MST-001 Solved Assignment 2021

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MST-001 Solved Assignment 2021 

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MST-001 Solved Assignment 2021 

MST-001 Assignment Question Paper

(Foundations in Mathematics and Statistics) 


MST-001: Foundation in Mathematics and Statistics

All questions are compulsory. Answer in your own words.

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

  1. Intersection of set of rational and irrational numbers is non-empty.
  2. The function is \( \left|x-2\right| \) differentiable everywhere on the real line.
  3. The trace of the matrix \( \begin{pmatrix}3&5&8\\ -1&7&9\\ 0&0&5\end{pmatrix}\) is 130.
  4. Six persons can sit on six chairs placed around a circular table in 120 numbers of ways.
  5. The range of the data shown in the following frequency distribution is 70.

Classes

0-10

10-20

20-30

30-40

40-50

50-60

60-70

Frequencies

2

7

3

8

4

1

0

2. (a)  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.     

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

(c) Find the sum – 7 + (– 12) + (– 17) + … + (– 507).                                                                            

3. (a) Express 5.10.15.20.25.30.35 in terms of factorial.

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

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

4. Discuss the continuity and differentiability of the following function at x = 5.

\(f\left(x\right)=\left\{\begin{pmatrix}\left|x-5\right|&x\ne 5\\ 0&x=5\end{pmatrix}\right\}\)

5. Evaluate the following integrals:

(a) \(\int \:x^5\cdot e^{x^3}dx\) 

(b) \(\int _{-4}^3\:\left|x^2+x-6\right|dx\)

6.The cost of 2 pens, 3 note-books, and 4 books is Rs 260. The cost of 4 pens, 5 note-books, and 3 books is Rs 290. The cost of 3 pens, 2 note-books, and 5 books is Rs 320. Find the cost of 3 pens, 2 note-books and 4 books. You are bound to use the matrix techniques to solve the given equations.

7 (a) If \(A=\begin{pmatrix}3&7\\ 2&5\end{pmatrix}\:and\:B=\begin{pmatrix}6&8\\ 7&0\end{pmatrix}\:then\:verify\:that\:\left(AB\right)^{-1}=B^{-1}\cdot A^{-1}.\)

(b) Distinguish characteristic features of each of the four measurement scales: (I) Nominal (II) Ordinal (III) Interval, and (IV) Ratio Scale. Name the measurement scale for each of the following variable.

  1. Waiting time for a bus at a particular bus stop in a certain city.
  2. Number of pages in a book.
  3. The temperature in degree Celsius.
  4. Classification of cancer patients according to their severity of diseases.
  5. Monthly income of the family
  6. Saving (Income in that particular month − expenditure in the same month) of the family. Keep in mind that expenditure may be more than income in that particular month of some family(ies)
  7. The temperature of water by touch: cold, lukewarm and hot
  8. Height of students of a class
  9. State of residence of each student of PGDAST programme
  10. Balance of Smart card of Delhi Metro hold of different passengers                              

8 (a) Compare the following two ratio scale data sets using a 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.

(b) 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.

 

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MST-001 Solved Assignment 2021

MST-001 Solved Assignment 2021

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