If (2, 4) is a point interior to the circle x2+y2−6x−10y+λ=0 and the circle does not cut the axes at any point, then

We have,  x2+y2−6x−10y+λ=0                         …(i)The circle does not cut the coordinate axes. Therefore,   9-λ<0 and 25-λ<0        [Using : g2-c<0, f2-c<0]⇒      λ>25                   ...(ii)It is given that the point (2, 4) lies inside the circle (i).∴ 4+16−12−40+λ<0⇒λ<32 … (iii) From (ii) and (iii), we get λ∈(25, 32)               ...(iii)