Number of real solution of the equation... - Solved | MCA Prep

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Question 50

Mathematics Sequence And Series Hard

Number of real solution of the equation sin (e<sup>x</sup>) = 5<sup>x</sup> + 5<sup>-x</sup> is

(A) 0

(B) 1

(C) 2

(D) Infinitely many

✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

By AM–GM, \(5^x + 5^{-x} \ge 2\) for every real x.

But \(\sin(e^x) \le 1\).

So the two sides can never be equal, and there are no real solutions.

Answer: (A) 0

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