Question Number 5109 by shaikreshma last updated on 13/Apr/16 $$\mathrm{If}\:\:{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{scalar}\:\mathrm{and}\:{A}\:\mathrm{is}\:\mathrm{an}\:{n}×{n}\:\mathrm{square} \\ $$$$\mathrm{matrix}.\:\mathrm{Then}\:\mid{kA}\mid= \\ $$ Commented by prakash jain last updated on 13/Apr/16 $$={k}^{{n}} \mid{A}\mid \\…
Question Number 5018 by lec123 last updated on 02/Apr/16 $$\mathrm{If}\:\left({a}−{b}\right)^{\mathrm{2}} +\left({b}−{c}\right)^{\mathrm{2}} +\left({c}−{a}\right)^{\mathrm{2}} =\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{equal}. \\ $$ Commented by Rasheed Soomro last updated on 03/Apr/16…
Question Number 4891 by Rasheed Soomro last updated on 19/Mar/16 $$\mathrm{A}\:\mathrm{train}\:\mathrm{150}\:\mathrm{metres}\:\mathrm{long}\:\mathrm{completely} \\ $$$$\mathrm{passes}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{walking}\:\mathrm{in}\:\mathrm{the}\:\mathrm{opposite} \\ $$$$\mathrm{direction}\:\mathrm{at}\:\mathrm{6}\:\mathrm{kmph}\:\mathrm{in}\:\mathrm{9}\:\mathrm{seconds}\:\mathrm{and} \\ $$$$\mathrm{a}\:\mathrm{car}\:\:\mathrm{travelling}\:\:\mathrm{in}\:\mathrm{the}\:\:\mathrm{opposite}\: \\ $$$$\mathrm{direction}\:\mathrm{in}\:\mathrm{6}\:\mathrm{sec}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{car}. \\ $$ Commented by…
Question Number 4882 by Rishabh Jain last updated on 19/Mar/16 $$\mathrm{Roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{9}{x}^{\mathrm{2}} −\mathrm{18}\mid{x}\mid+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{belonging}\:\mathrm{to}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{definition} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)=\mathrm{log}\:\left({x}^{\mathrm{2}} −{x}−\mathrm{2}\right)\:\mathrm{is}/ \\ $$$$\mathrm{are} \\ $$ Answered by Yozzii last…
Question Number 70385 by ®Ëƒ ¬Ë°¹¾¨ ‰¦Í¦¿¨ ¸Ë¹Ç² last updated on 04/Oct/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{determinant} \\ $$$$\begin{vmatrix}{{x}+\mathrm{2}}&{\:{x}+\mathrm{3}}&{{x}+\mathrm{5}}\\{{x}+\mathrm{4}}&{\:{x}+\mathrm{6}}&{{x}+\mathrm{9}}\\{{x}+\mathrm{8}}&{{x}+\mathrm{11}}&{{x}+\mathrm{15}}\end{vmatrix}\:\mathrm{is} \\ $$ Answered by $@ty@m123 last updated on 04/Oct/19 $$=\begin{vmatrix}{−\mathrm{1}}&{\:−\mathrm{2}}&{{x}+\mathrm{5}}\\{−\mathrm{2}}&{\:−\mathrm{3}}&{{x}+\mathrm{9}}\\{−\mathrm{3}}&{−\mathrm{4}}&{{x}+\mathrm{15}}\end{vmatrix}\begin{cases}{{by}\:{C}_{\mathrm{1}}…
Question Number 70383 by ®Ëƒ ¬Ë°¹¾¨ ‰¦Í¦¿¨ ¸Ë¹Ç² last updated on 04/Oct/19 $$\mathrm{If}\:\mathrm{a}\:\mathrm{matrix}\:{A}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that}\:\mathrm{3}{A}^{\mathrm{3}} +\mathrm{2}{A}^{\mathrm{2}} +\mathrm{5}{A}+{I}=\mathrm{0}, \\ $$$$\mathrm{then}\:{A}^{−\mathrm{1}} \mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by mathmax by abdo…
Question Number 69734 by mhmd last updated on 27/Sep/19 $$\mathrm{If}\:{I}_{{n}} =\:\underset{\mathrm{0}\:} {\overset{\pi/\mathrm{4}} {\int}}\mathrm{tan}^{{n}} {x}\:{dx},\:{n}\:\in\:{N},\:\mathrm{then}\:{I}_{{n}+\mathrm{2}} +{I}_{{n}} = \\ $$ Commented by mathmax by abdo last updated…
Question Number 69735 by mhmd last updated on 27/Sep/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 27/Sep/19 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 69328 by mhmd last updated on 22/Sep/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\phi\left({x}\right)}{\phi\left({x}\right)+\phi\left(\frac{\pi}{\mathrm{2}}\:−{x}\right)}\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 22/Sep/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 69327 by mhmd last updated on 22/Sep/19 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} −\:\mathrm{5}^{\mathrm{2}{x}−\mathrm{1}} }{\mathrm{10}^{{x}} }\:{dx}\:=\: \\ $$ Answered by MJS last updated on 22/Sep/19 $$\int\frac{\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}}…