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Question Number 103409    Answers: 0   Comments: 1

What will be the state of a system(isolated)when its entropy tends to zero or zero? Time get stopped?? or another things may happen I am thinking about this

$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{state}\:\mathrm{of}\:\mathrm{a}\:\mathrm{system}\left(\mathrm{isolated}\right)\mathrm{when}\:\mathrm{its}\:\mathrm{entropy}\:\mathrm{tends} \\ $$$$\mathrm{to}\:\mathrm{zero}\:\mathrm{or}\:\mathrm{zero}? \\ $$$$ \\ $$$$\mathrm{T}\boldsymbol{\mathrm{ime}}\:\boldsymbol{\mathrm{get}}\:\boldsymbol{\mathrm{stopped}}?? \\ $$$$\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{another}}\:\boldsymbol{\mathrm{things}}\:\boldsymbol{\mathrm{may}}\:\boldsymbol{\mathrm{happen}} \\ $$$$\boldsymbol{\mathrm{I}}\:\boldsymbol{\mathrm{am}}\:\boldsymbol{\mathrm{thinking}}\:\boldsymbol{\mathrm{about}}\:\boldsymbol{\mathrm{this}} \\ $$

Question Number 103406    Answers: 0   Comments: 3

100 students are standing in a row. 4 students should be selected in the way that no two of them are next to each other. how many ways do you have to do this?

$$\mathrm{100}\:{students}\:{are}\:{standing}\:{in}\:{a}\:{row}. \\ $$$$\mathrm{4}\:{students}\:{should}\:{be}\:{selected}\:{in}\:{the} \\ $$$${way}\:{that}\:{no}\:{two}\:{of}\:{them}\:{are}\:{next}\:{to} \\ $$$${each}\:{other}.\:{how}\:{many}\:{ways}\:{do}\:{you} \\ $$$${have}\:{to}\:{do}\:{this}? \\ $$

Question Number 103400    Answers: 3   Comments: 1

A particle′s trajectory is described by x=e^t +e^(−t) y=2t Find the distance that the particle traveled for 0≤t≤2

$$\mathrm{A}\:\mathrm{particle}'\mathrm{s}\:\mathrm{trajectory}\:\mathrm{is}\:\mathrm{described}\:\mathrm{by} \\ $$$$\mathrm{x}=\mathrm{e}^{\mathrm{t}} +\mathrm{e}^{−\mathrm{t}} \:\:\:\:\:\mathrm{y}=\mathrm{2t} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{that}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{traveled}\:\mathrm{for}\:\mathrm{0}\leqslant\mathrm{t}\leqslant\mathrm{2} \\ $$

Question Number 103397    Answers: 1   Comments: 0

I(n)=∫_0 ^∞ ((ln x)/(cosh^n x ))dx is there a simpler way to calculat those values

$${I}\left({n}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\:{x}}{\mathrm{cosh}^{{n}} {x}\:}{dx} \\ $$$${is}\:{there}\:{a}\:{simpler}\:{way}\:{to} \\ $$$${calculat}\:{those}\:{values} \\ $$

Question Number 103393    Answers: 2   Comments: 0

Question Number 103389    Answers: 2   Comments: 1

Question Number 103377    Answers: 0   Comments: 0

y′′(x)+((2x)/(1+x^2 ))y′(x)+(2−x^2 )y(x)=0

$$\mathrm{y}''\left(\mathrm{x}\right)+\frac{\mathrm{2x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{y}'\left(\mathrm{x}\right)+\left(\mathrm{2}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}\left(\mathrm{x}\right)=\mathrm{0} \\ $$

Question Number 103367    Answers: 1   Comments: 0

many words with 4 letters can be formed using letters from the word TINKUTARA is ___

$${many}\:{words}\:{with}\:\mathrm{4}\:{letters}\:{can}\:{be}\:{formed} \\ $$$${using}\:{letters}\:{from}\:{the}\:{word} \\ $$$${TINKUTARA}\:{is}\:\_\_\_ \\ $$

Question Number 103366    Answers: 4   Comments: 0

Question Number 103357    Answers: 1   Comments: 0

There are 21 students will be trained with 6 trainers available. Every students is trained by 1 coach and every coach trains students with different amounts. many ways of grouping students who will be trained are .... (a) ((21!)/(6!)) (b) 6!.21! (c) ((21!)/(2!.3!.4!.5! )) (d) 6×21! (e) ((21!)/(15!))×6!

