MHT CET · Maths · Straight Lines
The abscissa of the point on the curve \(y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{-\frac{x}{a}}\right)\) where the tangent is parallel to the X -axis is
- A 0
- B a
- C 2 a
- D -2 a
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \quad y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{\frac{-x}{a}}\right) \\
& \therefore \quad \frac{\mathrm{d} y}{\mathrm{~d} x}=\mathrm{e}^{\frac{x}{a}}-\mathrm{e}^{-\frac{x}{a}}
\end{aligned}\)
Since the tangent is parallel to X -axis, \(\frac{\mathrm{d} y}{\mathrm{~d} x}=0\)
\(\begin{aligned}
& \Rightarrow \mathrm{e}^{\frac{x}{\mathrm{a}}}-\mathrm{e}^{-\frac{x}{\mathrm{a}}}=0 \\
& \Rightarrow \mathrm{e}^{\frac{2 x}{\mathrm{a}}}=0 \\
& \Rightarrow x=0
\end{aligned}\)
& \quad y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{\frac{-x}{a}}\right) \\
& \therefore \quad \frac{\mathrm{d} y}{\mathrm{~d} x}=\mathrm{e}^{\frac{x}{a}}-\mathrm{e}^{-\frac{x}{a}}
\end{aligned}\)
Since the tangent is parallel to X -axis, \(\frac{\mathrm{d} y}{\mathrm{~d} x}=0\)
\(\begin{aligned}
& \Rightarrow \mathrm{e}^{\frac{x}{\mathrm{a}}}-\mathrm{e}^{-\frac{x}{\mathrm{a}}}=0 \\
& \Rightarrow \mathrm{e}^{\frac{2 x}{\mathrm{a}}}=0 \\
& \Rightarrow x=0
\end{aligned}\)
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
- With usual notation, in triangle \(\mathrm{ABC}, \mathrm{m} \angle \mathrm{A}=30^{\circ}\), then the value of \(\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right)\) is equal toMHT CET 2025 Medium
- The cartesian equation of a line passing through \((1,2,3)\) and parallel to planes \(x-y+2 z=5\) and \(3 x+y+z=6\) isMHT CET 2022 Medium
- Equations of planes parallel to the plane which are at a distance of one unit from the point are …..MHT CET 2019 Easy
- If \(\mathrm{f}(\mathrm{x})=\int \frac{\mathrm{x}^2+\sin ^2 \mathrm{x}}{1+\mathrm{x}^2}, \sec ^2 \mathrm{x} d \mathrm{x}\) and \(\mathrm{f}(0)=0\), then \(\mathrm{f}(1)=\)MHT CET 2022 Hard
- If \(\bar{a}, \bar{b}, \bar{c}\) are three non-zero vectors, no two of them are collinear, \(\bar{a}+2 \bar{b}\) is collinear with \(\overline{\mathrm{c}}, \overline{\mathrm{b}}+3 \overline{\mathrm{c}}\) is collinear with \(\overline{\mathrm{a}}\), then \(\overline{\mathrm{a}}+2 \overline{\mathrm{b}}\) isMHT CET 2023 Easy
- If \(\int_a^b x^3 d x=0\) and if \(\int_a^b x^2 d x=\frac{2}{3}\), then \(a\) and \(b\) are respectivelyMHT CET 2022 Easy
More PYQs from MHT CET
- Moment of inertia of a disc about a diameter is \(I .\) Find the moment of inertia of disc about an axis perpendicular to its plane and passing through its rim?MHT CET 2010 Medium
- The average rate of reaction \(2 SO 2(g)+ O 2(g) \rightarrow 2 SO 3(g)\) is written asMHT CET 2016 Easy
- \(\int \cos ^3 x e^{\log (\sin x)^2} d x=\)MHT CET 2021 Easy
- In a CE transistor, a change of \(8.0 \mathrm{~mA}\) in the emitter current produces a change of \(7.8 \mathrm{~mA}\) in the collector current. What change in the base current is necessary to produce the same change in the collector current?MHT CET 2021 Medium
- Identify the CORRECT match from the Columns I, II and III.
I II III 1. Interstitial cells a. Cortex of ovary i. Follicular fluid 2. Sertoli cells b. Ovarian follicle ii. Progesterone 3. Granulosa cells c. Testis iii. Attachment of sperm bundle 4. Cells of corpus luteum d. Seminiferous tubules iv. Testosterone MHT CET 2014 Easy - In Young's double slit experiment, the \(6^{\text {th }}\) maximum with wavelength \({ }^{\prime} \lambda_{1}{ }^{\prime}\) is at a distance \({ }^{\prime} \mathrm{d}_{1}{ }^{\prime}\) from the central maximum and the \(4^{\text {th }}\) maximum with wavelength \(\lambda_{2}\)
is at distance \(\mathrm{d}_{2}\). Then \(\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\) isMHT CET 2020 Medium