Solved Question Papers - IIT JEE/MathsQP2005

=Two Mark Questions= 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)

Q6 The total number of runs scored in n matches is given by <B><I>f</I> (n)</B> (n > 1) and the number of runs scored in the kth match is given by <B><I>g</I> (k)</B> (1 ≤ k ≤ n). Find the value of n.<BR> $$f(n)=\left( \frac{n+1}{4} \right) \left(2^\left(n+1\right)-n-2\right) and g(k)=k2^\left(n+1-k\right)$$