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e total number of solutions of $ln invisible function application open vertical bar sin invisible function application x close vertical bar equals negative x to the power of 2 end exponent plus 2 x blank$ in $open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator 3 pi over denominator 2 end fraction close square brackets$ is equal to

1
2
4
None of these

The correct answer is: 2

$ln invisible function application open vertical bar sin invisible function application x close vertical bar equals negative x open parentheses x minus 2 close parentheses$
Graphs of $y equals ln invisible function application open vertical bar sin invisible function application x close vertical bar$ and $blank y equals negative x open parentheses x minus 2 close parentheses blank$ meet exactly two times in $blank open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator 3 pi over denominator 2 end fraction close square brackets$

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Member of solutions of $tan invisible function application open parentheses fraction numerator pi over denominator 2 end fraction sin invisible function application theta close parentheses equals cot invisible function application open parentheses fraction numerator pi over denominator 2 end fraction cos invisible function application theta close parentheses comma blank theta element of open square brackets 0 comma blank 6 pi close square brackets comma blank$ is

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parallel

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