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Question Number 26241    Answers: 0   Comments: 2

∫(√(sin θ))dθ integration ?? solve quickly

$$\int\sqrt{\mathrm{sin}\:\theta}{d}\theta \\ $$$${integration}\:?? \\ $$$${solve}\:{quickly} \\ $$

Question Number 26240    Answers: 1   Comments: 1

y^((2)) −y=(1−e^(2x) )^((−1)/2)

$${y}^{\left(\mathrm{2}\right)} −{y}=\left(\mathrm{1}−{e}^{\mathrm{2}{x}} \right)^{\frac{−\mathrm{1}}{\mathrm{2}}} \\ $$

Question Number 26237    Answers: 1   Comments: 1

Question Number 26235    Answers: 1   Comments: 0

Find the real root of x^2 +(1/x)=c .

$${Find}\:{the}\:{real}\:{root}\:{of} \\ $$$$\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}}={c}\:. \\ $$

Question Number 26229    Answers: 1   Comments: 1

after factorise (x2+2x+1)we get

$$\mathrm{after}\:\mathrm{factorise}\:\left(\mathrm{x2}+\mathrm{2x}+\mathrm{1}\right)\mathrm{we}\:\mathrm{get} \\ $$

Question Number 26228    Answers: 0   Comments: 1

if x^4 +(1/x^4 )=322 find x^3 −(1/x^3 )

$$\mathrm{if}\:\mathrm{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{322}\:\mathrm{find}\:\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 26227    Answers: 1   Comments: 0

if x^2 +(1/x^2 )=98 find x^3 +(1/x^3 )

$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{98}\:\mathrm{find}\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 26222    Answers: 0   Comments: 2

find the value of Σ_(n=1) ^∝ (1/((n+1)(n+2)n^3 )) in terms of ξ(3) we give ξ(x)= Σ_(n=1) ^∝ (1/n^x ) and x>1 (zeta function of Rieman)

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right){n}^{\mathrm{3}} }\:{in}\:{terms}\:{of}\:\xi\left(\mathrm{3}\right) \\ $$$${we}\:{give}\:\xi\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\:{and}\:{x}>\mathrm{1} \\ $$$$\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$

Question Number 26224    Answers: 1   Comments: 1

find the value of x−(1/x).when x^4 +(1/x^4 )=332

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}.\mathrm{when}\:{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{332} \\ $$

Question Number 26218    Answers: 0   Comments: 2

∫_2 ^4 sinθ dθ

$$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\mathrm{sin}\theta\:{d}\theta \\ $$

Question Number 26207    Answers: 1   Comments: 0

I think of a two digit number.The sum of the digits is 9. When the number is reversed and subtracted from the original, the result is 45. Find the original number

$$\mathrm{I}\:\mathrm{think}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}.\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{9}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reversed}\:\mathrm{and}\:\mathrm{subtracted}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{original},\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{45}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number} \\ $$

Question Number 26205    Answers: 1   Comments: 1

Question Number 26200    Answers: 1   Comments: 0

Question Number 26198    Answers: 1   Comments: 0

(2x(√x)+x^2 +y^2 )dx+2y(√x)dy=0

$$\left(\mathrm{2}{x}\sqrt{{x}}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dx}+\mathrm{2}{y}\sqrt{{x}}{dy}=\mathrm{0} \\ $$

Question Number 26192    Answers: 0   Comments: 3

find the rsdius of convergence for theserie Σ_(n=0) ^∝ (x^n /(2n+1)) and calculate its sum s(x) find the value of Σ_(n=0) ^∝ (1/(2^n (2n+1))) .

$${find}\:{the}\:{rsdius}\:{of}\:{convergence}\:{for}\:{theserie} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\propto} \:\frac{{x}^{{n}} }{\mathrm{2}{n}+\mathrm{1}}\:{and}\:{calculate}\:{its}\:{sum}\:{s}\left({x}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \:\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)}\:\:. \\ $$

Question Number 26191    Answers: 1   Comments: 0

2(dy/dx)+x=4(√y)

$$\mathrm{2}\frac{{dy}}{{dx}}+{x}=\mathrm{4}\sqrt{{y}} \\ $$

Question Number 26181    Answers: 2   Comments: 0

Find the moment of inertia and the radius of gyration of a circular plate about an axis through its centre,perpendicular to the plane of the plate.

