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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

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

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 ?

$$\left(\mathrm{1}\right)\:\:\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{are}}\:\mathrm{60}\:\boldsymbol{\mathrm{tickets}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{bag}} \\ $$$$\boldsymbol{\mathrm{numbered}}\:\mathrm{1}\:\boldsymbol{\mathrm{through}}\:\mathrm{60}.\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{ticket}}\: \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{picked}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{random}},\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{probability}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{is}} \\ $$$$\boldsymbol{\mathrm{divisible}}\:\boldsymbol{\mathrm{by}}\:\mathrm{3}\:\boldsymbol{\mathrm{or}}\:\mathrm{4}\:? \\ $$

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

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

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