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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $\text{y}^2=\text{ax}^2+\text{bx}+\text{c},$ then $\text{y}^3\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is :
  • A
    a constant
  • B
    a function of $x$ only
  • ✓
    a function of $y$ only
  • D
    a function of $x$ and only
✓

Answer

Correct option: C.
a function of $y$ only
$\text{y}^2=\text{ax}^2+\text{bx}+\text{c}$
$\frac{\text{dy}}{\text{dx}}=2\text{ax}+\text{b}$
$\frac{\text{d}^2\text{y}}{\text{d}^2}=2\text{a}$
$=\text{y}^2\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{ay}^3$
$=$ A function of $y$ only

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