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Maths #maths formula #maths #Maths guru #exams
Maths guru - ShareChat
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"Scientific Approach"
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Maths#maths #math tricks
maths - POLYGON Polygon Basics Polygon closed figure with 3 or more sides 2 Types: polygon 180' all diagonals inside Convex all interior angles 7 Concave polygon at least one interior 180', some diagonals outside: ongle 2 Regular Polygon n-sided polygon hqs: Always convex n vertices interior All sides equdl angles All interior gngles equql n exterior qngles. Interior Angles Exterior Angles 2) x 1809 Sum of interior angles (n Sum of all exterior angles = 3609 360 Each interior angle (regular polygon): Each exterior angle (regular polygon): [(n 2) 18091 Internal angle + External angle = 1809 360% Number of sides: n Exterior angle Diagonals 3) Number of diogonols in 0 polygon Regular Hexagon Large diqgonals: FC = AD = BE = 2g Number of sides = 6 Short diagonals: FD BF = V3a 0B Each interior angle = १२०० Regular hexagon = 6 equilateral triangles Each exterior angle 60% Also = 3 rhombus of equql qred Number of diagonals = 9 (3v3/2)q2' Area Perimeter 6a Circumrodius R = 0 Area Relations in Regular Hexagon Triangle EAC is equilateral If P, Q R dre midpoints: APQR is equilateral with side (3a/2) with side V3a Area(EAC) Area(APQR) 2 8 Area(hexagon)| Area(ABCDEF) Regular Octagon] 2(12' Area 1)02 Number of sides = 8 Perimeter 8a Inradius: r = 2v2 _ 2 135% Each interior angle 12+12 . 0 Each exterior angle = ४५९ Circumradius: R = 12 - 12 Number of diagonals = 20 POLYGON Polygon Basics Polygon closed figure with 3 or more sides 2 Types: polygon 180' all diagonals inside Convex all interior angles 7 Concave polygon at least one interior 180', some diagonals outside: ongle 2 Regular Polygon n-sided polygon hqs: Always convex n vertices interior All sides equdl angles All interior gngles equql n exterior qngles. Interior Angles Exterior Angles 2) x 1809 Sum of interior angles (n Sum of all exterior angles = 3609 360 Each interior angle (regular polygon): Each exterior angle (regular polygon): [(n 2) 18091 Internal angle + External angle = 1809 360% Number of sides: n Exterior angle Diagonals 3) Number of diogonols in 0 polygon Regular Hexagon Large diqgonals: FC = AD = BE = 2g Number of sides = 6 Short diagonals: FD BF = V3a 0B Each interior angle = १२०० Regular hexagon = 6 equilateral triangles Each exterior angle 60% Also = 3 rhombus of equql qred Number of diagonals = 9 (3v3/2)q2' Area Perimeter 6a Circumrodius R = 0 Area Relations in Regular Hexagon Triangle EAC is equilateral If P, Q R dre midpoints: APQR is equilateral with side (3a/2) with side V3a Area(EAC) Area(APQR) 2 8 Area(hexagon)| Area(ABCDEF) Regular Octagon] 2(12' Area 1)02 Number of sides = 8 Perimeter 8a Inradius: r = 2v2 _ 2 135% Each interior angle 12+12 . 0 Each exterior angle = ४५९ Circumradius: R = 12 - 12 Number of diagonals = 20 - ShareChat
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"Scientific Approach"
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Maths #math #maths formula
maths formula - ShareChat
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Maths #maths #maths formula #Maths guru
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Maths #maths #maths formula
