MHT CET · Maths · Application of Derivatives
The equation of the tangent to the curve \(y=b e^{-x / a}\) at the point where it crosses the Y axis is
- A \(x+\mathrm{y}=\mathrm{ab}\)
- B \(\frac{x}{a}+\frac{\mathrm{y}}{\mathrm{~b}}=1\)
- C \(a x+b y=1\)
- D \(x+y=a+b\)
Answer & Solution
Correct Answer
(B) \(\frac{x}{a}+\frac{\mathrm{y}}{\mathrm{~b}}=1\)
Step-by-step Solution
Detailed explanation
Point where curve crosses Y-axis: \(x=0 \implies y=b e^{-0/a} = b\). Point: \((0, b)\) Derivative: \(\frac{dy}{dx} = b e^{-x/a} \left(-\frac{1}{a}\right) = -\frac{b}{a} e^{-x/a}\)
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 a random variable X has the p.d.f.
\(\mathrm{f}(x)=\left\{\begin{array}{cl}\frac{\mathrm{k}}{x^2+1} & , \text { if } 0 < x < \infty \\ 0 & , \text { otherwise }\end{array}\right.\)
then c.d.f. of X isMHT CET 2025 Medium - If p, \(q\) are true statement and \(\mathrm{r}\) is false statement, then which of the following atements is a true statement.MHT CET 2020 Easy
- In \(\triangle \mathrm{ABC}\), with usual notations \(\frac{\mathrm{b} \sin \mathrm{B}-\mathrm{c} \sin \mathrm{C}}{\sin (\mathrm{B}-\mathrm{C})}=\)MHT CET 2021 Medium
- The solution of the differential equation \(\mathrm{e}^{-x}(y+1) \mathrm{d} y+\left(\cos ^2 x-\sin 2 x\right) y \mathrm{~d} x=0\) at \(x=0\), \(y=1\) isMHT CET 2023 Medium
- If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]\), and \(A(\operatorname{adj} A)=k I\), then the value of \((k+1)^4\) isMHT CET 2021 Easy
- The equation of the tangent parallel to \(y-x+5=0\) drawn to \(\frac{x^{2}}{3}-\frac{y^{2}}{2}=1\) isMHT CET 2008 Easy
More PYQs from MHT CET
- An element crystallises in bcc type crystal structure with edge length of unit cell \(300 \mathrm{pm} .\) Calculate radius of element?MHT CET 2020 Medium
- The direction cosines of the line which is perpendicular to the lines \(\frac{x-7}{2}=\frac{y+17}{-3}=\frac{z-6}{1}\) and \(\frac{x+5}{1}=\frac{y+3}{2}=\frac{z-6}{-2}\) areMHT CET 2022 Easy
- Water rises up to a height \(h\) in a capillary tube immersed vertically in water. When this whole arrangement is taken to a depth \(d\) in a mine, the water level rises up to a height \(h^{\prime}\). If \(R\) is the radius of the earth, then the ratio \(\frac{h}{h^{\prime}}\) isMHT CET 2022 Hard
- Let a force \(\overrightarrow{\mathrm{F}}=-\mathrm{F} \mathrm{k}\) acts on the origin of cartesian frame of reference. The moment of force about a point \((1,-1)\) will beMHT CET 2020 Easy
- \(\sin \left(\frac{\pi}{3}+x\right)-\cos \left(\frac{\pi}{6}+x\right)=\)MHT CET 2020 Easy
- \(\int_0^{\pi / 4} \sqrt{1-\sin 2 x} d x=\)MHT CET 2022 Hard