jee-main 2025 Q84

jee-main · India · session2_02apr_shift1 Sign Change & Interval Methods
Q84. If $\lim _ { x \rightarrow 1 } \frac { ( 5 x + 1 ) ^ { 1 / 3 } - ( x + 5 ) ^ { 1 / 3 } } { ( 2 x + 3 ) ^ { 1 / 2 } - ( x + 4 ) ^ { 1 / 2 } } = \frac { \mathrm { m } \sqrt { 5 } } { \mathrm { n } ( 2 \mathrm { n } ) ^ { 2 / 3 } }$, where $\operatorname { gcd } ( \mathrm { m } , \mathrm { n } ) = 1$, then $8 \mathrm {~m} + 12 \mathrm { n }$ is equal to
Q84. If $\lim _ { x \rightarrow 1 } \frac { ( 5 x + 1 ) ^ { 1 / 3 } - ( x + 5 ) ^ { 1 / 3 } } { ( 2 x + 3 ) ^ { 1 / 2 } - ( x + 4 ) ^ { 1 / 2 } } = \frac { \mathrm { m } \sqrt { 5 } } { \mathrm { n } ( 2 \mathrm { n } ) ^ { 2 / 3 } }$, where $\operatorname { gcd } ( \mathrm { m } , \mathrm { n } ) = 1$, then $8 \mathrm {~m} + 12 \mathrm { n }$ is equal to\\