NIMCET 2019 Question Paper with solutions

Question : 50 of 120

Marks: +1, -0

Number of real solution of the equation sin

(\e^\x)

5^\X

5^{-\x}

Solution:

We know that
AM ≥ GM

⇒{5^x+5^{-x}}/2 ≥ √{5^x⋅5^{-x}}

⇒5^x⋅5^{-x} ≥ 2

Now

\sin(e^x)=5^x⋅5^{-x}

⇒\sin(e^x) ≥ 2

Which is not possible
∴ No solution exists

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