1) If sin x is the integrating factor (IF) of the linear differential equation $\frac{dy}{dx}+Py$=Q, then P is A) log sin x B) cos x C) tan x D) cot x Answer: Option DExplanation:We know that IF of $\frac{dy}{dx}+Py$=Q is $IF=e^{\int pdx }$ $\sin x= e^{\int pdx }$ On differentiating both sides , we get $\cos x=e^{\int pdx }P$ cos x= sin x P $\Rightarrow$ P= cot x
