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Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
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== The set comprising all rational and irrational numbers is referred to as the real numbers, denoted as \( \mathbb{R} \). ====Terminating Decimal==== A decimal nu... and denominator. They often represent irrational numbers. ===Example=== \( \pi \) (pi) is a well-known n... nt of \( A \). ===Example=== In the set of real numbers \( \mathbb{R} \), two important binary operations
Definitions: FSc Part 1 (Mathematics): PTB
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umber:** The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted $\mathbb{R}$. * **Terminating decimal:*... are addition and multiplication in a set of real numbers. * **Complex number:** The number of the form ... am:** The figure representing one or more complex numbers on the complex plane is called argand diagram.
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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ad> The main topics of this exercise are complex numbers, real part and imaginary part of complex numbers, properties of the fundamental operation on complex numbers, complex number as ordered pair of real numbers and special subset of complex numbers. These notes are bas
MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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$ - The figure representing one or more complex numbers on the complex plane is called -------- diagram. ... \mathbb{R}$ where $\mathbb{R}$ is the set of real numbers is called the -------- plane. - ordered -... e of these - If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1+z_2}$ is - $z_1+z_2$ ... e of these - If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1-z_2}$ is - $z_1+z_2$
Ch 07: Permutation, Combination and Probability @fsc-part1-ptb:important-questions
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// BISE Gujranwala(2015)// * How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How ... _{n-r}$ ---// BISE Gujrawala(2017)// * Find the numbers of diagonals of a $6-digits$ figures ---// BISE ... n $^nP_2=30$ ---// BISE Sargodha(2015)// * Find numbers of diagonals of $6-dided$ figure. ---// BISE Sarg... nd probability that the dots on the top are prime numbers or odd numbers. ---// BISE Lahore(2017)// * F
MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
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f these - The objects in a set are called - Numbers - Terms - Elements - None of these ... ther number when performed on --------- - Two numbers - A single number - Three numbers - All of these - The constant function is ------- - $y... roup is said to be -------- if it contains finite numbers of elements - Finite group - Semi group
Multiple Choice Questions (MCQs)
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mber - Multiplicative property of order of real numbers is that $\forall a, b, c \in R$ * $a<b \wedge... $ - The figure representing one or more complex numbers on a complex plane is called ------- diagram.
Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
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in topics of this exercise are properties of real numbers, binary operation, addition and multiplication la... ng equations (Letters, where used, represent real numbers). **Solutions** (i) $(4+9)=(9+4)$ **Property:*