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JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \([\mathrm{x}]\) denote the greatest integer less than or equal to \(\mathrm{x}\). Then, the values of \(x \in R\) satisfying the equation \(\left[e^{x}\right]^{2}+\left[e^{x}+1\right]-3=0\) lie in the interval:
- A \(\left[\log _{e} 2, \log _{e} 3\right)\)
- B \([0,1 / \mathrm{e})\)
- C \(\left[0, \log _{e} 2\right)\)
- D \([1, e)\)
Answer & Solution
Correct Answer
(C) \(\left[0, \log _{e} 2\right)\)
Step-by-step Solution
Detailed explanation
\({\left[e^{x}\right]^{2}+\left[e^{x}+1\right]-3=0}\) \(\Rightarrow\left[e^{x}\right]^{2}+\left[e^{x}+1\right]+1-3=0\) \(\text { Let }\left[e^{x}\right]=t\) \(\Rightarrow t^{2}+t-2=0\) \(\Rightarrow t=-2,1\) \({\left[e^{x}\right]=-2 \text { (Not possible) }}\)…
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