IGNOU MTM 10 SOLVED ASSIGNMENT

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IGNOU MTM 10 SOLVED ASSIGNMENT

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IGNOU MTM 10 SOLVED ASSIGNMENT

~~Rs. 90~~
Rs. 15

Last Date of Submission of IGNOU MTM-010 (MTM) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Semester Wise
January 2025 Session: 30th March, 2025 (for June 2025 Term End Exam).
July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).

Title Name	IGNOU MTM 10 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	MASTER DEGREE PROGRAMMES
Course Code	MTM
Course Name	Master of Arts in Tourism Management
Subject Code	MTM 10
Subject Name	Tourism Impacts
Year	2025
Session
Language	English Medium
Assignment Code	MTM-010/Assignmentt-1//2025
Product Description	Assignment of MTM (Master of Arts in Tourism Management) 2025. Latest MTM 010 2025 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU MTM-010 (MTM) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2025 (for June 2025 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).

~~Rs. 90~~
Rs. 15

Questions Included in this Help Book

Ques 1.

The equation $x^3-x-1=0$ has a positive root in the interval ]1, 2[. Write a fixed point iteration method and show that it converges. Starting with initial approximation x = 1.5 find the root of the equation correct to three decimal places.

Ques 2.

Find an appropriate root of $x^3+2x^2-5=0\text{in}[1,2]$ with 10^-5 accuracy by

i) Newton Raphson Method

ii) Secant Method

What conclusions can you draw from here about the two methods?

Ques 3.

Using Maclaurin’s expansion for sin x , find the approximate value of 4 sin $\frac{\pi}{4}$ with the error bound 5 10 ^-5

Ques 4.

Find an approximate value of the positive real root of xe ^x= 1 using graphical method. Use this value to find the positive real root of xe^x = 1 correct to three decimal places by fixed point iteration method.

Ques 5.

Using x _o= 0 find an approximation to one of the zeros of x³-4x+1=0 by using Birge-Vieta Method. Perform two iterations.

Ques 6.

Solve the system of equations

$2x_1+3x_2+4x_3+x_4=3$

$x_1+2x_2+x_4=2$

$2x_1+3x_2+x_3-x_4=1$

$x_1-2x_2-x_3+4x_4=5$

using Gauss elimination method with pivoting.

Ques 7.

Find the inverse of the matrix $\begin{bmatrix}3&1&2\\-2&3&-5\\1&2&4\end{bmatrix}$ using Gauss Jordan Method.

Ques 8.

Solve the following linear system Ax = b of equations with partial pivoting

$x_1-x_2+3x_3=3$

$2x_1+x_2+4x_3=7$

$3x_1+5x_2-2x_3=6.$

Store the multipliers and also write the pivoting vectors.

Ques 9.

Solve the system of equations

$8x_1-x_2+2x_3=4$

$-3x_1+11x_2-x_3+3x_4=23$

$-x_2+10x_3-x_4=-13$

$-2x_1+x_2-x_3+8x_4=13$

$\text{with}\mathbf{x}^{(0)}=\begin{bmatrix}0&0&0&0\end{bmatrix}^T.$ by using the Gauss Jacboi and Gauss Seidel method. The exact solution of the system is $\mathbf{x}=\begin{bmatrix}1&2&-1&1\end{bmatrix}^T.$ Perform the required number of iterations so that the same accuracy is obtained by both the methods. What conclusions can you draw from the results obtained?

Ques 10.

Starting with $\mathbf{x}^{(0)}=\begin{bmatrix}1&1&1&1\end{bmatrix}^T,$ find the dominant eigenvalue and corresponding eigenvector for the matrix $A=\begin{bmatrix}4&-1&1\\4&-8&1\\-2&1&5\end{bmatrix}$ using the power method.

Ques 11.

The solution of the system of equations $\begin{pmatrix}1&2\\2&1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}4\\-2\end{pmatrix}$ is attempted by the Gauss

Jacobi and Gauss Seidel iteration schemes. Set up the two schemes in matrix form. Will the iteration schemes converge? Justify your answer.

Ques 12.

