1. Determine the equation of the curve passing through the origin, in the form y = f(x), which satisfies the differential equation dy/dx = sin (10x+6y).
2. Determine the points of maxima and minima of the function
f(x) = (1/8)ln x - bx +x², x is g.t. 0, and where b≥0 is a constant.
3. General value of θ satisfying the equation tan²θ + sec 2θ = 1 is ________ .
4. For any odd integer n≥1, n³ - (n-1)³+...+(-1)n-1 1³ = _________ .
5. If xexy = y + sin²x, then x = 0, dy/dx = _________.
All problems are from 1996 JEE paper.
Don't waste lot of time on any problem.