In a bag containing X red stones and Y blue stones, `X,Y >2` , you remove them one by one without replacement. What is the chance that the second last stone removed is red?

Use the binomial expansion to estimate `1.1^9` correct to three decimal places.

A straight line has general equation of `r=((1),(0),(-1))+t((1),(2),(2))`

Find both coordinates on the line which lie exactly 2 units either side of the point (1,0,-1).

An object in the 2D plane can only jump one unit at a time, either to the left, right, up or down.

If it starts at the origin and takes 12 steps, how many different points could be its final destination?

The acute angle `theta` is increased at a constant rate of `x ` radians per second, causing A , the area of the triangle enclosed within the bold lines, to change. Let `R_(0)` represent the initial rate of change of A. Let `theta_max` represent the value of `theta` when A is maximized. Find `R_0*theta_max`

At a Chinese restaurant, there are 18 individual chopsticks: 6 red chopsticks, 10 white chopsticks, and 2 golden chopsticks. After the chopsticks are washed and placed randomly into a row, the kitchen workers are surprised to see that all of the chopsticks are already in a matching pair! What is the probability of such an occurrence?

In photography, the distance `d` of an object from a lens, the distance `D` of the image from the lens and the focal length of the lens `f` are related through the following formula: `1/d+1/D=1/f` .

For each lens, `f` is a constant whereas `d` and `D` are variables, in a particular instant, a racing car is moving away from the lens at a rate of `250 km h^(-1)` , in which direction and how fast, in `km h^(-1)` , will the image be moving?