Obtain an approximate value of $\int_0^1\frac{dx}{1+x^2}$ using composite Simpson’s rule with h = 0.25 and

h = 0.125 Find also the improved value using Romberg integration.

Ques 13.

Find the minimum number of intervals required to evaluate $\int_0^1 e^{-x^2}\,dx$ with an accuracy of

$\frac{1}{2}\times 10^{-4},$ by using the Trapezoidal rule.

Ques 14.

From the following table, find the number of students who obtained less than 45 marks.

Marks	No. of Students
30-40	31
40-50	42
50-60	51
60-70	35
70-80	31

Ques 15.

Calculate the third-degree Taylor polynomial about $x_0=0\text{for}f(x)=(1+x)^{1/2}.$

Ques 16.

Use the polynomial in part (a) to approximate $\sqrt[]{1.1}$ and find a bound for the error involved.

Ques 17.

Use the polynomial in part (a) to approximate $\int_0^{0.1}(1+x)^{1/2}\,dx.$

Ques 18.

Using sin( 0.1) = 0.09983 and sin( 0.2) = 0.19867 , find an approximate value of sin( 0.15) by using Lagrange interpolation. Obtain a bound on the truncation error.

Ques 19.

Consider the following data

x	1.0	1.3	1.6	1.9	2.2
f(x	0.7651977	0.6200860	0.4554022	0.2818186	0.110362

Use Stirling’s formula to approximate $f(1.5)\text{with}x_0=1.6.$

Ques 20.

Solve the $\text{I.V.P.,}y'=-y+t+1,\quad(0\le t\le 1),\quad y(0)=1$ using R-K method of 0(h⁴ ) with

h = 0.1 and obtain the value of y(0.2) . Also find the error at t = 0.2 , if the exact solution is $y(t)=t+e^{-t}.$

Ques 21.

The position f(x) of a particle moving in a line at various times xk is given in the following

table. Estimate the velocity and acceleration of the particle at x =1.2

Ques 22.

A solid of revolution is formed by rotating about the x-axis the area bounded between $x=0,x=1\text{and}$ the curve given by the table

x	0	0.25	0.5	0.75	1.0
f(x)	1.0	0.9896	0.9587	0.9089	0.8415

Find the volume of the solid so formed using

i) Trapezodial rule ii) Simpson’s rule

Ques 23.

Take 10 figure logarithm to base 10 from $x=300\text{to}x=310$ by unit increment. Calculate the first derivative of log

$^{10}\log x\text{when}x=310.$

Ques 24.

For the table of values of x f(x) = xe ^xgiven by

x	1.8	1.9	2.0	2.1	2.2
f(x	10.8894	12.7032	14.7781	17.1489	19.8550

Find f"(2.0) using the central difference formula of 0(h²) for h = 0.1 and h = 0.2 . Calculate T.E. and actual error

Calculate T.E. and actual error

Ques 25.

Suppose n f denotes the value of $f(t)\text{at}t=t_n.\text{If}f(t)=t^3,$ then find the value of $\frac{(f_{n+1}-2f_n+f_{n-1})}{h^2}.$

Ques 26.

Use Runge-Kutta method of order four to solve $y'=x+y.\text{Start with}x=1,y=0$ carry to x =1.5 with h = 0.1.

Ques 27.

Find the solution of the difference equation $y_{k+2}-4y_{k+1}+4y_k=0,\quad k=0,1,\dots\text{Also find}$ the particular solution when $y_0=1\text{and}y_1=6.$

Ques 28.

The iteration method

$x_{n+1}=\frac{1}{8}\left[6x_n+\frac{3N}{x_n}-\frac{x_n^3}{N}\right],\quad n=0,1,2$

where N is positive constant, converges to some quantity. Determine this quantity. Also find the rate of convergence of this method.

Ques 29.

Determine the spacing h in a table of equally spaced values for the function

$f(x)=(2+x)^4,\quad 1\le x\le 2,\quad|\text{error}|\le 10^{-6}.$ so that the quadratic interpolation in this table satisfies

Ques 30.

Determine a unique polynomial f(x) of degree $\leq$ 3 such that

$f(x_0)=1,f'(x_0)=2,f(x_1)=2,f'(x_1)=3\text{where}x_1-x_0=h.$

Ques 31.

