CUET · MATHS · PYQ PAPER 2025
If \(x=a t^2, y=2 a t\); then \(\frac{d^2 y}{d x^2}\) is equal to
- A 0
- B \(\frac{1}{t}\)
- C \(-\frac{1}{t^2}\)
- D \(-\frac{1}{2 a t^3}\)
Answer & Solution
Correct Answer
(D) \(-\frac{1}{2 a t^3}\)
Step-by-step Solution
Detailed explanation
\(\frac{dx}{dt} = 2at\) \(\frac{dy}{dt} = 2a\) \(\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2a}{2at} = \frac{1}{t}\) \(\frac{d^2 y}{d x^2} = \frac{d}{dt}\left(\frac{dy}{dx}\right) \cdot \frac{dt}{dx}\)…
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