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Question Number 46973 Answers: 1 Comments: 0

Question Number 46972 Answers: 0 Comments: 0

let m,n denote any two possitive relative prime integers,then prove thatφ(mn)=φ(m)∙φ(n)

$$\boldsymbol{{let}}\:{m},{n}\:{denote}\:{any}\:{two}\:{possitive}\:{relative}\:{prime}\:{integers},{then}\:{prove}\:{that}\phi\left({mn}\right)=\phi\left({m}\right)\centerdot\phi\left({n}\right) \\ $$

Question Number 46962 Answers: 0 Comments: 1

Question Number 46959 Answers: 1 Comments: 5

The reminder when polynomial 1+x^2 +x^4 +x^6 +....+x^(22) is divided by 1+x^ +x^2 +x^3 +.....+x^(11) is =?

$${The}\:{reminder}\:{when}\:{polynomial} \\ $$$$\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} +{x}^{\mathrm{6}} +....+{x}^{\mathrm{22}} \:{is}\:{divided}\:{by} \\ $$$$\mathrm{1}+{x}^{} +{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +.....+{x}^{\mathrm{11}} \:{is}\:=? \\ $$

Question Number 46944 Answers: 1 Comments: 3

Question Number 46935 Answers: 1 Comments: 1

Question Number 46925 Answers: 1 Comments: 0

The third term of a GP is 4. The product of first five terms is

$$\mathrm{The}\:\mathrm{third}\:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{GP}\:\mathrm{is}\:\mathrm{4}.\:\mathrm{The}\:\mathrm{product} \\ $$$$\mathrm{of}\:\mathrm{first}\:\mathrm{five}\:\mathrm{terms}\:\mathrm{is} \\ $$

Question Number 46924 Answers: 1 Comments: 0

If ((a−x)/(px)) = ((a−y)/(qy)) = ((a−z)/(rz)) and p, q, r are in AP, then x, y, z will be in

$$\mathrm{If}\:\:\frac{{a}−{x}}{{px}}\:=\:\frac{{a}−{y}}{{qy}}\:=\:\frac{{a}−{z}}{{rz}}\:\mathrm{and}\:{p},\:{q},\:{r}\:\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{AP},\:\mathrm{then}\:{x},\:{y},\:{z}\:\:\mathrm{will}\:\mathrm{be}\:\mathrm{in} \\ $$

Question Number 46923 Answers: 1 Comments: 0

a, b, c are in AP or GP or HP according as ((a−b)/(b−c)) is equal to

$${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{or}\:\mathrm{GP}\:\mathrm{or}\:\mathrm{HP}\:\mathrm{according} \\ $$$$\mathrm{as}\:\frac{{a}−{b}}{{b}−{c}}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 46922 Answers: 1 Comments: 0

Thr 6th term of an AP is equal to 2, the value of the common difference of the AP. Which makes the product a_1 a_4 a_5 least is given by

$$\mathrm{Thr}\:\mathrm{6th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{2},\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}. \\ $$$$\mathrm{Which}\:\mathrm{makes}\:\mathrm{the}\:\mathrm{product}\:{a}_{\mathrm{1}} \:{a}_{\mathrm{4}} \:{a}_{\mathrm{5}} \:\mathrm{least} \\ $$$$\mathrm{is}\:\mathrm{given}\:\:\mathrm{by} \\ $$

Question Number 46921 Answers: 1 Comments: 0

The sum of first two terms of an infinite GP is 1 and every term is twice the sum of the successive terms. Its first term is

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{two}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{GP}\:\mathrm{is}\:\mathrm{1}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{successive}\:\mathrm{terms}.\:\mathrm{Its}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is} \\ $$

Question Number 46920 Answers: 0 Comments: 0

If the sides of a triangle are in AP, and the greatest angle of the triangle is double the smallest angle, the ratio of the sides of the triangle is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{double}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{angle},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$

Question Number 46919 Answers: 0 Comments: 9

Question Number 46918 Answers: 1 Comments: 0

Let S_n denote the sum of first n terms of an AP. If S_(2n) = 3 S_n , then the ratio (S_(3n) /S_n ) is equal to

$$\mathrm{Let}\:{S}_{{n}} \:\mathrm{denote}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:{n}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{an}\:\mathrm{AP}.\:\mathrm{If}\:\:\:{S}_{\mathrm{2}{n}} =\:\mathrm{3}\:{S}_{{n}} \:,\:\mathrm{then}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{S}_{\mathrm{3}{n}} }{{S}_{{n}} }\:\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 46907 Answers: 1 Comments: 0

Question Number 46906 Answers: 0 Comments: 1

Question Number 46898 Answers: 2 Comments: 2

∫((tanx)/((tanx+1)^2 −2tan^2 x ))dx=??

$$\int\frac{{tanx}}{\left({tanx}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2}{tan}^{\mathrm{2}} {x}\:\:}{dx}=?? \\ $$

Question Number 46891 Answers: 1 Comments: 0

X can finish a work in 15 days at 8hrs. a day. Y can finish it in 6(2/3) days at 9 hrs. a day. Find in how many days X and Y can finish it working together 10 hrs. a day?

$$\mathrm{X}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{15}\:\mathrm{days}\:\mathrm{at}\:\mathrm{8hrs}. \\ $$$$\mathrm{a}\:\mathrm{day}.\:\mathrm{Y}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{in}\:\mathrm{6}\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{days}\:\mathrm{at} \\ $$$$\mathrm{9}\:\mathrm{hrs}.\:\mathrm{a}\:\mathrm{day}.\:\mathrm{Find}\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{days} \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{working}\:\mathrm{together}\: \\ $$$$\mathrm{10}\:\mathrm{hrs}.\:\mathrm{a}\:\mathrm{day}? \\ $$

Question Number 46889 Answers: 1 Comments: 1

Question Number 46882 Answers: 0 Comments: 2

factorize inside C[x] x^2 +y^2 +z^2

$${factorize}\:{inside}\:{C}\left[{x}\right]\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} \\ $$

Question Number 46881 Answers: 0 Comments: 1

factorize inside C[x] the polynom x^n +y^n

$${factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:\:{x}^{{n}} \:+{y}^{{n}} \\ $$

Question Number 46880 Answers: 0 Comments: 0

factorize inside C[x] x^n −y^n with n natural integr

$${factorize}\:{inside}\:{C}\left[{x}\right]\:{x}^{{n}} −{y}^{{n}} \:\:{with}\:{n}\:{natural}\:{integr} \\ $$

Question Number 46864 Answers: 1 Comments: 2

Question Number 46860 Answers: 1 Comments: 2

Find the sum to infinity whose n^(th) term is (n/2^(n−1) ) .

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{whose}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\frac{\mathrm{n}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\:. \\ $$

Question Number 46858 Answers: 0 Comments: 0

solve (1+x^2 )y^(′′) −((2x)/(x^3 +1))y^′ +xy =x e^(−2x) .

$${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} \:−\frac{\mathrm{2}{x}}{{x}^{\mathrm{3}} \:+\mathrm{1}}{y}^{'} \:\:+{xy}\:={x}\:{e}^{−\mathrm{2}{x}} . \\ $$

Question Number 46857 Answers: 1 Comments: 2

solve 2x y^′ +(1+x^2 )y =xe^(−x) withy(o)=1

$${solve}\:\mathrm{2}{x}\:{y}^{'} \:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}\:={xe}^{−{x}} \:\:\:{withy}\left({o}\right)=\mathrm{1}\: \\ $$

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