MCQ 11 Mark
$\int\frac{\text{dx}}{\sqrt{2\text{ax}-\text{x}^2}}=\text{a}^{\text{n}}\sin^{-1}\Big[\frac{\text{x}}{\text{a}}-1\Big].$ The value of $n$ is$:$
- ✓$0$
- B$-1$
- C$1$
- DNone of these.
Answer
View full question & answer→Correct option: A.
$0$
$[ax] = [x^2]$
$\Rightarrow [a] = [x] ...(1)$
Dimension of $\text{LHS} =$ Dimension of $\text{RHS}$
$\Rightarrow\Big[\frac{\text{dx}}{\sqrt{\text{x}}^2}\Big]=\big[\text{a}^{\text{n}}\big]$
$\Rightarrow\Big[\frac{\text{L}}{\text{L}}\Big]=\big[\text{a}^{\text{n}}\big] \ ...(2)$
$\Rightarrow\big[\text{L}^{0}\big]=[\text{a}^{\text{n}}]$
$\text{n}=0$
$\Rightarrow [a] = [x] ...(1)$
Dimension of $\text{LHS} =$ Dimension of $\text{RHS}$
$\Rightarrow\Big[\frac{\text{dx}}{\sqrt{\text{x}}^2}\Big]=\big[\text{a}^{\text{n}}\big]$
$\Rightarrow\Big[\frac{\text{L}}{\text{L}}\Big]=\big[\text{a}^{\text{n}}\big] \ ...(2)$
$\Rightarrow\big[\text{L}^{0}\big]=[\text{a}^{\text{n}}]$
$\text{n}=0$