VITEEE 2010 Paper

Given curves are y=3x...(i)
and y=5x...(ii)
intersect at the point (0,1).
Now, differentiating eqs. (i) and (ii) w.r.t.x, we get

dy

dx

=3x‌log‌3 and

dy

dx

=5x‌log‌5
⇒ [

dy

dx

](0,1)=log‌3 and [

dy

dx

](0,1)=log‌5
⇒ m1=log‌3 and m2=log‌5
Angle between these curves is given by
tan‌θ=

m1−m2

1+m1m2

⇒ tan‌θ=

log‌3−log‌5

1+log‌3.‌log‌5

⇒ θ=tan−1(

log‌3−log‌5

1+log‌3‌log‌5

)