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![biology - PHYUM PRIEERD They ஈீD $ cewh catel Qute goneollப IoAnQ ೧ 8pongiLla )_ ( للط لللمم اعرم mukceiuLor organuims org syslom_৮ prexnk wbld ConcQ Ilcten tronspont 01 hop cion /and excretion o @huton r೮೦ i೧ Digestioo fs lotroce tlulo ع spongio,Gibres_or-Spiculea & Skelekool mmode ob not sepecate ) Cexe Hemaphrodiel QL FeriuboD &sA(oterocQ develanh preLent) ( LccUcL_Stcge is Ind(roue Syoon , Spongillc bcH Spoge ೭೦ PHVUN CDELENTEBBTA CCNIDBRIB moskut swlDomio Iheg ore {oe sessyel moul ue ) 0 Mulieuloک okaorisms levell w &AuQ 09` Aada[U The ore diploblooticzand Slmmak?t onidoudtoz Cnioob@b pue೨enh ٥ oD kotack Cod9 and |e Cnfoblasbs /e_uoed_kur_ccboraq-e_sdebente] 0 Q0d Ihe ophura n pr 8 Dioetioo intrateuulcc & extq ckiulaC , and howe LaLm CrboDote CeaAl SRelet Cniclariq xbubit மooy bmப ೧ bolyp abd meduAQ _ Polyps & %LQ ZrdcQ bom_LRe ODd hudro ) adamstql PHYUM PRIEERD They ஈீD $ cewh catel Qute goneollப IoAnQ ೧ 8pongiLla )_ ( للط لللمم اعرم mukceiuLor organuims org syslom_৮ prexnk wbld ConcQ Ilcten tronspont 01 hop cion /and excretion o @huton r೮೦ i೧ Digestioo fs lotroce tlulo ع spongio,Gibres_or-Spiculea & Skelekool mmode ob not sepecate ) Cexe Hemaphrodiel QL FeriuboD &sA(oterocQ develanh preLent) ( LccUcL_Stcge is Ind(roue Syoon , Spongillc bcH Spoge ೭೦ PHVUN CDELENTEBBTA CCNIDBRIB moskut swlDomio Iheg ore {oe sessyel moul ue ) 0 Mulieuloک okaorisms levell w &AuQ 09` Aada[U The ore diploblooticzand Slmmak?t onidoudtoz Cnioob@b pue೨enh ٥ oD kotack Cod9 and |e Cnfoblasbs /e_uoed_kur_ccboraq-e_sdebente] 0 Q0d Ihe ophura n pr 8 Dioetioo intrateuulcc & extq ckiulaC , and howe LaLm CrboDote CeaAl SRelet Cniclariq xbubit மooy bmப ೧ bolyp abd meduAQ _ Polyps & %LQ ZrdcQ bom_LRe ODd hudro ) adamstql - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_227536_1f4fe84f_1772261226310_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=310_sc.jpg "biology - PHYUM PRIEERD They ஈீD $ cewh catel Qute goneollப IoAnQ ೧ 8pongiLla )_ ( للط لللمم اعرم mukceiuLor organuims org syslom_৮ prexnk wbld ConcQ Ilcten tronspont 01 hop cion /and excretion o @huton r೮೦ i೧ Digestioo fs lotroce tlulo ع spongio,Gibres_or-Spiculea & Skelekool mmode ob not sepecate ) Cexe Hemaphrodiel QL FeriuboD &sA(oterocQ develanh preLent) ( LccUcL_Stcge is Ind(roue Syoon , Spongillc bcH Spoge ೭೦ PHVUN CDELENTEBBTA CCNIDBRIB moskut swlDomio Iheg ore {oe sessyel moul ue ) 0 Mulieuloک okaorisms levell w &AuQ 09` Aada[U The ore diploblooticzand Slmmak?t onidoudtoz Cnioob@b pue೨enh ٥ oD kotack Cod9 and |e Cnfoblasbs /e_uoed_kur_ccboraq-e_sdebente] 0 Q0d Ihe ophura n pr 8 Dioetioo intrateuulcc & extq ckiulaC , and howe LaLm CrboDote CeaAl SRelet Cniclariq xbubit மooy bmப ೧ bolyp abd meduAQ _ Polyps & %LQ ZrdcQ bom_LRe ODd hudro ) adamstql PHYUM PRIEERD They ஈீD $ cewh catel Qute goneollப IoAnQ ೧ 8pongiLla )_ ( للط لللمم اعرم mukceiuLor organuims org syslom_৮ prexnk wbld ConcQ Ilcten tronspont 01 hop cion /and excretion o @huton r೮೦ i೧ Digestioo fs lotroce tlulo ع spongio,Gibres_or-Spiculea & Skelekool mmode ob not sepecate ) Cexe Hemaphrodiel QL FeriuboD &sA(oterocQ develanh preLent) ( LccUcL_Stcge is Ind(roue Syoon , Spongillc bcH Spoge ೭೦ PHVUN CDELENTEBBTA CCNIDBRIB moskut swlDomio Iheg ore {oe sessyel moul ue ) 0 Mulieuloک okaorisms levell w &AuQ 09` Aada[U The ore diploblooticzand Slmmak?t onidoudtoz Cnioob@b pue೨enh ٥ oD kotack Cod9 and |e Cnfoblasbs /e_uoed_kur_ccboraq-e_sdebente] 0 Q0d Ihe ophura n pr 8 Dioetioo intrateuulcc & extq ckiulaC , and howe LaLm CrboDote CeaAl SRelet Cniclariq xbubit மooy bmப ೧ bolyp abd meduAQ _ Polyps & %LQ ZrdcQ bom_LRe ODd hudro ) adamstql - ShareChat")
![neet - Dole Pege @০ Kngdom lum Dhu KINCDOL 0,0 Bodv OCdlum SYMMETRY Poxifera Asymmetrital Clluldn onimaliq Level Coeleotrata ( Cofdora) Rodiol Lissue Clenophoro Plaky Acoelomatex omgan bod५ @1iy belmiol Bilataal (uulkb out e8 Ocgan syslem ಉudocoಬomoror AscheQ Cwtth fakse miotbex CooLom) Coekmatex Lush] coolom) ৮ue Annelida Axtppod c Nolu ( Echnodenmat Hemthokdi Cordcq Dole Pege @০ Kngdom lum Dhu KINCDOL 0,0 Bodv OCdlum SYMMETRY Poxifera Asymmetrital Clluldn onimaliq Level Coeleotrata ( Cofdora) Rodiol Lissue Clenophoro Plaky Acoelomatex omgan bod५ @1iy belmiol Bilataal (uulkb out e8 Ocgan syslem ಉudocoಬomoror AscheQ Cwtth fakse miotbex CooLom) Coekmatex Lush] coolom) ৮ue Annelida Axtppod c Nolu ( Echnodenmat Hemthokdi Cordcq - ShareChat](https://cdn4.sharechat.com/33d5318_1c8/1ac44639_1772195024041_sc.jpeg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=41_sc.jpeg "neet - Dole Pege @০ Kngdom lum Dhu KINCDOL 0,0 Bodv OCdlum SYMMETRY Poxifera Asymmetrital Clluldn onimaliq Level Coeleotrata ( Cofdora) Rodiol Lissue Clenophoro Plaky Acoelomatex omgan bod५ @1iy belmiol Bilataal (uulkb out e8 Ocgan syslem ಉudocoಬomoror AscheQ Cwtth fakse miotbex CooLom) Coekmatex Lush] coolom) ৮ue Annelida Axtppod c Nolu ( Echnodenmat Hemthokdi Cordcq Dole Pege @০ Kngdom lum Dhu KINCDOL 0,0 Bodv OCdlum SYMMETRY Poxifera Asymmetrital Clluldn onimaliq Level Coeleotrata ( Cofdora) Rodiol Lissue Clenophoro Plaky Acoelomatex omgan bod५ @1iy belmiol Bilataal (uulkb out e8 Ocgan syslem ಉudocoಬomoror AscheQ Cwtth fakse miotbex CooLom) Coekmatex Lush] coolom) ৮ue Annelida Axtppod c Nolu ( Echnodenmat Hemthokdi Cordcq - ShareChat")
![study - 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](https://cdn4.sharechat.com/33d5318_1c8/c95932_1772180888879_sc.jpeg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=79_sc.jpeg "study - 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")
![basic maths knowledge - 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](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_117117_f7fc964_1772115115381_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=381_sc.jpg "basic maths knowledge - 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")