maths formula - Sets & Relations Complefe Formulas १. SETS BASIC DEFINITIONS 2. TYPES OF SETS Set: A well-defined collection of objects: Empty Null sef = only one element Singleton set Element: An object belonging to sef 2 Finite set belongs to A a € A Infinite set belong does nof To A U a#A Universal sef Equal sets Equivalenf sefs 3. SUBSETS ASB -> A is Q subsef of B 4. POWER SET Power set P(A) = set of all subsets of A A is a proper subset of B A subsef B ) elements, Then |P(A)| = 2" Number of subsets of a set with n If A has 2n elements 6. PROPERTIES OF SET OPERATIONS 5. OPERATIONS ON SETS Commufqfive Iqws: AUB = BUA Union: AUB = {x : x E A or x & B} An B = BnA Intersection: AnB = {x:x eA and xeB} Associafive laws: (AUB)UC = AU(BUc) Difference: A - B = {x : x E A ond x E B} (AnB)nc=An(Bnc) Complement: A = U - A Disfribufive laws: Au(Bnc) = (AUB)n(Auc) An(BUC) = (AnB)U(AnC) Idenfify laws: AU0 = A AnU = A 7 DE MORGANS LAWS AUB) = AnB' 8. VENN DIAGRAM RESULTS (An B)' = A'UB' n(AUB) = n(A) + n(B) - n(AnB) n(A)+n(B)+n(C)-n(An B) n(AUBUC) n(Bnc) -n(CnA)+n(AnBnc) १०. TYPES OF RELATIONS ११. EQUIVALENCE RELATION 9. RELATIONS A relation R is an equivalence] A relation R from set A to set B Reflexive relqtion if it is: Symmetric subset of A x B is Reflexive Number of relafions from A fo B Symmetric Tronsitive Transitive 2nm (where n = elements in A, elements in B) m Sets & Relations Complefe Formulas १. SETS BASIC DEFINITIONS 2. TYPES OF SETS Set: A well-defined collection of objects: Empty Null sef = only one element Singleton set Element: An object belonging to sef 2 Finite set belongs to A a € A Infinite set belong does nof To A U a#A Universal sef Equal sets Equivalenf sefs 3. SUBSETS ASB -> A is Q subsef of B 4. POWER SET Power set P(A) = set of all subsets of A A is a proper subset of B A subsef B ) elements, Then |P(A)| = 2" Number of subsets of a set with n If A has 2n elements 6. PROPERTIES OF SET OPERATIONS 5. OPERATIONS ON SETS Commufqfive Iqws: AUB = BUA Union: AUB = {x : x E A or x & B} An B = BnA Intersection: AnB = {x:x eA and xeB} Associafive laws: (AUB)UC = AU(BUc) Difference: A - B = {x : x E A ond x E B} (AnB)nc=An(Bnc) Complement: A = U - A Disfribufive laws: Au(Bnc) = (AUB)n(Auc) An(BUC) = (AnB)U(AnC) Idenfify laws: AU0 = A AnU = A 7 DE MORGANS LAWS AUB) = AnB' 8. VENN DIAGRAM RESULTS (An B)' = A'UB' n(AUB) = n(A) + n(B) - n(AnB) n(A)+n(B)+n(C)-n(An B) n(AUBUC) n(Bnc) -n(CnA)+n(AnBnc) १०. TYPES OF RELATIONS ११. EQUIVALENCE RELATION 9. RELATIONS A relation R is an equivalence] A relation R from set A to set B Reflexive relqtion if it is: Symmetric subset of A x B is Reflexive Number of relafions from A fo B Symmetric Tronsitive Transitive 2nm (where n = elements in A, elements in B) m - ShareChat
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Biology #biology #NEET PREPETION
NEET PREPETION - CLASS AVEQ The characterustics] Potuue oue te prosence 0b +೦೦ bbಲ Hom eolhemic.ie tamm blooded onio మ SEun dxy & பயு toL_Lonill 920d exceph Le cbatcl oilgLond +2 Heod [ Pur chombekd _ Respure Harougb_Lupos { Oooe> ctH hollou Q ப pheumabc buxi Lzatioo &intemo& Se XeA Bepecote ೨- 04& OYporo &9, Crow, Pien Pam ot Y೨l . ]12023 09 CLASS AVEQ The characterustics] Potuue oue te prosence 0b +೦೦ bbಲ Hom eolhemic.ie tamm blooded onio మ SEun dxy & பயு toL_Lonill 920d exceph Le cbatcl oilgLond +2 Heod [ Pur chombekd _ Respure Harougb_Lupos { Oooe> ctH hollou Q ப pheumabc buxi Lzatioo &intemo& Se XeA Bepecote ೨- 04& OYporo &9, Crow, Pien Pam ot Y೨l . ]12023 09 - ShareChat
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"Scientific Approach"
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English #english #grammer
english - NOUN NUMBER & GENDER S NOUN NUMBER A SINGULAR NOUN 1 thing Definition Names one petson , ploce , animol, o L bou,` book , pe1 Example PLURAL NOUN 2 Definition Names moie than one boys , books , pens Example Common Plual Rules book books > > box boxes es > babies baby ies ५ > > > leaf leaves f/fe =>ves > 7 GENDER 8 NOUN VVAN VNNNNNNNA VA MASCULINE GENDER 1 Ring' Definition Male Example unce man , 7 EEMININE GENDER 2 Definition Female Example queen , aunt woman, > COMMON GENDER 3 Can be_male o female Definition child, teacheh , student Example 7 NEUTER GENDER [tuble , book, city] Definition No Example gendex_ Pluiol nouns show numbe, nouns show sex Ov gendల