Write whether the following data are discrete or continuous. Give reason in support of your answer.

i) Number of children in a family in a colony of 100 families.

Number of pages in each of the 50 books having some mistake.

Height of students of IGNOU who enrolled in 2021.

iv) Waiting time of metro when a person reaches metro station.

v) Monthly income of the family.

Write flow charts of Cramer rule and matrix method.

Find values of x, y and z given that

You are bound to use the matrix techniques to solve the given equations.

Evaluate the following integrals:

i) 

ii) 

Discuss the continuity and differentiability of the following function at x = 2/3:

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 birthday in non-leap years.

How many different signals are possible with 5 blue, 4 red, 3 white and 2 green flags by using all at a time in a queue?

Express 700.1400.2100.2800.3500.42000 in terms of factorial.

How many words each of three vowels and two consonants can be formed from the letters of the words INVOLUTE?

Set having values  is countable.

A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days he will take to finish his job?

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

(a) Between any two different rational numbers there is another rational number.

(b)

(c) 210 is 51^st term of the sequence 10, 15, 20, 25, ...

(e) The range of the data shown in the following frequency distribution is 350.

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