NIMCET 2024 Paper

Section: Mathematics

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Question : 10 of 120

Marks: +1, -0

The number of solutions of

5^{1+| sin \;x|+| sin \;x|^2+. . . . . . ∞}=25

, where

x ∈(-π, π)

, is:

1
0
4
$∞$

Solution:

Let us assume that

| sin \;x|=a

, then

\;5^{\;{1}/{1-a}}=25

\;⇒ \;{1}/{1-a}=2 \;\text " or "\; a=\;{1}/{2}

So

sin \;x= ± \;{1}/{2}

, so there are 4 solutions in the interval

(-π, π)

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