type . NOUN NUMBER & GENDER S NOUN NUMBER A SINGULAR NOUN 1 thing Definition Names one petson , ploce , animol, o L bou,` book , pe1 Example PLURAL NOUN 2 Definition Names moie than one boys , books , pens Example Common Plual Rules book books > > box boxes es > babies baby ies ५ > > > leaf leaves f/fe =>ves > 7 GENDER 8 NOUN VVAN VNNNNNNNA VA MASCULINE GENDER 1 Ring' Definition Male Example unce man , 7 EEMININE GENDER 2 Definition Female Example queen , aunt woman, > COMMON GENDER 3 Can be_male o female Definition child, teacheh , student Example 7 NEUTER GENDER [tuble , book, city] Definition No Example gendex_ Pluiol nouns show numbe, nouns show sex Ov gendల type . - ShareChat
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"Scientific Approach"
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Maths #maths #maths formula
maths - Algebra Complete Formulas మ 2. LINEAR EQUATIONS १. ALGEBRAIC IDENTITIES (a + b)२ = a२ + २ab + b२ General form: ax + b = 0 -b (0- 0)2 = 02 _ 20b + b2 Solution:| X = (q + b)(d - b) = 02 _ b2 b)3 03 + 302b + 30b2 + b3 (a + ४. ARITHMETIC PROGRESSION (AP) (0 - bj3 = 03 _ 302b + 30b2 _ b3 General term: dn = a + (n - 1)d b) (02 _ 43 + b3 = (q + ab + b२) Sum of first n terms: ( -b) (02 _ a3 _ b3 = + ab + b२) 2 [2q + (n - 1)d] Sn a२ + b२ + c२ + २(ab + bc + ca ) a +b + c)2 = 2 (a+ 4) Also, Sn 3. QUADRATIC EQUATIONS Standard form: ax2 + bx + C = 0 BINOMIAL THEOREM 6 4ac =b + 1b2 _ Quadratic Formula: x 20 nCaxn 1a + nCoxn (x + এ)" = Discriminant (D): D = b2 40c nCzxn-242 . an *+ Nature of roots: Generdl term: Tr+1 = nCr xn-r dr D > 0 _ Reql & distinct D = ০ -> Real & equal D < 0 - No real roots 8. INDICES & EXPONENTS 0 Sum of roots = qm x qn = am+n Product of roots am-n (m)n = 5. GEOMETRIC PROGRESSION (GP) amn General term: dn = arn-1 00 Sum of first n terms: Sn = q(rn- 1),r#1 [ =1 Sum to infinity: $ = Ir| <1 9. LOGARITHMS loga1 = 0 FACTORIAL & COMBINATIONS loga9 a = n! = n(n - 2) loga (xy) | logax logay Permutation: np loga(y) logax - logay Combindtion : nCr logaxn logax n rl(n logx Change of base: logqX ' Relqtion: nP nCr X r! loga Algebra Complete Formulas మ 2. LINEAR EQUATIONS १. ALGEBRAIC IDENTITIES (a + b)२ = a२ + २ab + b२ General form: ax + b = 0 -b (0- 0)2 = 02 _ 20b + b2 Solution:| X = (q + b)(d - b) = 02 _ b2 b)3 03 + 302b + 30b2 + b3 (a + ४. ARITHMETIC PROGRESSION (AP) (0 - bj3 = 03 _ 302b + 30b2 _ b3 General term: dn = a + (n - 1)d b) (02 _ 43 + b3 = (q + ab + b२) Sum of first n terms: ( -b) (02 _ a3 _ b3 = + ab + b२) 2 [2q + (n - 1)d] Sn a२ + b२ + c२ + २(ab + bc + ca ) a +b + c)2 = 2 (a+ 4) Also, Sn 3. QUADRATIC EQUATIONS Standard form: ax2 + bx + C = 0 BINOMIAL THEOREM 6 4ac =b + 1b2 _ Quadratic Formula: x 20 nCaxn 1a + nCoxn (x + এ)" = Discriminant (D): D = b2 40c nCzxn-242 . an *+ Nature of roots: Generdl term: Tr+1 = nCr xn-r dr D > 0 _ Reql & distinct D = ০ -> Real & equal D < 0 - No real roots 8. INDICES & EXPONENTS 0 Sum of roots = qm x qn = am+n Product of roots am-n (m)n = 5. GEOMETRIC PROGRESSION (GP) amn General term: dn = arn-1 00 Sum of first n terms: Sn = q(rn- 1),r#1 [ =1 Sum to infinity: $ = Ir| <1 9. LOGARITHMS loga1 = 0 FACTORIAL & COMBINATIONS loga9 a = n! = n(n - 2) loga (xy) | logax logay Permutation: np loga(y) logax - logay Combindtion : nCr logaxn logax n rl(n logx Change of base: logqX ' Relqtion: nP nCr X r! loga - ShareChat
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English #grammer
