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Question Number 181973    Answers: 0   Comments: 1

please how can I get the proofs of the Putnam competition in pdf format?

$$ \\ $$please how can I get the proofs of the Putnam competition in pdf format?

Question Number 181971    Answers: 1   Comments: 0

How many words can be formed from different letters of the “Your answer is wrong” with not repeating? So that they shouldn′t start with ′o′ neither ′w′ and shouldn′t end with ′w′, and should be′r′ & ′s′ adjacents. Oya...n, Wen...y, Iog...w , Yourws...e : are invalid Enrsow...g : is valid Q.180162

$${How}\:{many}\:{words}\:{can}\:{be}\:{formed}\:{from}\:{different} \\ $$$${letters}\:{of}\:{the}\:``{Your}\:{answer}\:{is}\:{wrong}''\:{with}\:{not} \\ $$$${repeating}?\:{So}\:{that}\:{they}\:{shouldn}'{t}\:{start}\:{with}\:'{o}'\: \\ $$$$\:{neither}\:'{w}'\:{and}\:{shouldn}'{t}\:{end}\:{with}\:'{w}',\:{and} \\ $$$$\:{should}\:{be}'{r}'\:\&\:'{s}'\:{adjacents}. \\ $$$$ \\ $$$$\:\cancel{{O}ya}...{n},\:\cancel{{W}en}...{y},\:{Iog}...\cancel{{w}}\:,\:{You}\cancel{{r}w}\cancel{{s}}...{e}\:\::\:{are}\:{invalid} \\ $$$$\:{Enrsow}...{g}\::\:{is}\:{valid} \\ $$$${Q}.\mathrm{180162} \\ $$

Question Number 181945    Answers: 1   Comments: 0

Question Number 181939    Answers: 2   Comments: 0

If 10 different balls are to be placed in 4 boxes at random , then the probability that two of these boxes contain exactly 2 and 3 balls

$${If}\:\mathrm{10}\:{different}\:{balls}\:{are}\:{to}\:{be}\:{placed} \\ $$$${in}\:\mathrm{4}\:{boxes}\:{at}\:{random}\:,\:{then}\:{the}\:{probability} \\ $$$${that}\:{two}\:{of}\:{these}\:{boxes}\:{contain} \\ $$$${exactly}\:\mathrm{2}\:{and}\:\mathrm{3}\:{balls}\: \\ $$

Question Number 181952    Answers: 0   Comments: 0

Question Number 181954    Answers: 3   Comments: 0

Question Number 181923    Answers: 1   Comments: 0

Question Number 181935    Answers: 2   Comments: 0

Question Number 181918    Answers: 4   Comments: 0

Question Number 181917    Answers: 0   Comments: 1

Question Number 181903    Answers: 1   Comments: 0

Question Number 181902    Answers: 3   Comments: 0

Question Number 181901    Answers: 0   Comments: 0

Question Number 181897    Answers: 2   Comments: 0

Question Number 181875    Answers: 4   Comments: 3

if a+b+c=0, find the maximum of ((∣a+2b+3c∣)/( (√(a^2 +b^2 +c^2 )))).

$${if}\:{a}+{b}+{c}=\mathrm{0},\:{find}\:{the}\:{maximum}\:{of} \\ $$$$\frac{\mid{a}+\mathrm{2}{b}+\mathrm{3}{c}\mid}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }}. \\ $$

Question Number 181872    Answers: 1   Comments: 0

∫_(−1) ^4 (1/(∣x∣)) dx

$$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{1}}{\mid{x}\mid}\:{dx} \\ $$

Question Number 181869    Answers: 0   Comments: 1

Question Number 181863    Answers: 0   Comments: 0

cos 56°. cos (2.56°). cos (2^2 .56°). cos (2^3 .56°)... cos (2^(23) .56°)=?

$$\:\mathrm{cos}\:\mathrm{56}°.\:\mathrm{cos}\:\left(\mathrm{2}.\mathrm{56}°\right).\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{2}} .\mathrm{56}°\right).\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{3}} .\mathrm{56}°\right)...\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{23}} .\mathrm{56}°\right)=? \\ $$

Question Number 181858    Answers: 2   Comments: 0

Question Number 181857    Answers: 1   Comments: 0

Question Number 181853    Answers: 0   Comments: 3

∫ cos^(−1) (tan^3 (tan(x))) dx= ?

$$\: \\ $$$$\int\:\boldsymbol{\mathrm{cos}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{tan}}^{\mathrm{3}} \left(\boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{x}}\right)\right)\right)\:\boldsymbol{\mathrm{dx}}=\:? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 181852    Answers: 2   Comments: 0

Question Number 181851    Answers: 0   Comments: 0

∫ arccos(tg^3 (tg(x))) dx=?

$$\:\:\:\int\:\boldsymbol{\mathrm{arccos}}\left(\boldsymbol{\mathrm{tg}}^{\mathrm{3}} \left(\boldsymbol{\mathrm{tg}}\left(\boldsymbol{\mathrm{x}}\right)\right)\right)\:\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 181841    Answers: 3   Comments: 0

what is larger, (√(11))+(√(13)) or 7?

$${what}\:{is}\:{larger},\:\sqrt{\mathrm{11}}+\sqrt{\mathrm{13}}\:{or}\:\mathrm{7}? \\ $$

Question Number 181840    Answers: 0   Comments: 3

∫_(−1) ^4 ln x dx

$$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}{ln}\:{x}\:{dx} \\ $$

Question Number 181839    Answers: 1   Comments: 5

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