Solved Question Papers - IIT JEE/MathsQP2005  Two Mark
QuestionsEdit  Q1. A person goes to office either by car,
scooter, bus or train the probabilities for which are 1/7, 3/7,
2/7 and 1/7 respectively. The probabilities that he reaches
office late, if he takes car, scooter, bus or train are 2/9,
1/9, 4/9 and 1/9 respectively. Given that he reached office in
time, what is the probability that he travelled by a car?  Q2
Find the range of values of t for which 2\sin
t=\frac{1-2x+5x^2}{3x^2-2x-1} Q3 Circles with radii 3,4 and 5
units touch each other externally. Let P be the point of
intersection of tangents to these circles at their points of
contact. Find the distance of P from the points of contact.  Q4
Find the equation of the plane containing the line 2x – y + z –
3 = 0, 3x + y + z = 5 and at a distance of \frac{1}{\sqrt 6}
from the point (2,1,–1).  Q5 A function f(x) is such that | f
(x1)-f (x2) | < (x1-x2)2 for all real x1 and x2. Find the
equation of the tangent to the curve y = f (x) at the point
(1,2)