1) Let f:R→ R be a differentable function such that f(0)=0, f(π2)=3 and f ' (0)=1 if g(x)=∫π20f′(t)cosec tf(t)−cot tcosec tf(t)]dt for xϵ(0,π2], then limx→0g(x)= A) 4 B) 2 C) 1 D) 3 Answer: Option BExplanation:g(x)=∫π2xf′(t)cosec tf(t)−cot tcosec tf(t)]dt g(x)=f(π2)cosec π2−f(x)cosec x ⇒ g(x)=3−f(x)sinx limx→0g(x)=limx→0(3sinx−f(x)sinx) =limx→03cosx−f′(x)cosx 3−11=2