The option(s) with the values of a and L that satisfy the following equation is(are) _0^ 4 e^t( ^6at+ ^4at) ,dt _0^ e^t( ^6at+ ^4at) ,dt =L?

JEE Advanced 2015 Mathematics question

The option(s) with the values of and that satisfy the following equation is(are)

\frac{\int_0^{4π}e^t(\sin^6at+\cos^4at) dt}{\int_0^{π}e^t(\sin^6at+\cos^4at) dt}=L?

Answer: (A),(C)

Let ; its period is , so for or it is also periodic with period . Let . Substituting :

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Question ID VK-026476