Ques 32.

Find an appropriate root of $x^3+2x^2-5=0\text{in}[1,2]$ with 10^-5 accuracy by

i) Newton Raphson Method

ii) Secant Method

What conclusions can you draw from here about the two methods?

Ques 33.

Using Maclaurin’s expansion for sin x , find the approximate value of 4 sin $\frac{\pi}{4}$ with the error bound 5 10 ^-5

Ques 34.

Ques 35.

Using x _o= 0 find an approximation to one of the zeros of x³-4x+1=0 by using Birge-Vieta Method. Perform two iterations.

Ques 36.

Solve the system of equations

$2x_1+3x_2+4x_3+x_4=3$

$x_1+2x_2+x_4=2$

$2x_1+3x_2+x_3-x_4=1$

$x_1-2x_2-x_3+4x_4=5$

using Gauss elimination method with pivoting.

Ques 37.

Find the inverse of the matrix $\begin{bmatrix}3&1&2\\-2&3&-5\\1&2&4\end{bmatrix}$ using Gauss Jordan Method.

Ques 38.

Solve the following linear system Ax = b of equations with partial pivoting

$x_1-x_2+3x_3=3$

$2x_1+x_2+4x_3=7$

$3x_1+5x_2-2x_3=6.$

Store the multipliers and also write the pivoting vectors.

Ques 39.

Solve the system of equations

$8x_1-x_2+2x_3=4$

$-3x_1+11x_2-x_3+3x_4=23$

$-x_2+10x_3-x_4=-13$

$-2x_1+x_2-x_3+8x_4=13$

Ques 40.

Ques 41.

The solution of the system of equations $\begin{pmatrix}1&2\\2&1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}4\\-2\end{pmatrix}$ is attempted by the Gauss

Jacobi and Gauss Seidel iteration schemes. Set up the two schemes in matrix form. Will the iteration schemes converge? Justify your answer.

Ques 42.

Obtain an approximate value of $\int_0^1\frac{dx}{1+x^2}$ using composite Simpson’s rule with h = 0.25 and

h = 0.125 Find also the improved value using Romberg integration.

Ques 43.

Find the minimum number of intervals required to evaluate $\int_0^1 e^{-x^2}\,dx$ with an accuracy of

$\frac{1}{2}\times 10^{-4},$ by using the Trapezoidal rule.

Ques 44.

From the following table, find the number of students who obtained less than 45 marks.

Marks	No. of Students
30-40	31
40-50	42
50-60	51
60-70	35
70-80	31

Ques 45.

Calculate the third-degree Taylor polynomial about $x_0=0\text{for}f(x)=(1+x)^{1/2}.$

Ques 46.

Use the polynomial in part (a) to approximate $\sqrt[]{1.1}$ and find a bound for the error involved.

Ques 47.

Use the polynomial in part (a) to approximate $\int_0^{0.1}(1+x)^{1/2}\,dx.$

Ques 48.

Using sin( 0.1) = 0.09983 and sin( 0.2) = 0.19867 , find an approximate value of sin( 0.15) by using Lagrange interpolation. Obtain a bound on the truncation error.

Ques 49.

Consider the following data

x	1.0	1.3	1.6	1.9	2.2
f(x	0.7651977	0.6200860	0.4554022	0.2818186	0.110362

Use Stirling’s formula to approximate $f(1.5)\text{with}x_0=1.6.$

Ques 50.

Solve the $\text{I.V.P.,}y'=-y+t+1,\quad(0\le t\le 1),\quad y(0)=1$ using R-K method of 0(h⁴ ) with

h = 0.1 and obtain the value of y(0.2) . Also find the error at t = 0.2 , if the exact solution is $y(t)=t+e^{-t}.$

Ques 51.

The position f(x) of a particle moving in a line at various times xk is given in the following

table. Estimate the velocity and acceleration of the particle at x =1.2

Ques 52.

A solid of revolution is formed by rotating about the x-axis the area bounded between $x=0,x=1\text{and}$ the curve given by the table

x	0	0.25	0.5	0.75	1.0
f(x)	1.0	0.9896	0.9587	0.9089	0.8415

Find the volume of the solid so formed using

i) Trapezodial rule ii) Simpson’s rule

Ques 53.