grammer - NOUN is the name ofl A noun a thing, or idea person, place , Kinds of Nouns 5. Abstract Noun 1. Proper Noun Examples: Indid; Examples: honesty; Radha Sunday, Diwali, Tqj Mahal bravery, childhood, kindness , wisdom 2. Common Noun Examples: country, girl; 6. Countable Noun dqy, festival , monument Examples: book, pen, boy, dpple, city 3. Collective Noun Exqmples: teqm, clqss, army, bunch, herd 7 Uncountoble Noun Examples: water; rice, ४. Material Noun sugor, knowledge, hair Examples : iron, gold , water, milk wood, NOUN is the name ofl A noun a thing, or idea person, place , Kinds of Nouns 5. Abstract Noun 1. Proper Noun Examples: Indid; Examples: honesty; Radha Sunday, Diwali, Tqj Mahal bravery, childhood, kindness , wisdom 2. Common Noun Examples: country, girl; 6. Countable Noun dqy, festival , monument Examples: book, pen, boy, dpple, city 3. Collective Noun Exqmples: teqm, clqss, army, bunch, herd 7 Uncountoble Noun Examples: water; rice, ४. Material Noun sugor, knowledge, hair Examples : iron, gold , water, milk wood, - ShareChat
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Maths #maths formula #math
math - Differentidl Equdtions Complefe Formulas DIFFERENTIAL EQUATION 2. ORDER & DEGREE DEFINITION 1 An equafion involving derivafives of a highesf order derivafive presenf Order dependent variable with respect to an power of highest order Degree derivative (when equation is polynomial | independent vqriqble is cqlled differenfiql equqtion . in derivatives) FORMATION OF DIFFERENTIAL EQUATION 3. GENERAL & PARTICULAR SOLUTION Eliminate arbitrary constants from the Generql solufion contains arbitrary given equation to form the differential constant(s) equarion. obfained by Particular solution assigning specific values to constants HOMOGENEOUS DIFFERENTIAL EQUATION 5. VARIABLES SEPARABLE FORM 6. A differenfial equafion of Ihe form: If equation is of the form: dx | f(x) g(y) dx =F(X) (gt)dy f(x) dx Then; Put ٧ VX dx d = v + * Infegrafe bofh sides 8. BERNOULLIS DIFFERENTIAL EQUATION ७. LINEAR DIFFERENTIAL EQUATION (LDE) Form : Standard form: Py Qy Py = Q efP dx Infegrafing Facfor (IF): Divide by Y and convert into linear IF = form. ((Q *IF) dx + C Solution : ٧ x I٤ 10. ORTHOGONAL TRAJECTORIES (BASIC IDEA) 9. EXACT DIFFERENTIAL EQUATION dy Slope Mdx + Ndy Given: 0 of curve dx M N Condition for exactness of orfhogonal frajecfory Slope y 0x dx Solution obtained by integrating M with] respect to * and N with respect to Y 12. IMPORTANT POINTS ll. IMPORTANT STANDARD RESULTS Every differential equation has dX = X + C infinitely many solutions Xn+1 xn dx గ+1 + C particular Inifial condifions give J ex d ' e* + C solution xdx = Inlxl + C Integration constant is compulsory Differentidl Equdtions Complefe Formulas DIFFERENTIAL EQUATION 2. ORDER & DEGREE DEFINITION 1 An equafion involving derivafives of a highesf order derivafive presenf Order dependent variable with respect to an power of highest order Degree derivative (when equation is polynomial | independent vqriqble is cqlled differenfiql equqtion . in derivatives) FORMATION OF DIFFERENTIAL EQUATION 3. GENERAL & PARTICULAR SOLUTION Eliminate arbitrary constants from the Generql solufion contains arbitrary given equation to form the differential constant(s) equarion. obfained by Particular solution assigning specific values to constants HOMOGENEOUS DIFFERENTIAL EQUATION 5. VARIABLES SEPARABLE FORM 6. A differenfial equafion of Ihe form: If equation is of the form: dx | f(x) g(y) dx =F(X) (gt)dy f(x) dx Then; Put ٧ VX dx d = v + * Infegrafe bofh sides 8. BERNOULLIS DIFFERENTIAL EQUATION ७. LINEAR DIFFERENTIAL EQUATION (LDE) Form : Standard form: Py Qy Py = Q efP dx Infegrafing Facfor (IF): Divide by Y and convert into linear IF = form. ((Q *IF) dx + C Solution : ٧ x I٤ 10. ORTHOGONAL TRAJECTORIES (BASIC IDEA) 9. EXACT DIFFERENTIAL EQUATION dy Slope Mdx + Ndy Given: 0 of curve dx M N Condition for exactness of orfhogonal frajecfory Slope y 0x dx Solution obtained by integrating M with] respect to * and N with respect to Y 12. IMPORTANT POINTS ll. IMPORTANT STANDARD RESULTS Every differential equation has dX = X + C infinitely many solutions Xn+1 xn dx గ+1 + C particular Inifial condifions give J ex d ' e* + C solution xdx = Inlxl + C Integration constant is compulsory - ShareChat