MHT CET202411 May 2024Morning ShiftMathematicsLimitsActual
_ x 2 ( 5^x+5^ 3-x -30 5^ 3-x -5^ x 2 )=
Options
- A-16 3
- B8 3
- C-8 3
- D16 3
Correct answer
C. -8 3
Step-by-step solution
Let aligned L & = _ x 2 ( 5^x+5^ 3-x -30 5^ 3-x -5^ x 2 ) & = _ x 2 ( 5^x+ 5^3 5^x -30 5^3 5^x - (5^x )^ 1 2 ) aligned aligned & Let t=5^x x & 2 t 25 L & = _ t 25 ( t+ 125 t -30 125 t - t ) & = _ t 25 ( t^2-30 t+125 25 25 -t t ) & = _ t 25 ( (t-25)(t-5) 25^ 3 2 -t^ 3 2 ) aligned aligned & = _ t 25 t -5 - ( 25^ 3 2 - t ^ 3 2 25- t ) & = 25-5 - 3 2 (25)^ 1 2 & = -8 3 aligned