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Author: Tinku Tara

determinant-

Question Number 194482 by horsebrand11 last updated on 08/Jul/23 $$\:\:\:\:\:\begin{array}{|c|}{\:\cancel{\underline{\underbrace{\Subset}}}}\\\hline\end{array} \\ $$ Answered by cortano12 last updated on 08/Jul/23 $$\:\:\:\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:\left(\frac{\mathrm{2}}{\mathrm{cos}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}−\mathrm{3}\right)\right] \\ $$$$\:\:\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{cos}\:^{\mathrm{2}}…

Question-194509

Question Number 194509 by pascal889 last updated on 08/Jul/23 Answered by horsebrand11 last updated on 09/Jul/23 $$\:\:\left.\begin{matrix}{\mathrm{u}=\mathrm{x}+\mathrm{2y}}\\{\mathrm{v}=\mathrm{2x}+\mathrm{y}}\end{matrix}\right\}\Rightarrow\mathrm{3}\left(\mathrm{x}+\mathrm{y}\right)=\mathrm{u}+\mathrm{v} \\ $$$$\:\Rightarrow\left.\begin{matrix}{\mathrm{u}+\mathrm{v}=\mathrm{uv}}\\{\frac{\mathrm{1}}{\mathrm{u}}+\frac{\mathrm{1}}{\mathrm{v}^{\mathrm{2}} }=\mathrm{3}}\end{matrix}\right\}\Rightarrow\begin{cases}{\mathrm{u}+\mathrm{v}^{\mathrm{2}} =\mathrm{3uv}^{\mathrm{2}} }\\{\mathrm{u}+\mathrm{v}=\mathrm{uv}}\end{cases} \\ $$$$\:\Rightarrow\begin{cases}{\mathrm{u}=\frac{\mathrm{v}^{\mathrm{2}} }{\mathrm{3v}^{\mathrm{2}}…

How-many-sets-of-two-factors-of-720-are-coprime-to-each-other-A-63-B-64-C-65-D-67-

Question Number 194475 by BaliramKumar last updated on 08/Jul/23 $$\mathrm{How}\:\mathrm{many}\:\mathrm{sets}\:\mathrm{of}\:\mathrm{two}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{720}\:\mathrm{are}\: \\ $$$$\mathrm{coprime}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$\left(\mathrm{A}\right)\:\mathrm{63}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{64}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{65}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{67} \\ $$$$ \\ $$ Commented by MM42 last updated on 08/Jul/23…

Gyanashram-classes-shivkund-Munger-by-Bittu-sir-12-th-physics-test-1-2-

Question Number 194506 by Biteshwar last updated on 08/Jul/23 $$\:\:\:\:\:\:\:\:\:\:\mathrm{Gyanashram}\:\mathrm{classes} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{shivkund}\left(\mathrm{Munger}\right)\:\:\:\:\mathrm{by}−\mathrm{Bittu}\:\mathrm{sir} \\ $$$$\:\:\:\mathrm{12}\:\:\mathrm{th}\:\mathrm{physics}\:\mathrm{test} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1}. \: \: \: \: \: \: \: \: \\…

3-x-4-x-5-x-find-x-

Question Number 194499 by Mastermind last updated on 08/Jul/23 $$\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{4}^{\mathrm{x}} \:=\:\mathrm{5}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$ Commented by Frix last updated on 08/Jul/23 $$\mathrm{I}\:\mathrm{am}\:\mathrm{a}\:\mathrm{bit}\:\mathrm{blind}\:\mathrm{today}…\:\mathrm{just}\:\mathrm{guessing}: \\…

Question-194467

Question Number 194467 by horsebrand11 last updated on 08/Jul/23 $$\:\:\:\underline{\downdownarrows} \\ $$ Answered by mr W last updated on 08/Jul/23 $${f}\left({x}\right)=\sqrt{\mathrm{4}^{\mathrm{2}} −\left({x}−\mathrm{4}\right)^{\mathrm{2}} }−\sqrt{\mathrm{1}^{\mathrm{2}} −\left({x}−\mathrm{7}\right)^{\mathrm{2}} }…