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