1. The point of intersection of the tangents at the ends of the latus rectum of the parabola y² = 4x is _______________ .
2. The curve y = ax³+bx²+cx+5, touches the x-axis at P(-2,0) and cuts the y-axis at a point Q where its gradient is 3. Find a,b,c.
3. Find the indefinite integral
∫ cos 2θ ln[(cos θ + sin θ )/(cos θ - sin θ)]dθ
4. If, in the binomial expression of (a-b)n, n≥5, the sum of the 5th and 6th terms = 0, find a/b in terms of n (JEE 2001)
5. Find the integral part of (√2 + 1)8
Problems 1,2,3 are from IIT JEE paper 1994
Don't waste too much time on a problem. Allot some limited time and try to do. Ask your friends. If you still cannot solve just ignore and go ahead with your remaining preparation. Not time to waste lot of time on any one question.