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Question Number 45517    Answers: 0   Comments: 0

find S(x)=Σ_(n=1) ^∞ (x^n /n^2 ) with ∣x∣<1 .

$${find}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} }\:\:{with}\:\mid{x}\mid<\mathrm{1}\:\:. \\ $$

Question Number 45514    Answers: 0   Comments: 1

Question Number 45512    Answers: 0   Comments: 11

Calculate: (((2^4 + (1/4)) (4^4 + (1/4))(6^4 + (1/4))(8^4 + (1/4))(10^4 + (1/4))(12^4 + (1/4)))/((1^4 + (1/4))(3^4 + (1/4)) (5^4 + (1/4)) (7^4 + (1/4)) (9^4 + (1/4))(11^4 + (1/4))))

$$\mathrm{Calculate}:\:\:\:\frac{\left(\mathrm{2}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{4}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{6}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{8}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{10}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{12}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)}{\left(\mathrm{1}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{3}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{5}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{7}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\:\left(\mathrm{9}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{11}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)} \\ $$

Question Number 45511    Answers: 0   Comments: 0

In a triangle ABC , ∠ ABC = 30^0 , and AC = 10. A circle is drawn to circumscribe the triangle . Find the radius of the circle.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{ABC}\:,\:\:\angle\:\mathrm{ABC}\:=\:\mathrm{30}^{\mathrm{0}} \:,\:\:\mathrm{and}\:\:\mathrm{AC}\:=\:\mathrm{10}.\:\mathrm{A}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{to} \\ $$$$\mathrm{circumscribe}\:\mathrm{the}\:\mathrm{triangle}\:.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}. \\ $$

Question Number 45506    Answers: 1   Comments: 0

If ax^2 +by^2 +2hxy+2gx+2fy+c=0 be the equation of an ellipse, find coordinates of its centre.

$${If}\:\:\:{ax}^{\mathrm{2}} +{by}^{\mathrm{2}} +\mathrm{2}{hxy}+\mathrm{2}{gx}+\mathrm{2}{fy}+{c}=\mathrm{0} \\ $$$${be}\:{the}\:{equation}\:{of}\:{an}\:{ellipse},\:{find} \\ $$$${coordinates}\:{of}\:{its}\:{centre}. \\ $$

Question Number 45500    Answers: 1   Comments: 0

Question Number 45498    Answers: 1   Comments: 3

Question Number 45495    Answers: 1   Comments: 0

Question Number 45494    Answers: 0   Comments: 0

Question Number 45477    Answers: 0   Comments: 4

Question Number 45482    Answers: 1   Comments: 0

Question Number 45464    Answers: 1   Comments: 3

Differentiate with respect to x arctan(((a^2 +x^2 )/(a^2 −x^2 )))

$$\boldsymbol{\mathrm{D}}\mathrm{ifferentiate}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{arctan}}\left(\frac{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right) \\ $$

Question Number 45456    Answers: 1   Comments: 5

Question Number 45451    Answers: 1   Comments: 0

Question Number 45450    Answers: 1   Comments: 1

Question Number 45448    Answers: 0   Comments: 5

Question Number 45443    Answers: 0   Comments: 0

Question Number 45440    Answers: 1   Comments: 0

show that ((1+2sin2θ−cos2θ)/(1+sin2θ+cos2θ)) ≡ tanθ

$${show}\:{that}\: \\ $$$$\frac{\mathrm{1}+\mathrm{2}{sin}\mathrm{2}\theta−{cos}\mathrm{2}\theta}{\mathrm{1}+{sin}\mathrm{2}\theta+{cos}\mathrm{2}\theta}\:\equiv\:{tan}\theta \\ $$

Question Number 45439    Answers: 2   Comments: 0

Show that the square of every odd integer is of the form 8m + 1

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{every}\:\mathrm{odd}\:\mathrm{integer}\:\mathrm{is}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\:\:\mathrm{8m}\:+\:\mathrm{1} \\ $$

Question Number 45433    Answers: 1   Comments: 0

find the of differnt ways in which a cricket team consisting of 11people,can be choosen from the group of 16

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{differnt}}\:\boldsymbol{\mathrm{ways}}\: \\ $$$$\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{cricket}}\:\boldsymbol{\mathrm{team}}\:\boldsymbol{\mathrm{consisting}}\:\boldsymbol{\mathrm{of}} \\ $$$$\mathrm{11}\boldsymbol{\mathrm{people}},\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{choosen}} \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{group}}\:\boldsymbol{\mathrm{of}}\:\mathrm{16} \\ $$

Question Number 45429    Answers: 0   Comments: 0

a set containing (k+1) elements has 8 more subsets that of a set containing k elements. find the value of k

$$\mathrm{a}\:\mathrm{set}\:\mathrm{containing}\:\left(\boldsymbol{\mathrm{k}}+\mathrm{1}\right)\:\mathrm{elements} \\ $$$$\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{that}\:\mathrm{of}\: \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{containing}\:\boldsymbol{\mathrm{k}}\:\mathrm{elements}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{k}} \\ $$

Question Number 45427    Answers: 0   Comments: 4

Question Number 45422    Answers: 1   Comments: 0

Three consecutive terms of a G.P are the 3rd, 5th and 8th term of an A.P. Find the common ratio.

$$\mathrm{Three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}\:\mathrm{are}\:\mathrm{the}\:\mathrm{3rd},\:\mathrm{5th}\:\mathrm{and}\:\mathrm{8th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}. \\ $$

Question Number 45417    Answers: 1   Comments: 0

Find image of plane x−y+z−3=0 in plane 2x+y−z+4=0 ?

$${Find}\:{image}\:{of}\:{plane}\:{x}−{y}+{z}−\mathrm{3}=\mathrm{0}\:{in}\: \\ $$$${plane}\:\mathrm{2}{x}+{y}−{z}+\mathrm{4}=\mathrm{0}\:? \\ $$

Question Number 45413    Answers: 2   Comments: 1

if y=((sin^(−1) x)/(√(1+x^2 ))) show that (dy/dx)(1+x^2 )+xy=1

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{{y}}=\frac{\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \boldsymbol{{x}}}{\sqrt{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }}\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}\left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} \right)+\boldsymbol{{xy}}=\mathrm{1} \\ $$

Question Number 45410    Answers: 1   Comments: 1

given the AP a,a +d ,a+2d,a+3d,... show that S_n = (n/2){(2a+(n−1)d}

$${given}\:{the}\:{AP} \\ $$$${a},{a}\:+{d}\:,{a}+\mathrm{2}{d},{a}+\mathrm{3}{d},... \\ $$$${show}\:{that}\: \\ $$$${S}_{{n}} =\:\frac{{n}}{\mathrm{2}}\left\{\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right\}\right. \\ $$

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