Match List-I with List-II
| List-I | List-II | ||
| Parametric function | \( \displaystyle\frac{dy}{dx}= \) | ||
| (A) | \( x=t^{2},\ y=2t \) | (I) | \( \displaystyle\frac{2t}{3} \) |
| (B) | \( x=t^{3},\ y=t^{2} \) | (II) | \( \displaystyle\frac{1}{t} \) |
| (C) | \( x=3t,\ y=t^{2} \) | (III) | \( \displaystyle\frac{2}{3t} \) |
| (D) | \( x=t^{2},\ y=2t^{3} \) | (IV) | \( 3t \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) - (II), (B) - (III), (C) - (I), (D) - (IV)
For a parametric function:
\( \displaystyle \frac{dy}{dx}=\frac{dy/dt}{dx/dt} \)
(A) \( \frac{2}{2t}=\frac{1}{t} \). This matches (II).
(B) \( \frac{2t}{3t^{2}}=\frac{2}{3t} \). This matches (III).
(C) \( \frac{2t}{3} \). This matches (I).
(D) \( \frac{6t^{2}}{2t}=3t \). This matches (IV).
So the matching is (A) - (II), (B) - (III), (C) - (I), (D) - (IV).