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Question Number 27294 Answers: 0 Comments: 1

∫_(1/e) ^(tan x) (t/(1+t^2 )) dt + ∫_(1/e) ^(cot x) (1/(t(1+t^2 ))) dt =

$$\underset{\mathrm{1}/{e}} {\overset{\mathrm{tan}\:{x}} {\int}}\frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt}\:+\:\underset{\mathrm{1}/{e}} {\overset{\mathrm{cot}\:{x}} {\int}}\:\frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\:{dt}\:= \\ $$

Question Number 27293 Answers: 1 Comments: 0

L^(−1) ((s^3 /(s^4 +4)))=?

$${L}^{−\mathrm{1}} \left(\frac{{s}^{\mathrm{3}} }{{s}^{\mathrm{4}} +\mathrm{4}}\right)=? \\ $$

Question Number 27287 Answers: 0 Comments: 1

Question Number 27283 Answers: 0 Comments: 0

Question Number 27282 Answers: 0 Comments: 1

∫log(2+x^2 )dx

$$\int{log}\left(\mathrm{2}+{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 27281 Answers: 1 Comments: 1

∫_(−1) ^1 (x^2 +cos x) log (((2+x)/(2−x)))dx = 0

$$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\left({x}^{\mathrm{2}} +\mathrm{cos}\:{x}\right)\:\mathrm{log}\:\left(\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}\right){dx}\:=\:\mathrm{0} \\ $$

Question Number 27280 Answers: 1 Comments: 1

If for a real number y, [y] is the greatest integer less than or equal to y, then the value of the integeral ∫_(π/2) ^(3π/2) [2 sin x]dx is

$$\mathrm{If}\:\mathrm{for}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:{y},\:\left[{y}\right]\:\mathrm{is}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to}\:{y},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integeral}\:\underset{\pi/\mathrm{2}} {\overset{\mathrm{3}\pi/\mathrm{2}} {\int}}\left[\mathrm{2}\:\mathrm{sin}\:{x}\right]{dx}\:\mathrm{is} \\ $$

Question Number 27274 Answers: 0 Comments: 0

Question Number 27271 Answers: 1 Comments: 0

Proof ∫(1/(a^2 −x^2 ))dx =(1/(2a))ln∣((a+x)/(a−x))∣+c

$$\boldsymbol{{P}}{roof}\: \\ $$$$\int\frac{\mathrm{1}}{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}\:=\frac{\mathrm{1}}{\mathrm{2}{a}}{ln}\mid\frac{{a}+{x}}{{a}−{x}}\mid+{c} \\ $$

Question Number 27270 Answers: 0 Comments: 0

(1) There are 20 boys and 10 girls in a class.If a committee of 6 is to be chosen at random having atleast 2 boys and 2 girls,find the probability that (i) there ara 3 boys in the committee (ii) there are 4 boys in the committee

Question Number 27266 Answers: 1 Comments: 0

2.8.4.7.8.6.16−what next number

$$\mathrm{2}.\mathrm{8}.\mathrm{4}.\mathrm{7}.\mathrm{8}.\mathrm{6}.\mathrm{16}−{what}\:{next}\:{number} \\ $$$$ \\ $$

Question Number 27258 Answers: 0 Comments: 1

If 9^x −4×3^(x+2) +3^5 =0, then the solution set is

$$\mathrm{If}\:\:\mathrm{9}^{{x}} −\mathrm{4}×\mathrm{3}^{{x}+\mathrm{2}} +\mathrm{3}^{\mathrm{5}} =\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{solution} \\ $$$$\mathrm{set}\:\mathrm{is} \\ $$

Question Number 27254 Answers: 1 Comments: 0

Question Number 27253 Answers: 0 Comments: 0

Question Number 27235 Answers: 1 Comments: 0

(1) There are 60 tickets in a bag numbered 1 through 60.If a ticket is picked at random,find the probability that the number is divisible by 3 or 4 ?

Question Number 27224 Answers: 1 Comments: 4

Question Number 27215 Answers: 1 Comments: 0

find the value of ∫_(−1) ^1 (dx/((√(1−x^2 )) +(√(1+x^2 )))) .

$${find}\:{the}\:{value}\:{of}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:\:. \\ $$

Question Number 27213 Answers: 1 Comments: 1

[(16x^4 −1)]/[2x−1] factorise it

$$\left[\left(\mathrm{16}{x}^{\mathrm{4}} −\mathrm{1}\right)\right]/\left[\mathrm{2}{x}−\mathrm{1}\right]\:{factorise}\:{it} \\ $$

Question Number 27204 Answers: 1 Comments: 0

if g(x)=f(x)+f(1−x) and f^((2)) (x)<0 then show that g(x) is increasing in (0,1/2) and g(x) is decreasing in (1/2,1)

$$\mathrm{if}\:{g}\left({x}\right)={f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right) \\ $$$$\mathrm{and}\:{f}^{\left(\mathrm{2}\right)} \left({x}\right)<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{increasing}\:\mathrm{in}\:\left(\mathrm{0},\mathrm{1}/\mathrm{2}\right)\:\mathrm{and} \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{in}\:\left(\mathrm{1}/\mathrm{2},\mathrm{1}\right) \\ $$

Question Number 27198 Answers: 1 Comments: 0

Question Number 27197 Answers: 1 Comments: 1

Question Number 27203 Answers: 2 Comments: 0

Let S ⊂ (0, π) denote the set of values of x satisfying the equation 8^(1+∣cos x∣+cos^2 x+∣cos^3 x∣+... to ∞) = 4^3 then S =

$$\mathrm{Let}\:{S}\:\subset\:\left(\mathrm{0},\:\pi\right)\:\mathrm{denote}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{8}^{\mathrm{1}+\mid\mathrm{cos}\:{x}\mid+\mathrm{cos}^{\mathrm{2}} {x}+\mid\mathrm{cos}^{\mathrm{3}} {x}\mid+...\:\mathrm{to}\:\infty} =\:\mathrm{4}^{\mathrm{3}} \\ $$$$\mathrm{then}\:{S}\:=\: \\ $$

Question Number 27202 Answers: 1 Comments: 0

Question Number 27527 Answers: 0 Comments: 1

(√5)=2.236 then the valve of 100/(√(125))=?

$$\sqrt{\mathrm{5}}=\mathrm{2}.\mathrm{236}\:{then}\:{the}\:{valve}\:{of}\:\mathrm{100}/\sqrt{\mathrm{125}}=? \\ $$

Question Number 27526 Answers: 1 Comments: 0

(256)^(0.16) ×(256)^(0.09) =?

$$\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{16}} ×\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{09}} =? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 27189 Answers: 1 Comments: 0

let give S_(n ) = Σ_(p=1) ^(p=n) arctan ((1/(2p^2 )) ) find lim_(n−>∝) S_n .

$${let}\:{give}\:{S}_{{n}\:} =\:\sum_{{p}=\mathrm{1}} ^{{p}={n}} \:{arctan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{p}^{\mathrm{2}} }\:\right)\:\:{find}\:{lim}_{{n}−>\propto} \:{S}_{{n}} \:\:. \\ $$

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