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Question Number 7710    Answers: 1   Comments: 0

If n(A∪B)=32, n(B)=12 and n(A∩B)=5 then n(A)=?

$$\mathrm{If}\:{n}\left(\mathrm{A}\cup\mathrm{B}\right)=\mathrm{32},\:{n}\left(\mathrm{B}\right)=\mathrm{12}\:\mathrm{and}\:{n}\left(\mathrm{A}\cap\mathrm{B}\right)=\mathrm{5} \\ $$$$\mathrm{then}\:{n}\left(\mathrm{A}\right)=? \\ $$

Question Number 7692    Answers: 1   Comments: 0

d efine the Σ_(i=1) ^5 a_i =10 Σ kya hai

$${d}\:{efine}\:{the}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{5}} {\sum}}\:{a}_{{i}} \:=\mathrm{10}\:\:\:\Sigma\:{kya}\:{hai} \\ $$

Question Number 7686    Answers: 0   Comments: 1

f ×=(81)(1/3)+2(9)(1/3)+4 (2+(1/×))^3 =...

$${f}\:×=\left(\mathrm{81}\right)\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{2}\left(\mathrm{9}\right)\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{4} \\ $$$$\left(\mathrm{2}+\frac{\mathrm{1}}{×}\right)^{\mathrm{3}} =... \\ $$$$ \\ $$

Question Number 7683    Answers: 0   Comments: 1

If sin θ+2cos θ=1 Prove that 2sin θ−cos θ=2

$$\mathrm{If}\:\mathrm{sin}\:\theta+\mathrm{2cos}\:\theta=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2sin}\:\theta−\mathrm{cos}\:\theta=\mathrm{2} \\ $$

Question Number 7668    Answers: 0   Comments: 3

Question Number 7667    Answers: 1   Comments: 0

lim_(x→α) [x−x^2 log (1+(1/x))]

$$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\left[{x}−{x}^{\mathrm{2}} \mathrm{log}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\right] \\ $$

Question Number 7665    Answers: 1   Comments: 0

(d/dx)(√(x^2 −4))

$$\frac{{d}}{{dx}}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$

Question Number 7663    Answers: 0   Comments: 0

∫tan(√(x ))dx

$$\int{tan}\sqrt{{x}\:}{dx} \\ $$$$ \\ $$

Question Number 7659    Answers: 0   Comments: 1

What is the sum of this sequence sin^2 (x) + sin^2 (2x)+ sin^2 (3x) + ... + sin^2 (nx)

$${What}\:{is}\:{the}\:{sum}\:{of}\:{this}\:{sequence} \\ $$$${sin}^{\mathrm{2}} \left({x}\right)\:+\:{sin}^{\mathrm{2}} \left(\mathrm{2}{x}\right)+\:{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)\:+\:...\:+\:{sin}^{\mathrm{2}} \left({nx}\right) \\ $$

Question Number 7656    Answers: 1   Comments: 1

If S_n (sum of sequence) = 2n^2 + n Find the value of the 1002 term

$${If}\:\:{S}_{{n}} \:\left({sum}\:{of}\:{sequence}\right)\:=\:\mathrm{2}{n}^{\mathrm{2}} \:+\:{n} \\ $$$${Find}\:{the}\:{value}\:{of}\:{the}\:\mathrm{1002}\:{term} \\ $$

Question Number 7655    Answers: 2   Comments: 1

((8/x))^x = x^2 Show that x = 4

$$\left(\frac{\mathrm{8}}{{x}}\right)^{{x}} \:=\:\:{x}^{\mathrm{2}} \\ $$$$ \\ $$$${Show}\:{that}\:\:{x}\:=\:\mathrm{4} \\ $$

