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