$${Find}\:{the}\:{moment}\:{of}\:{inertia}\:{and} \\ $$$${the}\:{radius}\:{of}\:{gyration}\:{of}\:{a}\: \\ $$$${circular}\:{plate}\:{about}\:{an}\:{axis}\:{through} \\ $$$${its}\:{centre},{perpendicular}\:{to}\:{the} \\ $$$${plane}\:{of}\:{the}\:{plate}. \\ $$

Question Number 26179    Answers: 1   Comments: 0

For an axis passing through the centre of mass of a rectangular plate(along its length).Show that its moment of inertia is ((ML^2 )/(12)) and the radius of gyration is (L/(2(√3).))

$${For}\:{an}\:{axis}\:{passing}\:{through}\:{the} \\ $$$${centre}\:{of}\:{mass}\:{of}\:{a}\:{rectangular} \\ $$$${plate}\left({along}\:{its}\:{length}\right).{Show}\:{that} \\ $$$${its}\:{moment}\:{of}\:{inertia}\:{is}\:\frac{{ML}^{\mathrm{2}} }{\mathrm{12}}\:{and} \\ $$$${the}\:{radius}\:{of}\:{gyration}\:{is}\:\frac{{L}}{\mathrm{2}\sqrt{\mathrm{3}}.} \\ $$

Question Number 26176    Answers: 0   Comments: 1

find the radius of convergence for the serie Σ_(n=0) ^∝ e^(−(√n)) z^n ...z from C.

$${find}\:{the}\:{radius}\:{of}\:{convergence}\:{for}\:{the} \\ $$$${serie}\:\sum_{{n}=\mathrm{0}} ^{\propto} {e}^{−\sqrt{{n}}} \:{z}^{{n}} \:\:...{z}\:{from}\:{C}. \\ $$

Question Number 26174    Answers: 0   Comments: 0

Question Number 26162    Answers: 1   Comments: 0

Find the volume of the solid generated when the region enclosed by y= (√x) y=0 and x=9 about the line x=9

$${Find}\:\:{the}\:{volume}\:\:{of}\:{the}\:{solid}\:{generated}\:{when}\:{the}\:{region}\:\:{enclosed} \\ $$$${by}\:\:{y}=\:\sqrt{{x}} \\ $$$$\:{y}=\mathrm{0}\:\:{and}\:\:{x}=\mathrm{9}\:{about}\:{the}\:\:{line}\:{x}=\mathrm{9} \\ $$

Question Number 26166    Answers: 0   Comments: 0

Question Number 26159    Answers: 1   Comments: 0

If x^2 + y^2 + 2xy + 2x + 2y + k = 0 represents pair of straight lines then find the value of k.

$$\mathrm{If}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{xy}\:+\:\mathrm{2}{x}\:+\:\mathrm{2}{y}\:+\:{k}\:=\:\mathrm{0} \\ $$$$\mathrm{represents}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}. \\ $$

Question Number 26156    Answers: 1   Comments: 0

a two digit number is 3 more than 4 times the sum of its digits. if 18 is added to this number .the sum is equal to number obtained by interchanging the digits.find the number

$${a}\:{two}\:{digit}\:{number}\:{is}\:\mathrm{3}\:{more}\:{than} \\ $$$$\mathrm{4}\:{times}\:{the}\:{sum}\:{of}\:{its}\:{digits}.\:{if} \\ $$$$\mathrm{18}\:{is}\:{added}\:{to}\:{this}\:{number}\:.{the}\: \\ $$$${sum}\:{is}\:{equal}\:{to}\:{number}\:{obtained} \\ $$$${by}\:{interchanging}\:{the}\:{digits}.{find}\:{the}\:{number} \\ $$

Question Number 26153    Answers: 1   Comments: 0

ratio of income of two persons is 9 is to 7.ratio of their expenses is 4 is to 3 .every person saves rupees 200. find income of each.

$${ratio}\:{of}\:{income}\:{of}\:{two}\:{persons}\:{is} \\ $$$$\mathrm{9}\:{is}\:{to}\:\mathrm{7}.{ratio}\:{of}\:{their}\:{expenses} \\ $$$${is}\:\mathrm{4}\:{is}\:{to}\:\mathrm{3}\:.{every}\:{person}\:{saves}\: \\ $$$${rupees}\:\mathrm{200}.\:{find}\:{income}\:{of}\:{each}. \\ $$

Question Number 26148    Answers: 2   Comments: 2

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