Question Number 7654    Answers: 3   Comments: 0

Q.1 which term of the sequence 2005, 2000,1995,1990,1985,........................ is the first negative term. plese give answer Q.2 for an A.P. show that t_m +t_(2n+m) = 2t_(m+n) give answer Q.3 find the maximum sum of the A.P. 40+38+36+34+32+........ give answer plese sir

$${Q}.\mathrm{1}\:{which}\:{term}\:{of}\:{the}\:{sequence}\:\mathrm{2005}, \\ $$$$\mathrm{2000},\mathrm{1995},\mathrm{1990},\mathrm{1985},........................ \\ $$$${is}\:{the}\:{first}\:{negative}\:{term}. \\ $$$${plese}\:{give}\:{answer} \\ $$$${Q}.\mathrm{2}\:{for}\:{an}\:{A}.{P}.\:{show}\:{that}\:{t}_{{m}} +{t}_{\mathrm{2}{n}+{m}} \\ $$$$=\:\mathrm{2}{t}_{{m}+{n}} \\ $$$${give}\:{answer} \\ $$$${Q}.\mathrm{3}\:{find}\:{the}\:{maximum}\:{sum}\:{of}\:{the}\: \\ $$$${A}.{P}.\:\mathrm{40}+\mathrm{38}+\mathrm{36}+\mathrm{34}+\mathrm{32}+........ \\ $$$${give}\:{answer}\:{plese}\:{sir} \\ $$$$ \\ $$

Question Number 7651    Answers: 0   Comments: 2

P=Π_(n=1) ^k n^n P=???

$${P}=\underset{{n}=\mathrm{1}} {\overset{{k}} {\prod}}{n}^{{n}} \\ $$$${P}=??? \\ $$

Question Number 7649    Answers: 1   Comments: 1

the sum of n term of two A.P are in ratio ((7n+1)/(4n+27)) .find the ratio of their 11^(th) term.

$${the}\:{sum}\:{of}\:{n}\:{term}\:{of}\:{two}\:{A}.{P}\:{are}\:{in}\: \\ $$$${ratio}\:\frac{\mathrm{7}{n}+\mathrm{1}}{\mathrm{4}{n}+\mathrm{27}}\:.{find}\:{the}\:{ratio}\:{of}\:{their}\:\:\mathrm{11}^{{th}} \\ $$$${term}. \\ $$

Question Number 7637    Answers: 1   Comments: 0

∫x^x dx

$$\int{x}^{{x}} \:{dx} \\ $$

Question Number 7630    Answers: 1   Comments: 5

Question Number 7628    Answers: 0   Comments: 0

By the use of substitution x = μ^2 , show that the legendary equation , (1 − μ^2 )y′′ − 2μy′ + n(n + 1)y = 0, where n is a constant change to hyper geometric equation . hence obtain the solution to the resulting hyper geometric differential equation by way of comparison.

$${By}\:{the}\:{use}\:{of}\:{substitution}\:\:{x}\:=\:\mu^{\mathrm{2}} ,\:{show}\:{that} \\ $$$${the}\:{legendary}\:{equation}\:, \\ $$$$\left(\mathrm{1}\:−\:\mu^{\mathrm{2}} \right){y}''\:−\:\mathrm{2}\mu{y}'\:+\:{n}\left({n}\:+\:\mathrm{1}\right){y}\:=\:\mathrm{0},\: \\ $$$${where}\:{n}\:{is}\:{a}\:{constant}\:{change}\:{to}\:{hyper}\:{geometric} \\ $$$${equation}\:.\:{hence}\:{obtain}\:{the}\:{solution}\:{to}\:{the}\: \\ $$$${resulting}\:{hyper}\:{geometric}\:{differential}\:{equation}\: \\ $$$${by}\:{way}\:{of}\:{comparison}. \\ $$

Question Number 7621    Answers: 1   Comments: 0

Prove that π=4Σ_(k=0) ^∞ (((−1)^k )/(2k+1))

$${Prove}\:{that}\: \\ $$$$\pi=\mathrm{4}\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{2}{k}+\mathrm{1}} \\ $$

Question Number 7612    Answers: 1   Comments: 3

If ax + by + cz = 0, and, a^2 x + b^2 y + c^2 z = 0 Find the ratio x:y:z

$${If}\:\:{ax}\:+\:{by}\:+\:{cz}\:=\:\mathrm{0},\: \\ $$$${and},\:\:{a}^{\mathrm{2}} {x}\:+\:{b}^{\mathrm{2}} {y}\:+\:{c}^{\mathrm{2}} {z}\:=\:\mathrm{0} \\ $$$${Find}\:{the}\:{ratio}\:\:{x}:{y}:{z} \\ $$

