Match List – I with List – II.
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LIST I |
LIST II |
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A. $y=x^3 \log x$ |
I. $\frac{d^2 y}{d x^2}=25 e^{5 x}$ |
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B. $y=e^{5 x}$ |
II. $\frac{d y}{d x}=x^x(1+\log x)$ |
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C. $y=x^x$ |
III. $\frac{d^2 y}{d x^2}=-\frac{1}{2 a t^3}$ |
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D. $y=at^2, y=2 a t$ |
IV. $\frac{d^2 y}{d x^2}=x(5+6 \log x)$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A - IV, B - I, C - II, D - III
$\text{(A)}\; y=x^3\log x$
$y'=3x^2\log x + x^2$
$y''=6x\log x + 3x + 2x = x(6\log x + 5) \Rightarrow \text{(IV)}$
$\text{(B)}\; y=e^{5x}$
$y''=25e^{5x} \Rightarrow \text{(I)}$
$\text{(C)}\; y=x^x$
$y'=x^x(1+\log x) \Rightarrow \text{(II)}$
$\text{(D)}\; y=at^2,\; x=2at$
$\frac{d^2y}{dx^2}=\frac{1}{2a t^3}(-1) = -\frac{1}{2at^3} \Rightarrow \text{(III)}$
A–IV,\; B–I,\; C–II,\; D–III