Question Number 96845 by DELETED last updated on 05/Jun/20 $$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{5}}\:+\:\mathrm{cosec}^{−\mathrm{1}} \frac{\mathrm{5}}{\mathrm{4}}\:=\:\frac{\pi}{\mathrm{2}},\:\mathrm{then}\:{x}= \\ $$ Answered by Sourav mridha last updated on 05/Jun/20 $$\Rightarrow\mathrm{sin}^{−\mathrm{1}} \left(\frac{\boldsymbol{{x}}}{\mathrm{5}}\right)=\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{4}}{\mathrm{5}}\right)=\mathrm{sin}^{−\mathrm{1}}…
Question Number 31255 by Tip Top last updated on 04/Mar/18 $$\mathrm{2}{n}\:\mathrm{boys}\:\mathrm{are}\:\mathrm{randomly}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{two} \\ $$$$\mathrm{subgroups}\:\mathrm{containing}\:{n}\:\mathrm{boys}\:\mathrm{each}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{two}\:\mathrm{tallest}\:\mathrm{boys}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{different}\:\mathrm{groups}\:\mathrm{is} \\ $$ Answered by MJS last updated on…
Question Number 30939 by paddu1234 last updated on 01/Mar/18 $$\mathrm{If}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\:{r}^{\mathrm{2}} \:,\:\mathrm{then} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{{xy}}{{zr}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{yz}}{{xr}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{xz}}{{yr}}\right)\:= \\ $$ Answered by ajfour last…
Question Number 95986 by mpym last updated on 29/May/20 $$\mathrm{In}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{3}\:\mathrm{consecutive}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{2}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{3}\:\mathrm{times}\:\mathrm{the}\:\mathrm{first}\:\mathrm{numbers}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{three}\:\mathrm{numbers}. \\ $$ Commented by mr W last updated on…
Question Number 95985 by mpym last updated on 29/May/20 $$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{complete}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}\:\mathrm{in} \\ $$$$\mathrm{12}\:\mathrm{days}\:\mathrm{and}\:\mathrm{24}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{After} \\ $$$$\mathrm{A}\:\mathrm{had}\:\mathrm{worked}\:\mathrm{for}\:\mathrm{6}\:\mathrm{days},\:\mathrm{B}\:\mathrm{joined}\:\mathrm{him}, \\ $$$$\mathrm{and}\:\mathrm{then}\:\mathrm{they}\:\mathrm{completed}\:\mathrm{the}\:\mathrm{work}.\:\mathrm{How} \\ $$$$\mathrm{much}\:\mathrm{should}\:\:\mathrm{A}\:\mathrm{receive}\:\mathrm{as}\:\mathrm{his}\:\mathrm{share}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{Rs}.\:\mathrm{180}\:\mathrm{paid}\:\mathrm{for} \\ $$$$\mathrm{completing}\:\mathrm{the}\:\mathrm{work}? \\ $$ Answered…
Question Number 95982 by mpym last updated on 29/May/20 $$\Sigma{x}\left({y}^{\mathrm{3}} −{z}^{\mathrm{3}} \right)=\_\_\_\_\_. \\ $$ Answered by mr W last updated on 29/May/20 $$={x}\left({y}^{\mathrm{3}} −{z}^{\mathrm{3}} \right)+{y}\left({z}^{\mathrm{3}}…
Question Number 30356 by soksan last updated on 21/Feb/18 $$\mathrm{If}\:\mathrm{sin}\:\mathrm{2}\theta=\:\mathrm{cos}\:\mathrm{3}\theta\:\:\mathrm{and}\:\theta\:\mathrm{is}\:\mathrm{an}\:\mathrm{acute} \\ $$$$\mathrm{angle},\:\mathrm{then}\:\mathrm{sin}\:\theta\:\mathrm{equals} \\ $$ Answered by mrW2 last updated on 21/Feb/18 $$\mathrm{sin}\:\mathrm{2}\theta=\:\mathrm{cos}\:\mathrm{3}\theta \\ $$$$\mathrm{2sin}\:\theta\mathrm{cos}\:\theta=\mathrm{4cos}^{\mathrm{3}} \:\theta−\mathrm{3cos}\:\theta…
Question Number 30354 by soksan last updated on 21/Feb/18 $$\mathrm{If}\:\:{g}\left({x}\right)=\overset{{x}} {\int}_{\mathrm{0}} \mathrm{cos}^{\mathrm{4}} {t}\:{dt},\:\mathrm{then}\:{g}\:\left({x}+\pi\right)\:= \\ $$ Answered by ajfour last updated on 21/Feb/18 $${g}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\:{x}} \left(\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 30183 by Surajitzzz last updated on 17/Feb/18 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{ax}^{\mathrm{2}} −{bx}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{4}:\:\mathrm{5},\:\mathrm{then}\:\mathrm{4}{b}^{\mathrm{2}} =\mathrm{81}{ac}. \\ $$ Answered by Rasheed.Sindhi last updated on 18/Feb/18 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{are}\:\mathrm{4k}\:\&\:\mathrm{5k} \\…
Question Number 30156 by naybr last updated on 17/Feb/18 $$\mathrm{If}\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:{x}+\mathrm{3},\:{y}+\mathrm{3},\:{z}+\mathrm{3}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{HP},\:\mathrm{then} \\ $$ Answered by ajfour last updated on 17/Feb/18 $${Then} \\ $$$$\:\:\:\frac{{y}}{{x}}=\frac{{z}}{{y}}\:={r}\:\:\:{and}\:\:\:\frac{\mathrm{2}}{{y}+\mathrm{3}}=\frac{\mathrm{1}}{{x}+\mathrm{3}}+\frac{\mathrm{1}}{{z}+\mathrm{3}} \\…