Take 10 figure logarithm to base 10 from $x=300\text{to}x=310$ by unit increment. Calculate the first derivative of log

$^{10}\log x\text{when}x=310.$

Ques 54.

For the table of values of x f(x) = xe ^xgiven by

x	1.8	1.9	2.0	2.1	2.2
f(x	10.8894	12.7032	14.7781	17.1489	19.8550

Find f"(2.0) using the central difference formula of 0(h²) for h = 0.1 and h = 0.2 . Calculate T.E. and actual error

Calculate T.E. and actual error

Ques 55.

Suppose n f denotes the value of $f(t)\text{at}t=t_n.\text{If}f(t)=t^3,$ then find the value of $\frac{(f_{n+1}-2f_n+f_{n-1})}{h^2}.$

Ques 56.

Use Runge-Kutta method of order four to solve $y'=x+y.\text{Start with}x=1,y=0$ carry to x =1.5 with h = 0.1.

Ques 57.

Find the solution of the difference equation $y_{k+2}-4y_{k+1}+4y_k=0,\quad k=0,1,\dots\text{Also find}$ the particular solution when $y_0=1\text{and}y_1=6.$

Ques 58.

The iteration method

$x_{n+1}=\frac{1}{8}\left[6x_n+\frac{3N}{x_n}-\frac{x_n^3}{N}\right],\quad n=0,1,2$

where N is positive constant, converges to some quantity. Determine this quantity. Also find the rate of convergence of this method.

Ques 59.

Determine the spacing h in a table of equally spaced values for the function

$f(x)=(2+x)^4,\quad 1\le x\le 2,\quad|\text{error}|\le 10^{-6}.$ so that the quadratic interpolation in this table satisfies

Ques 60.

Determine a unique polynomial f(x) of degree $\leq$ 3 such that

$f(x_0)=1,f'(x_0)=2,f(x_1)=2,f'(x_1)=3\text{where}x_1-x_0=h.$

Ques 61.

Ques 62.

Find an appropriate root of $x^3+2x^2-5=0\text{in}[1,2]$ with 10^-5 accuracy by

i) Newton Raphson Method

ii) Secant Method

What conclusions can you draw from here about the two methods?

Ques 63.

Using Maclaurin’s expansion for sin x , find the approximate value of 4 sin $\frac{\pi}{4}$ with the error bound 5 10 ^-5

Ques 64.

Ques 65.

Using x _o= 0 find an approximation to one of the zeros of x³-4x+1=0 by using Birge-Vieta Method. Perform two iterations.

Ques 66.

Solve the system of equations

$2x_1+3x_2+4x_3+x_4=3$

$x_1+2x_2+x_4=2$

$2x_1+3x_2+x_3-x_4=1$

$x_1-2x_2-x_3+4x_4=5$

using Gauss elimination method with pivoting.

Ques 67.

Find the inverse of the matrix $\begin{bmatrix}3&1&2\\-2&3&-5\\1&2&4\end{bmatrix}$ using Gauss Jordan Method.

Ques 68.

Solve the following linear system Ax = b of equations with partial pivoting

$x_1-x_2+3x_3=3$

$2x_1+x_2+4x_3=7$

$3x_1+5x_2-2x_3=6.$

Store the multipliers and also write the pivoting vectors.

Ques 69.

Solve the system of equations

$8x_1-x_2+2x_3=4$

$-3x_1+11x_2-x_3+3x_4=23$

$-x_2+10x_3-x_4=-13$

$-2x_1+x_2-x_3+8x_4=13$

Ques 70.

Ques 71.

The solution of the system of equations $\begin{pmatrix}1&2\\2&1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}4\\-2\end{pmatrix}$ is attempted by the Gauss

Jacobi and Gauss Seidel iteration schemes. Set up the two schemes in matrix form. Will the iteration schemes converge? Justify your answer.

Ques 72.

Obtain an approximate value of $\int_0^1\frac{dx}{1+x^2}$ using composite Simpson’s rule with h = 0.25 and

h = 0.125 Find also the improved value using Romberg integration.

Ques 73.

