jee-main 2023 Q74

jee-main · India · session2_15apr_shift1 Integration by Substitution Substitution Combined with Symmetry or Companion Integral

If $\int _ { 0 } ^ { 1 } \frac { 1 } { \left( 5 + 2 x - 2 x ^ { 2 } \right) \left( 1 + e ^ { ( 2 - 4 x ) } \right) } d x = \frac { 1 } { \alpha } \log _ { e } \left( \frac { \alpha + 1 } { \beta } \right) , \alpha , \beta > 0$, then $\alpha ^ { 4 } - \beta ^ { 4 }$ is equal to
(1) 19
(2) $- 21$
(3) 0
(4) 21

If $\int _ { 0 } ^ { 1 } \frac { 1 } { \left( 5 + 2 x - 2 x ^ { 2 } \right) \left( 1 + e ^ { ( 2 - 4 x ) } \right) } d x = \frac { 1 } { \alpha } \log _ { e } \left( \frac { \alpha + 1 } { \beta } \right) , \alpha , \beta > 0$, then $\alpha ^ { 4 } - \beta ^ { 4 }$ is equal to\\
(1) 19\\
(2) $- 21$\\
(3) 0\\
(4) 21

Paper Questions

Q21 Q22 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79