State whether the following statements are True or False. Give reason in support of your answer:

(a) Intersection of set of rational and irrational numbers is non-empty.

(b) The function |x-2| is differentiable everywhere on the real line.

(c) The trace of the matrix is 130.

 (d) Six persons can sit on six chairs placed around a circular table in 120 numbers of ways.

(e) The range of the data shown in the 60-70frequency distribution is 70.

An institution made a policy for delay of payment beyond a certain date to be paid by its customers. Penalty as per policy are as follows: Rs 50 for the first day, Rs 100 for the second day, Rs 150 for the third day, and so on. If a customer makes the payment on a delay of 31 days then how much he/she has to pay as penalty charges.

If in a hall there are 10 randomly selected students then how many numbers of ways are there such that all of them have different birthday. Assume that all of them have their birth day in non-leap years

Comment on the height of a bar in a bar diagram and height of a bin in a histogram. Are two heights have the same meaning? Explain it with the help of an example

Compare the following two ratio scale data sets using suitable graphical analysis tool: Score before training: 12, 17, 15, 23, 27, 21, 24, 19, 20, 23, 16 Score after training: 16, 22, 20, 24, 30, 20, 30, 17, 27, 31, 19 Also interpret the finding on the basis of the graph.

If A = {3, 6, 9, 12, ...} and B = {15, 30, 45, ...} then verify whether two sets A and B are equivalent or not.

Evaluate the following integrals: