99 Percentile Qs Bank for JEE MainMathematicsLimits

_ x 0 27^x-9^x-3^x+1 5 - 4+ x =

Options

A8 5 3
B16 5 3
C8 5 ( 3)^2
D5 ( 3)^2

Correct answer

C. 8 5 ( 3)^2

Step-by-step solution

aligned & _ x 0 27^x-9^x-3^x+1 5 - 4+ x = _ x 0 (9^x-1 ) (3^x-1 ) 5-(4+ x) 5 + 4+ x & = _ x 0 (9^x-1 ) (3^x+1 ) 1- x 5 + 4+ x & = _ x 0 (9^x-1 ) (3^x-1 ) 2 ^2 ( x 2 ) 5 + 4+ x & = _ x 0 ( 9^x-1 x ) ( 3^x-1 x ) 2 ^2 x 2 x^2 4 1 4 5 + 4+ x aligned aligned & = 9 3 1 2 5 + 5 & =2 9 3 (2 5 ) & =8 5 ( 3)^2 aligned

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