Question Number 883 by 112358 last updated on 12/Apr/15 $${How}\:{many}\:{even}\:{numbers}\: \\ $$$${between}\:\mathrm{3000}\:{and}\:\mathrm{7000}\:{can}\:{be} \\ $$$${formed}\:{using}\:{the}\:{digits}\: \\ $$$$\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:{and}\:\mathrm{8}\:{if}\:{repetition} \\ $$$${of}\:{digits}\:{is}\:{not}\:{allowed}? \\ $$ Answered by prakash jain last…
Question Number 880 by arnav last updated on 11/Apr/15 $${Solve} \\ $$$$\frac{{x}+\mathrm{3}}{{x}−\mathrm{3}}<\mathrm{1} \\ $$ Answered by 123456 last updated on 11/Apr/15 $$\frac{{x}+\mathrm{3}}{{x}−\mathrm{3}}−\mathrm{1}<\mathrm{0} \\ $$$$\frac{{x}+\mathrm{3}−{x}+\mathrm{3}}{{x}−\mathrm{3}}<\mathrm{0} \\…
Question Number 66412 by aliesam last updated on 14/Aug/19 $${if} \\ $$$$ \\ $$$${f}\left({x}\right)={ln}\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$ \\ $$$${find} \\ $$$$ \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\…
Question Number 877 by sagarwal last updated on 07/Apr/15 $$\mathrm{An}\:\mathrm{8}×\mathrm{8}\:\mathrm{checkerboard}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{coloured} \\ $$$$\mathrm{with}\:\mathrm{6}\:\mathrm{colors}\:\:\mathrm{in}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{no}\:\mathrm{2}\:\mathrm{adjacent} \\ $$$$\mathrm{cells}\:\left(\mathrm{sharing}\:\mathrm{side}\right)\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}.\:\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{it}\:\mathrm{be}\:\mathrm{done}. \\ $$ Commented by 123456 last updated on 12/Apr/15…
Question Number 66413 by hmamarques1994@gmail.com last updated on 14/Aug/19 $$\: \\ $$$$\:\:\sqrt{\mathrm{8}+\boldsymbol{\mathrm{log}}_{\mathrm{6}} \left(\boldsymbol{\mathrm{x}}!\right)}+\sqrt{\mathrm{17}−\boldsymbol{\mathrm{log}}_{\boldsymbol{\mathrm{x}}!} \left(\mathrm{6}\right)}\:=\:\mathrm{7} \\ $$$$\: \\ $$ Answered by MJS last updated on 14/Aug/19…
Question Number 874 by 123456 last updated on 08/Apr/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)={g}\left({x}\right)−{f}\left(−{x}\right) \\ $$$${g}\left({x}\right)={f}\left({x}\right)+{g}\left(−{x}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$$${f}\left({x}\right)+{g}\left({x}\right)=? \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\overset{?} {=}\boldsymbol{{f}}\left(−\boldsymbol{{x}}\right)…
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Question Number 870 by 112358 last updated on 05/Apr/15 $${In}\:{how}\:{many}\:{ways}\:{may}\:{a}\:{line}\: \\ $$$${consisting}\:{of}\:\mathrm{4}\:{men}\:{and}\:\mathrm{4}\:{women} \\ $$$${be}\:{acquired}\:{if}\:{no}\:{two}\:{women}\:{are} \\ $$$${to}\:{be}\:{adjacent}\:{to}\:{each}\:{other}? \\ $$ Answered by prakash jain last updated on…
Question Number 66404 by ~ À ® @ 237 ~ last updated on 14/Aug/19 Commented by mathmax by abdo last updated on 14/Aug/19 $${let}\:{I}_{{n}} =\int_{\mathrm{0}}…
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