JEE Main 20245 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002The values of m,nm, nm,n, for which the system of equations x+y+z=4,2x+5y+5z=17,x+2y+mz=n\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\mathrm{m} z=\mathrm{n} \end{aligned}x+y+z=4,2x+5y+5z=17,x+2y+mz=n has infinitely many solutions, satisfy the equation :AOption A. m2+n2−m−n=46\mathrm{m}^2+\mathrm{n}^2-\mathrm{m}-\mathrm{n}=46m2+n2−m−n=46BOption B. m2+n2+mn=68\mathrm{m}^2+\mathrm{n}^2+\mathrm{mn}=68m2+n2+mn=68COption C. m2+n2−mn=39\mathrm{m}^2+\mathrm{n}^2-\mathrm{mn}=39m2+n2−mn=39DOption D. m2+n2+m+n=64\mathrm{m}^2+\mathrm{n}^2+\mathrm{m}+\mathrm{n}=64m2+n2+m+n=64CheckSkip · show solution
