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