Question Number 34930 by NECx last updated on 13/May/18 $${A}\:{committee}\:{of}\:\mathrm{4}\:{is}\:{to}\:{be}\:{formed} \\ $$$${from}\:\mathrm{4}\:{principals} \\ $$$${and}\:\mathrm{5}\:{students}.{In}\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}\:{if}\:{a}\:{particular} \\ $$$${student}\:{and}\:{a}\:{principal}\:{must}\:{be} \\ $$$${in}\:{the}\:{committee}. \\ $$$$ \\ $$ Commented…
Question Number 100444 by mr W last updated on 26/Jun/20 $${Find}\:{the}\:{number}\:{of}\:{five}−{digit}\:{numbers} \\ $$$${containing}\:{exactly}\:{three}\:{different} \\ $$$${digits}?\:{Examples}:\:\mathrm{12312},\:\mathrm{12224} \\ $$ Answered by Rasheed.Sindhi last updated on 28/Jun/20 $$\:^{\bullet}…
Question Number 34878 by NECx last updated on 12/May/18 $${show}\:{that} \\ $$$$\overset{{n}+{r}−\mathrm{1}} {{C}}_{{n}−\mathrm{1}} =\overset{{n}+{r}−\mathrm{1}} {{C}}_{{r}} \\ $$ Answered by Rasheed.Sindhi last updated on 12/May/18 $$\:^{\mathrm{n}}…
Question Number 34877 by NECx last updated on 12/May/18 $$\mathrm{4}\:{couples}\:{are}\:{to}\:{take}\:{a}\:{photograph} \\ $$$${with}\:{a}\:{newly}\:{wedded}\:{couple}\:{in}\:{a} \\ $$$${wedding}\:{party}.{In}\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}\:{if}: \\ $$$$\left.{i}\right){the}\:{celebrated}\:{couple}\:{must}\:{stand} \\ $$$${in}\:{the}\:{middle} \\ $$$$\left.{ii}\right){each}\:{couple}\:{must}\:{stand}\:{next}\:{to} \\ $$$${each}\:{other} \\…
Question Number 99985 by Rio Michael last updated on 24/Jun/20 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{length}\:\mathrm{4}.\mathrm{5}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{12}.\mathrm{3}\:\mathrm{g},\:\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{1}.\mathrm{1}\:\mathrm{m}\Omega.\:\mathrm{this}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{through}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{magnetic}\:\mathrm{field}\:\:\mathrm{with}\:\mathrm{flux}\:\mathrm{density}\:\mathrm{of}\:\mathrm{0}.\mathrm{35}\:\mathrm{T}.\:\mathrm{As}\:\mathrm{his}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{its}\:\mathrm{ends} \\ $$$$\mathrm{slide}\:\mathrm{smoothly}\:\mathrm{between}\:\mathrm{two}\:\mathrm{rails}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{negligible} \\ $$$$\mathrm{internal}\:\mathrm{resistance}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{energy} \\ $$$$\mathrm{resistance},\:\mathrm{neglecting}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}. \\ $$ Terms of…
Question Number 34410 by Tinkutara last updated on 05/May/18 $${Prove}\:{that}\:\frac{\left({n}^{\mathrm{2}} \right)!}{\left({n}!\right)^{{n}+\mathrm{1}} }\:{is}\:{always}\:{an}\:{integer} \\ $$$${for}\:{n}\in{N}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99905 by Rio Michael last updated on 23/Jun/20 Commented by Rio Michael last updated on 23/Jun/20 $$\mathrm{P}\:\mathrm{and}\:{Q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{identical}\:\mathrm{straight}\:\mathrm{cables}\:\mathrm{each}\:\mathrm{of}\:\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{20}.\mathrm{0}\Omega. \\ $$$$\mathrm{placed}\:\mathrm{4}.\mathrm{8}\:\mathrm{cm}\:\mathrm{apart}\:\mathrm{in}\:\mathrm{air}.\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{current}\:\mathrm{through}\:\mathrm{each}\:\mathrm{cable} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{draw}\:\mathrm{the}\:\mathrm{magnetic}\:\mathrm{field}\:\mathrm{pattern}\:\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:{P}\:\mathrm{and}\:{Q}…
Question Number 165385 by SLVR last updated on 31/Jan/22 $${Number}\:{of}\:\:{ways}..{n}\: \\ $$$${differrnt}\:\:{things}\:{be}\:{distributed} \\ $$$${in}\:{r}\:{identical}\:{boxes}\:{so}\:{as} \\ $$$$\left.\mathrm{1}\right){empty}\:{box}\:{is}\:{allowed} \\ $$$$\left.\mathrm{2}\right){empty}\:{box}\:{not}\:{allowed} \\ $$$${Number}\:{of}\:{ways}…{n}\:{identical} \\ $$$${things}\:{be}\:{distributed}\:{to}\:{r} \\ $$$${identical}\:{boxes}\:{so}\:{as} \\…
Question Number 165376 by MikeH last updated on 31/Jan/22 $$\mathrm{Verify}\:\mathrm{wether}\:{f}\:\mathrm{is}\:\mathrm{invertible}\: \\ $$$${f}\:\left({x}\right)\:=\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\ $$ Answered by Rasheed.Sindhi last updated on 31/Jan/22 $${f}\:\left({x}\right)\:=\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\ $$$${y}=\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\…
Question Number 165361 by MikeH last updated on 31/Jan/22 $$\mathrm{Obtain}\:\mathrm{a}\:\mathrm{general}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\:\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{5}},\frac{\mathrm{8}}{\mathrm{9}},\frac{\mathrm{16}}{\mathrm{17}},\frac{\mathrm{32}}{\mathrm{33}},… \\ $$$$\mathrm{assuming}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{continues}\:\mathrm{in}\:\mathrm{that} \\ $$$$\mathrm{pattern}. \\ $$ Commented by MJS_new last updated…