jee-main 2025 Q18

jee-main · India · session1_29jan_shift2 Simultaneous equations
Let $\alpha , \beta ( \alpha \neq \beta )$ be the values of m , for which the equations $x + y + z = 1 ; x + 2 y + 4 z = \mathrm { m }$ and $x + 4 y + 10 z = m ^ { 2 }$ have infinitely many solutions. Then the value of $\sum _ { n = 1 } ^ { 10 } \left( n ^ { \alpha } + n ^ { \beta } \right)$ is equal to :
(1) 3080
(2) 560
(3) 3410
(4) 440
Let $\alpha , \beta ( \alpha \neq \beta )$ be the values of m , for which the equations $x + y + z = 1 ; x + 2 y + 4 z = \mathrm { m }$ and $x + 4 y + 10 z = m ^ { 2 }$ have infinitely many solutions. Then the value of $\sum _ { n = 1 } ^ { 10 } \left( n ^ { \alpha } + n ^ { \beta } \right)$ is equal to :\\
(1) 3080\\
(2) 560\\
(3) 3410\\
(4) 440