Match List-I with List-II
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List-I (Parametric equations) |
List-II $(\frac{dy}{dx})$ |
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(A) $x =\frac{2}{t},y=2t$ |
(I) $4t^2$ |
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(B) $x=t^3,y=3t+ 2$ |
(II) $2(t+1)$ |
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(C) $x = \log t,y=2t^2$ |
(III) $-t^2$ |
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(D) $x = e^t,y=2te^t$ |
(IV) $t^{-2}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
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List-I (Parametric equations) |
List-II $(\frac{dy}{dx})$ |
|
(A) $x =\frac{2}{t},y=2t$ |
(III) $-t^2$ |
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(B) $x=t^3,y=3t+ 2$ |
(IV) $t^{-2}$ |
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(C) $x = \log t,y=2t^2$ |
(I) $4t^2$ |
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(D) $x = e^t,y=2te^t$ |
(II) $2(t+1)$ |
(A) $x=\frac{2}{t},\; y=2t$
$\frac{dx}{dt}=-\frac{2}{t^2},\;\frac{dy}{dt}=2$
$\frac{dy}{dx}=\frac{2}{-2/t^2}=-t^2 \;\;\;\Rightarrow\;$ (III)
(B) $x=t^3,\; y=3t+2$
$\frac{dx}{dt}=3t^2,\;\frac{dy}{dt}=3$
$\frac{dy}{dx}=\frac{3}{3t^2}=\frac{1}{t^2} \;\;\;\Rightarrow\;$ (IV)
(C) $x=\log t,\; y=2t^2$
$\frac{dx}{dt}=\frac{1}{t},\;\frac{dy}{dt}=4t$
$\frac{dy}{dx}=\frac{4t}{1/t}=4t^2 \;\;\;\Rightarrow\;$ (I)
(D) $x=e^t,\; y=2te^t$
$\frac{dx}{dt}=e^t,\;\frac{dy}{dt}=2e^t+2te^t=2(t+1)e^t$
$\frac{dy}{dx}=\frac{2(t+1)e^t}{e^t}=2(t+1) \;\;\;\Rightarrow\;$ (II)