Question

Assertion (A): The solution of the equation $xdx+ydy=\frac{xdy-ydx}{x^2+y^2}$ is $2{\tan }^{-1}\frac{y}{x}-1=x^2+y^2+c$
Reason (R): $d\left({\tan }^{-1}\frac{y}{x}\right)=\frac{xdy-ydx}{xy}$

• A. A and R both are true and R is correct explanation of A
• B. A and R both are true but R is not the correct explanation of A
• C. Only A is true
• D. Only R is true

Answer 1

The correct option is C Only A is true

$xdx+ydy=\frac{xdy-ydx}{x^2+y^2}$
$\Rightarrow d(x^2+y^2)=2d{\tan }^{-1}\frac{y}{x}$
by integrating, we get $x^2+y^2+c=2{\tan }^{-1}\frac{y}{x}$
Therefore, assertion is correct and reason is not
Ans: C