Question Number 15191 by arnabpapu550@gmail.com last updated on 08/Jun/17 $$\mathrm{If}\:{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and} \\ $$$$\bigtriangleup_{{r}} =\begin{vmatrix}{\:\:\:\mathrm{2}{r}−\mathrm{1}}&{\:^{{m}} {C}_{{r}} }&{\:\:\:\:\:\:\:\:\mathrm{1}}\\{\:\:{m}^{\mathrm{2}} −\mathrm{1}}&{\:\:\:\:\mathrm{2}^{{m}} }&{\:\:\:{m}+\mathrm{1}}\\{\mathrm{sin}^{\mathrm{2}} \left({m}^{\mathrm{2}} \right)}&{\mathrm{sin}^{\mathrm{2}} \left({m}\right)}&{\mathrm{sin}^{\mathrm{2}} \left({m}+\mathrm{1}\right)}\end{vmatrix} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\underset{{r}=\mathrm{0}} {\overset{{m}} {\sum}}\bigtriangleup_{{r}}…
Question Number 15190 by arnabpapu550@gmail.com last updated on 08/Jun/17 $$\mathrm{If}\:\:\:{I}_{\mathrm{3}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{identity}\:\mathrm{matrix}\:\mathrm{of}\:\mathrm{order}\:\mathrm{3},\: \\ $$$$\mathrm{then}\:\:\left({I}_{\mathrm{3}} \right)^{−\mathrm{1}} = \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 15189 by arnabpapu550@gmail.com last updated on 08/Jun/17 $$\mathrm{If}\:{A}=\begin{bmatrix}{{a}_{{ij}} }\end{bmatrix}_{{m}×{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{matrix}\:\mathrm{and}\:{B}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{non}−\mathrm{singular}\:\mathrm{square}\:\mathrm{submatrix}\:\mathrm{of} \\ $$$$\mathrm{order}\:\:{r}\:,\:\mathrm{then}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
If-is-a-cube-root-of-unity-then-a-root-of-the-following-polynomial-is-determinant-x-1-2-x-2-1-2-1-x-
Question Number 15180 by arnabpapu550@gmail.com last updated on 08/Jun/17 $$\mathrm{If}\:\:\:\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{then}\:\mathrm{a}\:\mathrm{root} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{polynomial}\:\mathrm{is} \\ $$$$\begin{vmatrix}{{x}+\mathrm{1}}&{\:\:\omega}&{\:\:\omega^{\mathrm{2}} }\\{\:\:\omega}&{{x}+\omega^{\mathrm{2}} }&{\:\:\mathrm{1}}\\{\:\:\omega^{\mathrm{2}} }&{\:\:\mathrm{1}}&{{x}+\omega}\end{vmatrix} \\ $$ Answered by ajfour last updated on…
Question Number 15158 by arnabpapu550@gmail.com last updated on 08/Jun/17 $$\mathrm{In}\:\mathrm{a}\:\mathrm{third}\:\mathrm{order}\:\mathrm{determinant},\:\mathrm{each} \\ $$$$\mathrm{element}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{column}\:\mathrm{consists}\:\mathrm{of} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{2}\:\mathrm{terms},\:\mathrm{each}\:\mathrm{element}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{second}\:\mathrm{column}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{3}\:\mathrm{terms} \\ $$$$\mathrm{and}\:\mathrm{each}\:\mathrm{element}\:\mathrm{of}\:\mathrm{the}\:\mathrm{third}\:\mathrm{column} \\ $$$$\mathrm{consists}\:\mathrm{of}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{4}\:\mathrm{terms}.\:\mathrm{Then}\:\mathrm{it}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{decomposed}\:\mathrm{into}\:{n}\:\mathrm{determinants}, \\ $$$$\mathrm{where}\:{n}\:\mathrm{has}\:\mathrm{the}\:\mathrm{value} \\…
Question Number 14572 by chux last updated on 02/Jun/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{pairs}\:\mathrm{of}\: \\ $$$$\mathrm{successive}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{them}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{40}\:\mathrm{and}\: \\ $$$$\mathrm{their}\:\mathrm{sum}\:\mathrm{is}\:\mathrm{atmost}\:\mathrm{100}\:\mathrm{is} \\ $$ Commented by mrW1 last updated on 02/Jun/17…
Question Number 80037 by Aashishyadavgangaria last updated on 30/Jan/20 $$\mathrm{A}\:\mathrm{matrix}\:{A}=\begin{bmatrix}{{a}_{{ij}} }\end{bmatrix}\:\mathrm{is}\:\mathrm{an}\:\mathrm{upper}\:\mathrm{triangular} \\ $$$$\mathrm{matrix}\:\mathrm{if} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 79950 by mhmd last updated on 29/Jan/20 $$\mathrm{If}\:\underset{{a}} {\overset{{b}} {\int}}\:\:\frac{{x}^{{n}} }{{x}^{{n}} +\left(\mathrm{16}−{x}\right)^{{n}} }\:{dx}\:=\:\mathrm{6},\:\mathrm{then}\: \\ $$ Commented by mr W last updated on 29/Jan/20…
Question Number 14128 by chux last updated on 28/May/17 $$\mathrm{If}\:\:\frac{\mathrm{P}{x}}{\left({b}−{c}\right)}\:=\:\frac{\mathrm{Q}{y}}{\left({c}−{a}\right)}\:=\:\frac{\mathrm{R}{z}}{\left({a}−{b}\right)}\:,\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{P}{ax}\:+\:\mathrm{Q}{by}\:+\:\mathrm{R}{cz}. \\ $$ Answered by ajfour last updated on 28/May/17 $${let}\:\:\frac{{Px}}{{b}−{c}}=\frac{{Qy}}{{c}−{a}}=\frac{{Rz}}{{a}−{b}}={m}\:\:\left({say}\right) \\ $$$${to}\:{find}:\:\:\: \\…
Question Number 79456 by Vishal Sharma last updated on 25/Jan/20 $$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{acute}\:\mathrm{positive}\:\mathrm{angles} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equations}\: \\ $$$$\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} {A}+\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} {B}=\mathrm{1}\:\mathrm{and}\: \\ $$$$\mathrm{3}\:\mathrm{sin}\:\mathrm{2}{A}−\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{B}=\mathrm{0},\:\mathrm{then}\:{A}+\mathrm{2}{B}= \\ $$ Commented by john santu…