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Author: Tinku Tara

If-1-x-n-C-0-C-1-x-C-2-x-2-C-3-x-3-C-n-x-n-Prove-that-0-i-lt-j-n-i-j-C-i-C-j-n-2-2n-1-1-2-2n-C-n-

Question Number 22739 by Tinkutara last updated on 22/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} , \\ $$$${Prove}\:{that}\:\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left({i}\:+\:{j}\right){C}_{{i}} {C}_{{j}} \:=…

If-0-lt-a-b-lt-1-then-a-b-a-b-a-b-1-xyz-1-xyz-3-dxdydz-a-b-1-x-3-1-x-3-dx-3-

Question Number 153808 by mathdanisur last updated on 10/Sep/21 $$\mathrm{If}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}<\mathrm{1}\:\:\mathrm{then}: \\ $$$$\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\left(\frac{\mathrm{1}\:-\:\mathrm{xyz}}{\mathrm{1}\:+\:\mathrm{xyz}}\right)^{\mathrm{3}} \mathrm{dxdydz}\:\geqslant\:\left(\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\frac{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{3}} }{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{3}} }\:\mathrm{dx}\right)^{\mathrm{3}} \\ $$…

Question-88270

Question Number 88270 by Rio Michael last updated on 09/Apr/20 Commented by Rio Michael last updated on 09/Apr/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{circuit}\:\mathrm{above}\:\mathrm{containing}\:\mathrm{two}\:\mathrm{cells}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y} \\ $$$$\mathrm{of}\:\mathrm{emf}\:\mathrm{6}\:\mathrm{V}\:,\mathrm{8}\:\mathrm{V}\:,\:\mathrm{2}\:\Omega\:\mathrm{and}\:\mathrm{4}\Omega\:\mathrm{of}\:\mathrm{emf}\:\mathrm{and}\:\mathrm{internal}\:\mathrm{resistance} \\ $$$$\mathrm{respectively}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{pd}\:\mathrm{of}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{if}\:\mathrm{both}\: \\ $$$$\mathrm{cells}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{to}\:\mathrm{a}\:\mathrm{10}\Omega\:\mathrm{resistor}.…

Question-153800

Question Number 153800 by AliRaza123 last updated on 10/Sep/21 Answered by nadovic last updated on 10/Sep/21 $$\:\:\mathrm{Speed}\:\:=\:\:\frac{\mathrm{distance}}{\mathrm{time}} \\ $$$$\:\:\mathrm{600}\:\:=\:\:\frac{\mathrm{7200}}{{t}}\: \\ $$$$\:\:\:\:\:\:\:{t}\:\:=\:\:\frac{\mathrm{7200}}{\mathrm{600}}\: \\ $$$$\:\:\:\:\:\:\:{t}\:\:=\:\:\mathrm{12}\:{hours} \\ $$$$\:\:…

Question-22730

Question Number 22730 by selestian last updated on 22/Oct/17 Commented by math solver last updated on 22/Oct/17 $$−\mathrm{1}.\:{we}\:{know}\:{tan}\:{is}\:{positive}\:{in}\: \\ $$$$\mathrm{1}{st}\:{and}\:\mathrm{3}{rd}\:{quadrant}\:. \\ $$$${so}\:{there}\:{are}\:{infinite}\:{values}\:{which} \\ $$$${we}\:{can}\:{take}\:. \\…