AP EAMCET · Maths · Application of Derivatives
The interval in which \(y=\ln (\ln (x)), x>1\) is decreasing is
- A \((-\infty, 0) \cup(2, \infty)\)
- B \((0,2)\)
- C \((0,1)\)
- D None of the above
Answer & Solution
Correct Answer
(D) None of the above
Step-by-step Solution
Detailed explanation
Given function \(y=l(\ln (x)), x > 1\) \(\therefore \quad \frac{d y}{d x}=\frac{1}{x \ln x}, x > 1\) \(\because y\) is a decreasing, then \(\frac{d y}{d x} 1 \Rightarrow \ln x 1\) \(\therefore x \in \phi\), for decreasing
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If and satisfies , then at isAP EAMCET 2022 Medium
- If \(f(x)=\left\{\begin{array}{cl}1+6 x-3 x^2, & x \leq 1 \\ x+\log _2\left(b^2+7\right), & x>1\end{array}\right.\) is continuous at all real \(x\), then \(b=\)AP EAMCET 2023 Easy
- Equation of the plane passing through the intersection of the lines \(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-5}{-3}\) and \(\frac{x+5}{3}=\frac{y-4}{-1}=\frac{z+3}{4}\) and parallel to the \(x y\)-plane isAP EAMCET 2020 Easy
- The pair of straight lines represented by the equation \(3 d x^2-5 x y+\left(d^2-2\right) y^2=0\). If the lines are perpendicular to each other, for how many values of \(d\) this condition will be satisfied?AP EAMCET 2020 Easy
- The sum of the minimum and maximum distance of the point \((4,-3)\) to the circle \(x^2+y^2+4 x-10 y-7=0\), isAP EAMCET 2015 Medium
- The equations \(x-y=4\) and \(x^2+4 x y+y^2=0\) represent the sides of a/anAP EAMCET 2020 Hard
More PYQs from AP EAMCET
- Two coherent light sources having intensity in the ratio \(2 \mathrm{x}\) produce an interference pattern. Then the value of \(\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}\) will beAP EAMCET 2023 Medium
- AP EAMCET 2021 Easy
- By multiplying with \(e^{\int P d x}\) on both sides of the equation \(\frac{d y}{d x}+P(x) y=Q(x)\), the left side of the equation takes the form \(\frac{d}{d x}(y f(x))\), then \(f(x)=\)AP EAMCET 2022 Medium
- If \(x, y\) and \(z\) are non-zero real numbers and \(\hat{\mathbf{a}}=x \hat{\mathbf{i}}+2 \hat{\mathbf{j}}, \hat{\mathbf{b}}=y \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\hat{\mathbf{c}}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{j}}\) are such that \(\hat{\mathbf{a}} \times \hat{\mathbf{b}}=z \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\), then \([\hat{\mathbf{a}} \hat{\mathbf{b}} \hat{\mathbf{c}}]\) equals toAP EAMCET 2014 Easy
- In an LCR series circuit, if the potential differences across inductor, capacitor and resistor are \(60 \mathrm{~V}, 30 \mathrm{~V}\) and 40 V respectively, then the ac voltage applied to the circuit isAP EAMCET 2025 Medium
- Which of the following statements are correct?
I) The energy of hydrogen atom in its ground state is -13.6 eV
II) On the basis of Bohr's model, the radius of the \(3^{\text {rd }}\) orbit of hydrogen atom is 158.7 pm
III) The order of radius of the first orbit of \(\mathrm{H}, \mathrm{He}^{+}, \mathrm{Li}^{2+}\) and \(\mathrm{Be}^{3+}\) is \(\mathrm{H}>\mathrm{He}^{+}>\) \(\mathrm{Li}^{2+}>\mathrm{Be}^{3+}\)AP EAMCET 2025 Medium