Find the minimum number of intervals required to evaluate $\int_0^1 e^{-x^2}\,dx$ with an accuracy of

$\frac{1}{2}\times 10^{-4},$ by using the Trapezoidal rule.

Ques 74.

From the following table, find the number of students who obtained less than 45 marks.

Marks	No. of Students
30-40	31
40-50	42
50-60	51
60-70	35
70-80	31

Ques 75.

Calculate the third-degree Taylor polynomial about $x_0=0\text{for}f(x)=(1+x)^{1/2}.$

Ques 76.

Use the polynomial in part (a) to approximate $\sqrt[]{1.1}$ and find a bound for the error involved.

Ques 77.

Use the polynomial in part (a) to approximate $\int_0^{0.1}(1+x)^{1/2}\,dx.$

Ques 78.

Using sin( 0.1) = 0.09983 and sin( 0.2) = 0.19867 , find an approximate value of sin( 0.15) by using Lagrange interpolation. Obtain a bound on the truncation error.

Ques 79.

Consider the following data

x	1.0	1.3	1.6	1.9	2.2
f(x	0.7651977	0.6200860	0.4554022	0.2818186	0.110362

Use Stirling’s formula to approximate $f(1.5)\text{with}x_0=1.6.$

Ques 80.

Solve the $\text{I.V.P.,}y'=-y+t+1,\quad(0\le t\le 1),\quad y(0)=1$ using R-K method of 0(h⁴ ) with

h = 0.1 and obtain the value of y(0.2) . Also find the error at t = 0.2 , if the exact solution is $y(t)=t+e^{-t}.$

Ques 81.

The position f(x) of a particle moving in a line at various times xk is given in the following

table. Estimate the velocity and acceleration of the particle at x =1.2

Ques 82.

A solid of revolution is formed by rotating about the x-axis the area bounded between $x=0,x=1\text{and}$ the curve given by the table

x	0	0.25	0.5	0.75	1.0
f(x)	1.0	0.9896	0.9587	0.9089	0.8415

Find the volume of the solid so formed using

i) Trapezodial rule ii) Simpson’s rule

Ques 83.

Take 10 figure logarithm to base 10 from $x=300\text{to}x=310$ by unit increment. Calculate the first derivative of log

$^{10}\log x\text{when}x=310.$

Ques 84.

For the table of values of x f(x) = xe ^xgiven by

x	1.8	1.9	2.0	2.1	2.2
f(x	10.8894	12.7032	14.7781	17.1489	19.8550

Find f"(2.0) using the central difference formula of 0(h²) for h = 0.1 and h = 0.2 . Calculate T.E. and actual error

Calculate T.E. and actual error

Ques 85.

Suppose n f denotes the value of $f(t)\text{at}t=t_n.\text{If}f(t)=t^3,$ then find the value of $\frac{(f_{n+1}-2f_n+f_{n-1})}{h^2}.$

Ques 86.

Use Runge-Kutta method of order four to solve $y'=x+y.\text{Start with}x=1,y=0$ carry to x =1.5 with h = 0.1.

Ques 87.

Find the solution of the difference equation $y_{k+2}-4y_{k+1}+4y_k=0,\quad k=0,1,\dots\text{Also find}$ the particular solution when $y_0=1\text{and}y_1=6.$

Ques 88.

The iteration method

$x_{n+1}=\frac{1}{8}\left[6x_n+\frac{3N}{x_n}-\frac{x_n^3}{N}\right],\quad n=0,1,2$

where N is positive constant, converges to some quantity. Determine this quantity. Also find the rate of convergence of this method.

Ques 89.

Determine the spacing h in a table of equally spaced values for the function

$f(x)=(2+x)^4,\quad 1\le x\le 2,\quad|\text{error}|\le 10^{-6}.$ so that the quadratic interpolation in this table satisfies

Ques 90.

Determine a unique polynomial f(x) of degree $\leq$ 3 such that

$f(x_0)=1,f'(x_0)=2,f(x_1)=2,f'(x_1)=3\text{where}x_1-x_0=h.$

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Course Name	Master of Arts in Tourism Management
Course Code	MTM
Programm	MASTER DEGREE PROGRAMMES Courses
Language	English

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