Match List-I with List-II
| List-I | List-II | ||
| (A) | $y=log(sin x)$ | (I) | $\frac{d^2y}{dx^2}=-\frac{1}{x^2}$ |
| (B) | $y=e^{(1+logx)}$ | (II) | $\frac{d^2y}{dx^2}=2$ |
| (C) | $y=log|x|$ | (III) | $\frac{d^2y}{dx^2}=0$ |
| (D) | $y=x^2+4x-1$ | (IV) | $\frac{d^2y}{dx^2}=-cosec^2x$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is option (4) → (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(A) $y=\log(\sin x)$
$\frac{dy}{dx}=\cot x⇒\frac{d^2y}{dx^2}=-cosec^2x$ (IV)
(B) $y=e^{(1+\log x)}$
$⇒\log y=1+\log x$
$\log y=\log ex⇒y=ex$
so $\frac{d^2y}{dx^2}=0$ (III)
(C) $y=\log x⇒\frac{d^2y}{dx^2}=\frac{-1}{x^2}$ (I)
(D) $y=x^2+4x-1⇒\frac{d^2y}{dx^2}=2$ (II)