$${There}\:{are}\:\mathrm{21}\:{students}\:{will}\:{be}\:{trained} \\ $$$${with}\:\mathrm{6}\:{trainers}\:{available}.\:{Every}\:{students} \\ $$$${is}\:{trained}\:{by}\:\mathrm{1}\:{coach}\:{and}\:{every}\:{coach} \\ $$$${trains}\:{students}\:{with}\:{different}\:{amounts}. \\ $$$${many}\:{ways}\:{of}\:{grouping}\:{students}\:{who} \\ $$$${will}\:{be}\:{trained}\:{are}\:.... \\ $$$$\left({a}\right)\:\frac{\mathrm{21}!}{\mathrm{6}!}\:\:\:\:\left({b}\right)\:\mathrm{6}!.\mathrm{21}!\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{21}!}{\mathrm{2}!.\mathrm{3}!.\mathrm{4}!.\mathrm{5}!\:\:}\:\: \\ $$$$\left({d}\right)\:\mathrm{6}×\mathrm{21}!\:\:\:\:\left({e}\right)\:\frac{\mathrm{21}!}{\mathrm{15}!}×\mathrm{6}! \\ $$

Question Number 103355    Answers: 0   Comments: 0

Question Number 103347    Answers: 1   Comments: 2

Question Number 103346    Answers: 0   Comments: 1

Question Number 103345    Answers: 4   Comments: 5

Question Number 103343    Answers: 1   Comments: 0

∫_0 ^1 x^(−x) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx} \\ $$

Question Number 103338    Answers: 0   Comments: 7

Question Number 103322    Answers: 2   Comments: 1

A differentiable function f(x) satisfies f(x^3 −x^2 +x)=2^(x+1) for every real number x. When g(x) is the inverse function of f(x), find g′(4)?

$$\mathrm{A}\:\mathrm{differentiable}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{satisfies} \\ $$$$\mathrm{f}\left(\mathrm{x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right)=\mathrm{2}^{\mathrm{x}+\mathrm{1}} \:\:\mathrm{for}\:\mathrm{every}\:\mathrm{real}\:\mathrm{number}\:{x}. \\ $$$$\mathrm{When}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{inverse}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right), \\ $$$$\mathrm{find}\:\mathrm{g}'\left(\mathrm{4}\right)? \\ $$

Question Number 103321    Answers: 2   Comments: 0

5+(√(5−(√(5+(√(5−(√(5+(√(5−(√(5+...))))))))))))

$$\mathrm{5}+\sqrt{\mathrm{5}−\sqrt{\mathrm{5}+\sqrt{\mathrm{5}−\sqrt{\mathrm{5}+\sqrt{\mathrm{5}−\sqrt{\mathrm{5}+...}}}}}} \\ $$

Question Number 103318    Answers: 1   Comments: 3

Question Number 103314    Answers: 1   Comments: 0

Linearise cos^(2(p−1)) (t)

$$\mathrm{Linearise}\:\mathrm{cos}^{\mathrm{2}\left(\mathrm{p}−\mathrm{1}\right)} \left(\mathrm{t}\right) \\ $$

Question Number 103313    Answers: 0   Comments: 0

lim_(n→+∞) (ln (n!))^(2/n)

$${li}\underset{{n}\rightarrow+\infty} {{m}}\left(\mathrm{ln}\:\left({n}!\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$

Question Number 103312    Answers: 4   Comments: 0

∫_0 ^∞ (1/((1+x^2 )^6 )) dx ?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{6}} }\:{dx}\:? \\ $$

Question Number 103310    Answers: 1   Comments: 1

Question Number 103306    Answers: 0   Comments: 0

Question Number 103305    Answers: 0   Comments: 0

Question Number 103300    Answers: 1   Comments: 0

many positive five−digit integers with the first number 1 and there are three equal numbers ? (a) 810 (b) 720 (c)120 (d) 60 (e) 20

$$\mathrm{many}\:\mathrm{positive}\:\mathrm{five}−\mathrm{digit} \\ $$$$\mathrm{integers}\:\mathrm{with}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{there}\:\mathrm{are}\:\mathrm{three}\:\mathrm{equal} \\ $$$$\mathrm{numbers}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{810}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{720}\:\:\:\:\left(\mathrm{c}\right)\mathrm{120} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{60}\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{20} \\ $$

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