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Question Number 27335 Answers: 0 Comments: 1

if 2 chords of ellipse have the same distance from the centre of ellipse and the eccentric angle of the end points of the chords are respectivly α β γ δ then prove that tan (α/2)×tan (β/2)×tan (γ/2)×tan (δ/2)=1

$${if}\:\mathrm{2}\:{chords}\:{of}\:{ellipse}\:{have}\:{the}\:{same} \\ $$$${distance}\:{from}\:{the}\:{centre}\:{of}\:{ellipse} \\ $$$${and}\:{the}\:{eccentric}\:{angle}\:{of}\:{the}\:{end}\:{points}\:{of}\:{the}\:{chords} \\ $$$${are}\:{respectivly}\:\alpha\:\beta\:\gamma\:\delta\:{then}\:{prove}\:{that} \\ $$$$\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}×\mathrm{tan}\:\frac{\beta}{\mathrm{2}}×\mathrm{tan}\:\frac{\gamma}{\mathrm{2}}×\mathrm{tan}\:\frac{\delta}{\mathrm{2}}=\mathrm{1} \\ $$

Question Number 27334 Answers: 1 Comments: 0

(q_1 /q_2 )=((x/(0.8−x)))^2 ; x=?

$$\frac{\mathrm{q}_{\mathrm{1}} }{\mathrm{q}_{\mathrm{2}} }=\left(\frac{\mathrm{x}}{\mathrm{0}.\mathrm{8}−\mathrm{x}}\right)^{\mathrm{2}} \:\:\:\:;\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 27332 Answers: 1 Comments: 1

Question Number 27328 Answers: 0 Comments: 1

Question Number 27327 Answers: 0 Comments: 4

lim_(n→∞) (x^(2n) /(1+∣x∣+x^(4n) ))

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{x}^{\mathrm{2n}} }{\mathrm{1}+\mid\mathrm{x}\mid+\mathrm{x}^{\mathrm{4n}} } \\ $$

Question Number 27326 Answers: 1 Comments: 0

What is the relationship between the centre of gravity and the centre of mass?

$${What}\:{is}\:{the}\:{relationship}\:{between} \\ $$$${the}\:{centre}\:{of}\:{gravity}\:{and}\:{the}\:{centre}\:{of} \\ $$$${mass}? \\ $$

Question Number 27321 Answers: 1 Comments: 1

Question Number 27751 Answers: 0 Comments: 0

what is relation between in tensity of diffraction anx slit width

$${what}\:{is}\:{relation}\:{between}\:{in} \\ $$$${tensity}\:{of}\:{diffraction}\:{anx} \\ $$$${slit}\:{width} \\ $$

Question Number 27309 Answers: 1 Comments: 0

find the value of ∫_0 ^∝ (((−1)^([x]) )/((2x+1)^2 ))dx

$${find}\:{the}\:{value}\:\:{of}\:\:\int_{\mathrm{0}} ^{\propto} \:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx}\: \\ $$

Question Number 27303 Answers: 1 Comments: 0

Question Number 27300 Answers: 3 Comments: 1

Question Number 27296 Answers: 1 Comments: 1

((sin^2 3A)/(sin^2 A)) − ((cos^2 3A)/(cos^2 A)) =

$$\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{3}{A}}{\mathrm{sin}^{\mathrm{2}} {A}}\:−\:\frac{\mathrm{cos}^{\mathrm{2}} \mathrm{3}{A}}{\mathrm{cos}^{\mathrm{2}} {A}}\:=\: \\ $$

Question Number 27295 Answers: 0 Comments: 1

The value of the integral ∫_( 0) ^π (1/(a^2 −2a cos x+1)) dx (a< 1) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\:\mathrm{cos}\:{x}+\mathrm{1}}\:{dx}\:\:\left({a}<\:\mathrm{1}\right)\:\mathrm{is} \\ $$

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

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