Consider the equation \int_1^e {(\log _{ {\e}} {\x})^{1 \/ 2}}/{ {\x}(a-(\log _{ {\e}} {\x})^{3 \/ 2})^2} {\dx}=1, a \in(-\infty, 0) \cup(1, \infty) . Which of the following statements is/are TRUE ? [JEE Adv 2022 P1]

No a satisfies the above equation

An integer a satisfies the above equation

An irrational number a satisfies the above equation

More than one a satisfy the above equation

Definite Integration

Section: Mathematics

Question : 7 of 46

Marks: +1, -0

Consider the equation

∫

e‌

(logex)1∕2

x(a−(logex)3∕2)2

‌dx=1,‌‌a∈(−∞,0)∪(1,∞).
Which of the following statements is/are TRUE ?

[JEE Adv 2022 P1]

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