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Definite Integration question

2022 · Shift 1 · Q27

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2022 · Shift 1 · Q27

Definite Integration question

2022 · Shift 1 · Q27

JEE AdvancedMathematicsDefinite IntegrationMultiple correct+4 / −2

Consider the equation

\int_{1}^{e} \frac{\left(\log _{\mathrm{e}} x\right)^{1 / 2}}{x\left(a-\left(\log _{\mathrm{e}} x\right)^{3 / 2}\right)^{2}} d x=1, \quad a \in(-\infty, 0) \cup(1, \infty)

Which of the following statements is/are TRUE?

A
No $a$ satisfies the above equation
B
An integer $a$ satisfies the above equation
C
An irrational number $a$ satisfies the above equation
D
More than one $a$ satisfy the above equation

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