WBJEE · Maths · Application of Derivatives
If the tangent to the curve \(y^{2}=x^{3}\) at \(\left(m^{2}, m^{3}\right)\) is also a normal to the curve at \(\left(M^{2}, M^{3}\right)\), then the value of \(m M\) is
- A \(-\frac{1}{9}\)
- B \(-\frac{2}{9}\)
- C \(-\frac{1}{3}\)
- D \(-\frac{4}{9}\)
Answer & Solution
Correct Answer
(D) \(-\frac{4}{9}\)
Step-by-step Solution
Detailed explanation
Hint: \(2 y y_{1}=3 x^{2}\) \(y_{1}=\frac{3 x^{2}}{2 y} \Rightarrow\left(y_{1}\right)_{m^{2}, m^{3}}=\frac{3 \times m^{4}}{2 \times m^{3}}=\frac{3 m}{2}\) Again; slope of normal \(=-\frac{2}{3 M}, m M=-\frac{4}{9}\)
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
- The solution of the differential equation \(y \sin \left(\frac{x}{y}\right) d x=\left\{x \sin \left(\frac{x}{y}\right)-y\right\} d y \quad\) satisfying \(y\left(\frac{\pi}{4}\right)=1 \mathrm{is}\)WBJEE 2013 Hard
- If \(\lim _{x \rightarrow 0} \frac{2 a \sin x-\sin 2 x}{\tan ^{3} x}\) exists and is equal to 1 then the value of \(a\) isWBJEE 2014 Easy
- If the letters of the word 'PROBABILITY' are written down at random in a row, then probability that two B's are together, isWBJEE 2015 Medium
- A poker hand consists of 5 cards drawn at random from a well-shuffled pack of 52 cards. Then, the probability that a poker hand consists of a pair and a triple of equal face values (for example, 2 sevens and 3 kings or 2 aces and 3 queens, etc. ) isWBJEE 2014 Medium
- If \(f(x)=\int_{-1}^{x}|t|\) dt, then for any \(x \geq 0, f(x)\) is equal toWBJEE 2017 Easy
- If \(I=\int \frac{x^2 d x}{(x \sin x+\cos x)^2}=f(x)+\tan x+c\), then \(f(x)\) isWBJEE 2023 Medium
More PYQs from WBJEE
- Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \text { cost } & \text { sint } \\ 0 & -\sin t & \cos t\end{array}\right)\)
Let \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) be the roots of \(\operatorname{det}\left(A-\lambda I_{3}\right)=0\), where \(I_{3}\) denotes the identity matrix. If \(\lambda_{1}+\lambda_{2}+\lambda_{3}=\sqrt{2}+1\), then the set of possible values of \(t,-\pi \leq t < \pi\) isWBJEE 2021 Hard - For the variable, the locus of the point of intersection of the lines \(3 t x-2 y+6 t=0\) and \(3 x+2 t y-6=0\) isWBJEE 2013 Hard
- A shell of mass \(5 M\), acted upon by no external force and initially at rest, bursts into three fragments of masses \(M, 2 M\) and \(2 M\) respectively. The first two fragments move in opposite directions with velocities of magnitudes 2v and \(v\) respectively. The third fragment willWBJEE 2013 Easy
- Let \(P(n)=3^{2 n+1}+2^{n+2}\) where \(n \in \mathbb{N}\). ThenWBJEE 2023 Easy
- Which structure has delocalised \(\pi\)-electrons?WBJEE 2021 Easy
- For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given byWBJEE 2025 Easy