Question Number 7611    Answers: 1   Comments: 0

Find the square root of 121x^6 + 44x^5 − 18x^4 + 18x^3 + 5x^2 − 2x + 1

$${Find}\:{the}\:{square}\:{root}\:{of}\: \\ $$$$\mathrm{121}{x}^{\mathrm{6}} \:+\:\mathrm{44}{x}^{\mathrm{5}} \:−\:\mathrm{18}{x}^{\mathrm{4}} \:+\:\mathrm{18}{x}^{\mathrm{3}} \:+\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$

Question Number 7610    Answers: 1   Comments: 2

obtain the value of (a^(1/2) +b^(1/2) +c^(1/2) )(a^(1/2) −b^(1/2) +c^(1/2) )(a^(1/2) −b^(1/2) +c^(1/2) )(b^(1/2) +c^(1/2) −a^(1/2) )

$${obtain}\:{the}\:{value}\:{of}\: \\ $$$$\left({a}^{\mathrm{1}/\mathrm{2}} +{b}^{\mathrm{1}/\mathrm{2}} +{c}^{\mathrm{1}/\mathrm{2}} \right)\left({a}^{\mathrm{1}/\mathrm{2}} −{b}^{\mathrm{1}/\mathrm{2}} +{c}^{\mathrm{1}/\mathrm{2}} \right)\left({a}^{\mathrm{1}/\mathrm{2}} −{b}^{\mathrm{1}/\mathrm{2}} +{c}^{\mathrm{1}/\mathrm{2}} \right)\left({b}^{\mathrm{1}/\mathrm{2}} +{c}^{\mathrm{1}/\mathrm{2}} −{a}^{\mathrm{1}/\mathrm{2}} \right)\: \\ $$

Question Number 7609    Answers: 1   Comments: 0

Divide a^(5/2) − 5a^2 b^(1/3) + 10a^(3/2) 6^(2/3) − 10ab + 5a^(1/2) b^(4/3) − b^(5/3) by a^(1/2) − b^(1/3)

$${Divide}\: \\ $$$${a}^{\mathrm{5}/\mathrm{2}} \:−\:\mathrm{5}{a}^{\mathrm{2}} {b}^{\mathrm{1}/\mathrm{3}} \:+\:\mathrm{10}{a}^{\mathrm{3}/\mathrm{2}} \mathrm{6}^{\mathrm{2}/\mathrm{3}} \:−\:\mathrm{10}{ab}\:+\:\mathrm{5}{a}^{\mathrm{1}/\mathrm{2}} {b}^{\mathrm{4}/\mathrm{3}} \:−\:{b}^{\mathrm{5}/\mathrm{3}} \\ $$$${by}\:\:{a}^{\mathrm{1}/\mathrm{2}} \:−\:{b}^{\mathrm{1}/\mathrm{3}} \\ $$

Question Number 7600    Answers: 1   Comments: 0

solve ∣((x^2 −3x−1)/(x^2 +x+1))∣<3 give solution

$${solve}\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\mid<\mathrm{3}\:\:{give}\:{solution} \\ $$

Question Number 7608    Answers: 1   Comments: 3

If x = cosΘ − sinΘ and y = cos2Θ Show that, y = x(√(2 − x^2 ))

$${If}\:\:{x}\:=\:{cos}\Theta\:−\:{sin}\Theta \\ $$$${and}\:\:{y}\:=\:{cos}\mathrm{2}\Theta \\ $$$${Show}\:{that},\:\: \\ $$$${y}\:=\:{x}\sqrt{\mathrm{2}\:−\:{x}^{\mathrm{2}} } \\ $$

Question Number 7598    Answers: 1   Comments: 0

solve ∣((x^2 −3x−1)/(x^2 +x+1))∣<3

$${solve}\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\mid<\mathrm{3} \\ $$

Question Number 7590    Answers: 0   Comments: 4

S = Σ_(n=2) ^k ((2(n+1))/(n(n−1))) S=?

$${S}\:=\:\underset{{n}=\mathrm{2}} {\overset{{k}} {\sum}}\:\frac{\mathrm{2}\left({n}+\mathrm{1}\right)}{{n}\left({n}−\mathrm{1}\right)} \\ $$$${S}=? \\ $$

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