IGNOU MST 11 SOLVED ASSIGNMENT

Included:

MST 011 (January 2025 - July 2025) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-011: Real Analysis, Calculus and Geometry

Course Code: MST-011

Assignment Code: MST-011/TMA/2025

Maximum Marks: 50

Note: All questions are compulsory. Answer in your own words.

1. Solve the following problems

(a) If f is a function from set X to a set Y then is it possible

(b) In R we have a built-in data set “trees”. A screenshot of the last four rows together with the R code to obtain it is given as follows. To get more detail about this data set you can run ?trees command on R console.

Note that all the three variables of this data set are numeric. So, assuming each row of this data set is a point in 3-dimension. Find the distances between the points corresponding to the 28th and the 32st rows using the Manhattan and Chebyshev distance formula

(c) Find the equation of a line passing through points A(0, 0, 1) and B(1, 1, 0). Also, find the coordinates of a point on this line which is at a distance of 10 units from point A opposite to the side of point B.

2. be a function defined by Show that f is Riemann integrable using both definitions. Also, verify that the results of both definition match.

3. (a) Evaluate the integral

by considering D as a region of Type I and then as a region of Type II.

(b) Evaluate the integrausing beta and gamma functions.

MST 011 (January 2026 - July 2026) - ENGLISH

**MST-011: Real Analysis, Calculus and Geometry**

**Course Code: MST-011**
**Assignment Code: MST-011/TMA/2026**
**Maximum Marks: 50**

**Note: All questions are compulsory. Answer in your own words.**

**1. Solve the following problems.**

(a) If f is a function from set X to a set Y then is it possible , ? where and

(b) In R we have a built-in data set "trees". A screenshot of the last four rows together with the R code to obtain it is given as follows. To get more detail about this data set you can run ?trees command on R console.

```
> tail(trees, 4)
Girth Height Volume
28 17.9 80 58.3
29 18.0 80 51.5
30 18.0 80 51.0
31 20.6 87 77.0
```

Note that all the three variables of this data set are numeric. So, assuming each row of this data set is a point in 3-dimension. Find the distances between the points corresponding to the and the rows using the Manhattan and Chebyshev distance formula.

(c) Find the equation of a line passing through points A(0, 1, 1) and B(1, 1, 0). Also, find the coordinates of a point on this line which is at a distance of 10 units from point A opposite to the side of point B.

**(2 + 3 + 5)**

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**2.** If be a function defined by , . Show that f is Riemann integrable using both definitions. Also, verify that the results of both definition match. **(20)**

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**3. (a)** Evaluate the integral , where , by considering D as a region of Type I and then as a region of Type II.

**(b)** Evaluate the integral using beta and gamma functions. **(14 + 6)**

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