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Question Number 194065    Answers: 0   Comments: 0

Question Number 194064    Answers: 1   Comments: 0

Question Number 194059    Answers: 0   Comments: 0

Question Number 194058    Answers: 0   Comments: 0

Ques. 1 Let G = C_5 × C_(25) × C_(625) . Determine the number of elements of each order in G Ques. 2 List the abelian groups of order 16 and of order 27 up to Isomorphism. Ques. 3 Describe a Sylow 2−subgroup in S_5 , and how many Sylow 2−subgroups are in S_5 ?

$$\mathrm{Ques}.\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Let}\:\mathrm{G}\:=\:\mathrm{C}_{\mathrm{5}} \:×\:\mathrm{C}_{\mathrm{25}} \:×\:\mathrm{C}_{\mathrm{625}} .\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{each}\:\mathrm{order}\:\mathrm{in}\:\mathrm{G} \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{List}\:\mathrm{the}\:\mathrm{abelian}\:\mathrm{groups}\:\mathrm{of}\:\mathrm{order}\:\mathrm{16} \\ $$$$\mathrm{and}\:\mathrm{of}\:\mathrm{order}\:\mathrm{27}\:\mathrm{up}\:\mathrm{to}\:\mathrm{Isomorphism}. \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{3}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Describe}\:\mathrm{a}\:\mathrm{Sylow}\:\mathrm{2}−\mathrm{subgroup}\:\mathrm{in}\:\mathrm{S}_{\mathrm{5}} , \\ $$$$\mathrm{and}\:\mathrm{how}\:\mathrm{many}\:\mathrm{Sylow}\:\mathrm{2}−\mathrm{subgroups}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{S}_{\mathrm{5}} \:? \\ $$

Question Number 194057    Answers: 0   Comments: 0

find all functions such that f(x)f(y) = x^a f((y/2))+y^b f((x/2))

$${find}\:{all}\:{functions}\:{such}\:{that} \\ $$$${f}\left({x}\right){f}\left({y}\right)\:=\:{x}^{{a}} {f}\left(\frac{{y}}{\mathrm{2}}\right)+{y}^{{b}} {f}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$

Question Number 194037    Answers: 3   Comments: 0

Let a_1 ,a_2 ....a_n ∈R^+ , a_1 +a_2 +.....a_n =1 prove that: (a_1 /(2−a_1 ))+(a_2 /(2−a_2 )).......(a_n /(2−a_n ))≥(n/(2n−1))

$$ \\ $$$${Let}\:{a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ....{a}_{{n}} \in{R}^{+} ,\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +.....{a}_{{n}} =\mathrm{1} \\ $$$${prove}\:{that}: \\ $$$$\frac{{a}_{\mathrm{1}} }{\mathrm{2}−{a}_{\mathrm{1}} }+\frac{{a}_{\mathrm{2}} }{\mathrm{2}−{a}_{\mathrm{2}} }.......\frac{{a}_{{n}} }{\mathrm{2}−{a}_{{n}} }\geqslant\frac{{n}}{\mathrm{2}{n}−\mathrm{1}} \\ $$

Question Number 194034    Answers: 0   Comments: 0

Question Number 194031    Answers: 1   Comments: 1

Question Number 194030    Answers: 0   Comments: 0

Question Number 194029    Answers: 1   Comments: 1

Question Number 194021    Answers: 2   Comments: 1

find ((1+(2)^(1/3) +(4)^(1/3) ))^(1/3) =?

$${find}\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{2}}+\sqrt[{\mathrm{3}}]{\mathrm{4}}}=? \\ $$

Question Number 194020    Answers: 0   Comments: 0

F_n = F_n _(−1) +F_(n−2) F_2 = F_1 =1 F_n : 1 , 1 , 2 , 3 ,5... f(x)= Σ_(n=1) ^∞ F_n x^( n) = x + x^( 2) +Σ_(n=3) ^∞ (F_(n−1) +F_(n−2) )x^( n) = x+x^2 + Σ_(n=3) ^∞ F_(n−1) x^( n) + x^( 2) f (x) = x + x^( 2) + x^( 2) f(x) +x Σ_(n=2) ^∞ F_n x^( n) = x + x^( 2) + x^( 2) f(x)−x^( 2) + xf(x) ∴ f(x)= (x/(1−x−x^( 2) )) (generating function ) (x/(1−x−x^( 2) )) =Σ_(n=1) ^∞ F_n x^( n) ⇒ (x^( 2) /(1−x−x^( 2) ))=Σ_(n=1) ^∞ F_n x^( n+1) x= (1/(10)) ⇒ ((1/(100))/(1−(1/(10))−(1/(100)))) = Σ_(n=1) ^∞ (F_n /(10^( n+1) )) ⇒ { Σ_(n=1) ^∞ (( F_n )/(10^( n+1) )) = (1/(89)) }

