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![maths - Linedr Inequdlities Complete Formulqs 2. LINEAR INEQUALITY IN ONE VARIABLE INEQUALITIES BASIC SYMBOLS General form: Greater than: ax + b > 0 Less thon: ax + b < 0 Greater than or equal toः > b > 0 ax Less than or equal to: < b<0 X 3. RULES FOR SOLVING INEQUALITIES 4. SOLUTION SET Adding or subtracting the same number on both The solution of an inequality is] the set of dll volues of the sides does not change the inequality sign. variable that satisfy it Multiplying or dividing both sides by a positive Inequdlity sign remdins the sume number Multiplying or dividing both sides by a negative Inequality sign is reversed number >2 6. LINEAR INEQUALITIES IN 5. GRAPHICAL REPRESENTATION ON NUMBER LINE TWO VARIABLES Open circle (o) for or General form: Closed circle for < or > by < c 5 X by > c shows direction of solution ax Arrow by < c X by > c aX SOLUTION OF LINEAR INEQUALITY IN 8. GRAPHICAL RULES TWO VARIABLES Dotted line for < or Steps: Solid line for < or 2 Replace inequality with equality: ax by = @ Shaded region represents solution set Draw the boundary line Choose a test point (usually origin) Check which region satisfies the inequality Shade the required region | 10. IMPORTANT POINTS 9. SYSTEM OF LINEAR INEQUALITIES Inequalities have infinitely many solutions The common shaded region satisfying all Graphical method is compulsory for two] inequdlities is the solution variables Boundary line may or may not be included) Linedr Inequdlities Complete Formulqs 2. LINEAR INEQUALITY IN ONE VARIABLE INEQUALITIES BASIC SYMBOLS General form: Greater than: ax + b > 0 Less thon: ax + b < 0 Greater than or equal toः > b > 0 ax Less than or equal to: < b<0 X 3. RULES FOR SOLVING INEQUALITIES 4. SOLUTION SET Adding or subtracting the same number on both The solution of an inequality is] the set of dll volues of the sides does not change the inequality sign. variable that satisfy it Multiplying or dividing both sides by a positive Inequdlity sign remdins the sume number Multiplying or dividing both sides by a negative Inequality sign is reversed number >2 6. LINEAR INEQUALITIES IN 5. GRAPHICAL REPRESENTATION ON NUMBER LINE TWO VARIABLES Open circle (o) for or General form: Closed circle for < or > by < c 5 X by > c shows direction of solution ax Arrow by < c X by > c aX SOLUTION OF LINEAR INEQUALITY IN 8. GRAPHICAL RULES TWO VARIABLES Dotted line for < or Steps: Solid line for < or 2 Replace inequality with equality: ax by = @ Shaded region represents solution set Draw the boundary line Choose a test point (usually origin) Check which region satisfies the inequality Shade the required region | 10. IMPORTANT POINTS 9. SYSTEM OF LINEAR INEQUALITIES Inequalities have infinitely many solutions The common shaded region satisfying all Graphical method is compulsory for two] inequdlities is the solution variables Boundary line may or may not be included) - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_398320_12a45ff5_1773486397161_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=161_sc.jpg "maths - Linedr Inequdlities Complete Formulqs 2. LINEAR INEQUALITY IN ONE VARIABLE INEQUALITIES BASIC SYMBOLS General form: Greater than: ax + b > 0 Less thon: ax + b < 0 Greater than or equal toः > b > 0 ax Less than or equal to: < b<0 X 3. RULES FOR SOLVING INEQUALITIES 4. SOLUTION SET Adding or subtracting the same number on both The solution of an inequality is] the set of dll volues of the sides does not change the inequality sign. variable that satisfy it Multiplying or dividing both sides by a positive Inequdlity sign remdins the sume number Multiplying or dividing both sides by a negative Inequality sign is reversed number >2 6. LINEAR INEQUALITIES IN 5. GRAPHICAL REPRESENTATION ON NUMBER LINE TWO VARIABLES Open circle (o) for or General form: Closed circle for < or > by < c 5 X by > c shows direction of solution ax Arrow by < c X by > c aX SOLUTION OF LINEAR INEQUALITY IN 8. GRAPHICAL RULES TWO VARIABLES Dotted line for < or Steps: Solid line for < or 2 Replace inequality with equality: ax by = @ Shaded region represents solution set Draw the boundary line Choose a test point (usually origin) Check which region satisfies the inequality Shade the required region | 10. IMPORTANT POINTS 9. SYSTEM OF LINEAR INEQUALITIES Inequalities have infinitely many solutions The common shaded region satisfying all Graphical method is compulsory for two] inequdlities is the solution variables Boundary line may or may not be included) Linedr Inequdlities Complete Formulqs 2. LINEAR INEQUALITY IN ONE VARIABLE INEQUALITIES BASIC SYMBOLS General form: Greater than: ax + b > 0 Less thon: ax + b < 0 Greater than or equal toः > b > 0 ax Less than or equal to: < b<0 X 3. RULES FOR SOLVING INEQUALITIES 4. SOLUTION SET Adding or subtracting the same number on both The solution of an inequality is] the set of dll volues of the sides does not change the inequality sign. variable that satisfy it Multiplying or dividing both sides by a positive Inequdlity sign remdins the sume number Multiplying or dividing both sides by a negative Inequality sign is reversed number >2 6. LINEAR INEQUALITIES IN 5. GRAPHICAL REPRESENTATION ON NUMBER LINE TWO VARIABLES Open circle (o) for or General form: Closed circle for < or > by < c 5 X by > c shows direction of solution ax Arrow by < c X by > c aX SOLUTION OF LINEAR INEQUALITY IN 8. GRAPHICAL RULES TWO VARIABLES Dotted line for < or Steps: Solid line for < or 2 Replace inequality with equality: ax by = @ Shaded region represents solution set Draw the boundary line Choose a test point (usually origin) Check which region satisfies the inequality Shade the required region | 10. IMPORTANT POINTS 9. SYSTEM OF LINEAR INEQUALITIES Inequalities have infinitely many solutions The common shaded region satisfying all Graphical method is compulsory for two] inequdlities is the solution variables Boundary line may or may not be included) - ShareChat")
![maths - Statistics - · Complete Formulas 1. Mean ( Arithmetic Mean ) ( a ) Individual Series Mean ( x ) = x n ( b ) Discrete Series Mean ( x ) = Σfx Σf ( c ) Continuous Series - Direct Method Mean ( x ) = fx Σf ( d ) Assumed Mean Method x = a + ( Efd ) Where : dx - a ( e ) Step Deviation Method x = a + ( Σfd ) x h Where : d = 3. Mode x - a h ( a ) Discrete / Individual Series Mode = Value occurring most frequently ( b ) Continuous Series Mode = 1 + [ f₁ - fo [ 2f1 - fo - f2 ] 5. Variance ( a ) Individual Series σ² = Σ ( x - x ) ² n ( b ) Discrete Series 02 Σf ( x - x ) ² Σf ( c ) Step Deviation Method 02 = x h [ Σf d² - ( 3rd ) ² ] × h² ΣΑ x 2. Median ( a ) Individual Series ( b ) Discrete Series Median n + 1 2 th observation Median = Value corresponding to cumulative frequency ≥2 ( c ) Continuous Series Median = 1+ [ ( ) ] xh n Where : lower limit of median class cf cumulative frequency before median class f = frequency of median class hclass width 4. Empirical Relation Mode = 3 Median - 2 Mean f1 = frequency of modal class fo frequency of preceeding class = = f2 frequency of succeeding class 6. Standard Deviation Standard Deviation ( σ ) = √Variance = 7. Coefficient of Variation ( CV ) σ CV = × 100 x 8. Comparison of Two Data Sets Greater CV Smaller CV Greater variability More consistency - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_185459_1913881c_1773454876584_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=584_sc.jpg "maths - Statistics - · Complete Formulas 1. Mean ( Arithmetic Mean ) ( a ) Individual Series Mean ( x ) = x n ( b ) Discrete Series Mean ( x ) = Σfx Σf ( c ) Continuous Series - Direct Method Mean ( x ) = fx Σf ( d ) Assumed Mean Method x = a + ( Efd ) Where : dx - a ( e ) Step Deviation Method x = a + ( Σfd ) x h Where : d = 3. Mode x - a h ( a ) Discrete / Individual Series Mode = Value occurring most frequently ( b ) Continuous Series Mode = 1 + [ f₁ - fo [ 2f1 - fo - f2 ] 5. Variance ( a ) Individual Series σ² = Σ ( x - x ) ² n ( b ) Discrete Series 02 Σf ( x - x ) ² Σf ( c ) Step Deviation Method 02 = x h [ Σf d² - ( 3rd ) ² ] × h² ΣΑ x 2. Median ( a ) Individual Series ( b ) Discrete Series Median n + 1 2 th observation Median = Value corresponding to cumulative frequency ≥2 ( c ) Continuous Series Median = 1+ [ ( ) ] xh n Where : lower limit of median class cf cumulative frequency before median class f = frequency of median class hclass width 4. Empirical Relation Mode = 3 Median - 2 Mean f1 = frequency of modal class fo frequency of preceeding class = = f2 frequency of succeeding class 6. Standard Deviation Standard Deviation ( σ ) = √Variance = 7. Coefficient of Variation ( CV ) σ CV = × 100 x 8. Comparison of Two Data Sets Greater CV Smaller CV Greater variability More consistency - ShareChat")
![grammer - PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_658125_2fa71c54_1773368625271_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=271_sc.jpg "grammer - PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: - ShareChat")
![neet - Muble Jలtuzatim SmbaNt షuouNg | pxp % Plax ( fgaoboaw Pkaneodand ) tne Two 7೮೬ SyNGAY Taple fuuen] + +e Se NPN embu0 ehopom ^~@_ T Muble Jలtuzatim SmbaNt షuouNg | pxp % Plax ( fgaoboaw Pkaneodand ) tne Two 7೮೬ SyNGAY Taple fuuen] + +e Se NPN embu0 ehopom ^~@_ T - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_120165_16f37678_1773305033874_sc_rotated.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=otated.jpg "neet - Muble Jలtuzatim SmbaNt షuouNg | pxp % Plax ( fgaoboaw Pkaneodand ) tne Two 7೮೬ SyNGAY Taple fuuen] + +e Se NPN embu0 ehopom ^~@_ T Muble Jలtuzatim SmbaNt షuouNg | pxp % Plax ( fgaoboaw Pkaneodand ) tne Two 7೮೬ SyNGAY Taple fuuen] + +e Se NPN embu0 ehopom ^~@_ T - ShareChat")
