# Solved Question Papers - IIT JEE/MathsQP2005

# Two Mark Questions[edit]

**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

**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 from the point (2,1,–1).

**Q5** A function *f*(x) is such that **| f (x_{1})-f (x_{2}) | < (x_{1}-x_{2})^{2}** for all real x

_{1}and x

_{2}. 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 ** f (n)** (n > 1) and the number of runs scored in the k

^{th}match is given by

**(1 ≤ k ≤ n). Find the value of n.**

*g*(k)