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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

  1. A 0
  2. B \(\frac{1}{t}\)
  3. C \(-\frac{1}{t^2}\)
  4. D \(-\frac{1}{2 a t^3}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(-\frac{1}{2 a t^3}\)

Step-by-step Solution

Detailed explanation

\(\frac{dx}{dt} = 2at\) \(\frac{dy}{dt} = 2a\) \(\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2a}{2at} = \frac{1}{t}\) \(\frac{d^2 y}{d x^2} = \frac{d}{dt}\left(\frac{dy}{dx}\right) \cdot \frac{dt}{dx}\)…