1) Let g(x)=cosx2,f(x)=√x and α,β(α<β) be the roots of the quadratic equation 18x2−9πx+π2=0 .Then , the area (in sq units) bounded by the curve y=(gof)(x) and the lines x=α, x=β and y=0, is A) 12(√3−1) B) 12(√3+1) C) 12(√3−√2) D) 12(√2−1) Answer: Option AExplanation:We have ⇒ 18x2−9πx+π2=0 ⇒ 18x2−6πx−3πx+π2=0 (6x−π)(3x−π)=0 ⇒ x=π6,π3 Now , α<β=π6,β=π3 Given g(x)=cosx2 and f(x)=√x y=gOf(x) ∴ y=g(f(x))=cosx Area of region bounded by x=α, x=β , y=0 and curve y=g(f(x)) is A=∫π3π6cosxdx A=[sinx]π3π6 A=sinπ3−sinπ6=√32−12 A=(√3−12)