
- Question 14 and 15 Exercise 6.2 @math-11-kpk:sol:unit06
- !$ And the two particular people can be arranged between them selves in $2 !=2$ ways. Hence, number of wa
- Mathematics 10 (Science Group) @matric
- angle in circular system) and prove the relation between radians and degree. * establish the rule $l=r\t
- Unit 04: Sequence and Series (Solutions) @math-11-kpk:sol
- ing arithmetic sequence. * Know arithmetic mean between two * Insert n arithmetic means tEtween two num... series. * Show that sum of $n$ arithmetic means between two numbers is equal to n times their arithmetic ... lving geometric sequence. * Know geometric mean between two numbers. * Insert $n$ geometric means between two numbers. * Define a geometric series. * Find t
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university