$$\:\:\:\:\:\:{F}_{{n}} =\:{F}_{{n}} \:_{−\mathrm{1}} +{F}_{{n}−\mathrm{2}} \:\:\:\:\:\:{F}_{\mathrm{2}} =\:{F}_{\mathrm{1}} =\mathrm{1}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:{F}_{{n}} \::\:\:\:\:\mathrm{1}\:,\:\mathrm{1}\:,\:\mathrm{2}\:,\:\mathrm{3}\:,\mathrm{5}...\:\: \\ $$$$\:\:\:\:\:\:\:{f}\left({x}\right)=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:{F}_{{n}} \:{x}^{\:{n}} \:=\:{x}\:+\:{x}^{\:\mathrm{2}} \:+\underset{{n}=\mathrm{3}} {\overset{\infty} {\sum}}\left({F}_{{n}−\mathrm{1}} +{F}_{{n}−\mathrm{2}} \right){x}^{\:{n}} \\ $$$$\:\:\:=\:\:{x}+{x}^{\mathrm{2}} \:+\:\underset{{n}=\mathrm{3}} {\overset{\infty} {\sum}}{F}_{{n}−\mathrm{1}} {x}^{\:{n}} \:+\:{x}^{\:\mathrm{2}} \:{f}\:\left({x}\right) \\ $$$$\:\:\:\:=\:{x}\:+\:{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{2}} {f}\left({x}\right)\:+{x}\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}{F}_{{n}} \:{x}^{\:{n}} \\ $$$$\:\:\:=\:{x}\:+\:{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{2}} {f}\left({x}\right)−{x}^{\:\mathrm{2}} +\:{xf}\left({x}\right) \\ $$$$ \\ $$$$\:\: \\ $$$$\:\: \\ $$$$\:\:\therefore\:\:\:{f}\left({x}\right)=\:\frac{{x}}{\mathrm{1}−{x}−{x}^{\:\mathrm{2}} }\:\:\:\left({generating}\:{function}\:\right)\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{{x}}{\mathrm{1}−{x}−{x}^{\:\mathrm{2}} }\:\:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{F}_{{n}} {x}^{\:{n}} \:\Rightarrow\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{1}−{x}−{x}^{\:\mathrm{2}} }=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{F}_{{n}} \:{x}^{\:{n}+\mathrm{1}} \\ $$$$\:\:\:{x}=\:\frac{\mathrm{1}}{\mathrm{10}}\:\Rightarrow\:\:\frac{\frac{\mathrm{1}}{\mathrm{100}}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{10}}−\frac{\mathrm{1}}{\mathrm{100}}}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{F}_{{n}} }{\mathrm{10}^{\:{n}+\mathrm{1}} } \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\left\{\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\:{F}_{{n}} }{\mathrm{10}^{\:{n}+\mathrm{1}} }\:=\:\frac{\mathrm{1}}{\mathrm{89}}\:\:\:\:\:\right\}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 194017    Answers: 1   Comments: 0

Question Number 194015    Answers: 1   Comments: 0

Question Number 194011    Answers: 0   Comments: 0

Give formula of the following complexes Compound (a)Diammine Silver (i) Chloride (b)Dichloro aqua tetra ammine Cobalt(iii) Chloride (c)Tetra ammine (ii) hexachloro platinum (iv) (d)Bromo cyano fluoro Carbonly Iron (iii)

$${Give}\:{formula}\:{of}\:{the}\:{following}\:{complexes} \\ $$$${Compound} \\ $$$$\left({a}\right){Diammine}\:{Silver}\:\left({i}\right)\:{Chloride} \\ $$$$ \\ $$$$\left({b}\right){Dichloro}\:{aqua}\:{tetra}\:{ammine}\:{Cobalt}\left({iii}\right)\:{Chloride} \\ $$$$ \\ $$$$\left({c}\right){Tetra}\:{ammine}\:\left({ii}\right)\:{hexachloro}\:{platinum}\:\left({iv}\right) \\ $$$$ \\ $$$$\left({d}\right){Bromo}\:{cyano}\:{fluoro}\:{Carbonly}\:{Iron}\:\left({iii}\right) \\ $$

Question Number 193987    Answers: 1   Comments: 0

Question Number 193984    Answers: 0   Comments: 1

Know f(x^(−1) )=f^( −1) (x) Find f(x)¿

$${Know}\:{f}\left({x}^{−\mathrm{1}} \right)={f}^{\:−\mathrm{1}} \left({x}\right) \\ $$$${Find}\:{f}\left({x}\right)¿ \\ $$

Question Number 193982    Answers: 3   Comments: 0

∫ ((6x^3 +9x^2 +15x+6)/( (√(x^2 +x+1)))) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{6x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{15x}+\mathrm{6}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$

Question Number 193981    Answers: 0   Comments: 0

Question Number 193978    Answers: 1   Comments: 0

Question Number 193976    Answers: 2   Comments: 0

Question Number 193975    Answers: 2   Comments: 1

Question Number 193972    Answers: 0   Comments: 4

Question Number 193971    Answers: 2   Comments: 0

y= ⌊ x^( 2) ⌋ + ⌊ x ⌋ ⇒ R_y =? Range

$$ \\ $$$$\:\:\:\:\:\:{y}=\:\lfloor\:{x}^{\:\mathrm{2}} \:\rfloor\:+\:\lfloor\:{x}\:\rfloor\:\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:{R}_{{y}} \:=?\:\:\:\:\:\:\:{Range} \\ $$

Question Number 193965    Answers: 2   Comments: 0

a,b,c are positive real numbers And (1/(a+b+1))+(1/(b+c+1))+(1/(a+c+1))≥1 prove that a+b+c≥ab+bc+ac

$${a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers} \\ $$$${And} \\ $$$$\frac{\mathrm{1}}{{a}+{b}+\mathrm{1}}+\frac{\mathrm{1}}{{b}+{c}+\mathrm{1}}+\frac{\mathrm{1}}{{a}+{c}+\mathrm{1}}\geqslant\mathrm{1} \\ $$$${prove}\:{that}\:{a}+{b}+{c}\geqslant{ab}+{bc}+{ac} \\ $$

Question Number 193962    Answers: 2   Comments: 0

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