Solve your IGNOU Doubts

Question:

a) If p^th term of an A.P is q and q^th term of the A.P. is p, find its r^th term.

b) Find the sum of all the integers between 100 and 1000 that are divisible by 9.

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Question:

Verify that 133 divides 11ⁿ⁺² + 12²ⁿ⁺¹ for every natural number n.

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Question:

Create a worksheet for yearly income, tax, expenses and saving as given below. Type in labels, year, income, expenses and saving .You are required to calculate tax(20% of the yearly income), expense(30% of the yearly income) , saving( yearly income - ( tax + expense)) and next year’s income which is 10% more than the previous year. Also calculate total income, total taxes, total expenses and total savings. Yearly Income ,Tax, Expenses and Saving Table Amounts are shown in Rupees

	A	B	C	D	E
1	Year	Income	Tax	Expenses	Saving
2	2014	1,0000.00
	2015
	2016
	2017
	2018
	2019
		Total Income	Total Tax	Tatal Expense	Total Saving

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Question:

Design a flyer for wedding function. Use different styles, sizes, fonts, colours and effects.

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Question:

$If A = \begin{bmatrix} 3 &-1 \\ 2 & 1 \end{bmatrix}$

Show that A² - 4 A + 5 I₂ = 0. Also, find A⁴ .

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Question:

Create multilevel month and week wise schedule for performing different academic tasks. Months should be numbered as A1…….to A12. Each month should be further broken into weeks numbered as W1…W4.For each week , academic activities such as attending counseling sessions,watching video lectures, etc., should be in numerical order(1,2,3…)

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Question:

Create a Power Point Presentation on the important features of Linux OS (minimum 10 slides)

(i) All slides should follow the common design format

(ii) Add a video to at least one slide which can be run on full screen option

(iii) All the slides should have timer based transition.

(iv) All the slides should have speaker notes. (v) Each slide should have one image related to Linux operating system.

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Question:

Perform the following tasks in Linux

(i) Display the first 15 lines and last 20 lines of a text file (you need to create a text file)

(ii) Identify all files in your home directory which a group has written permission on it

(iii) What will be the output of the following commands:

ls | head – 5 | tail -1 > myfile cat myfile
ls –l / etc | tail – n + 2 | sort

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Question:

(a) Run the following (Linux commands and write the output)

- who am i

- pwd

- grep

- chmod

- find

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Question:

Obtain the curl of the following vector field:

$\vec{F}=2p^{2\hat{e}_{p}}-z cos\phi \hat{e}_{\phi }+3zsin \phi \hat{e}_{z}$

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Question:

Obtain the divergence of the following vector field:

$\vec{A}=(\hat{e_{r}}+r\; cos\; \theta \hat{e_{\theta }}+r\hat{e_{\phi }})$

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Question:

Show that for any scalar field $\phi$

$\vec{\triangledown } \times (\phi \vec{\triangledown }\phi )=0$

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Question:

Determine the work done by a force $\hat{F}= xy\hat{i}+yz\hat{j}+xz\hat{K}$ in taking a particle along the path defined by the equation $\vec{r}(t)= t\hat{i}+2t^{2}\hat{j}+t^{3}\hat{K,}0 \leq t\leq1$ from t = 0 to t = 2. Is the force conservative?

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Question:

Determine the value of n for which the vector field $\vec{F}= r^{n}\vec{r}$ is solenoidal, where $\vec{r}= x\hat{i}+y \hat{j}+ z\hat{k}$

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Question:

Using Gauss’ theorem calculate the flux of the vector field $\vec{A}=x^{3}\hat{i}+x^{2}z\hat{j}+yz\hat{K}$ through the surface of a cube of side 2 units.

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Question:

Determine the direction of maximum increase of the scalar field

$f ( x ,y ,z )= xe^{y}+z^{2}$ at the poin $0 (1 ,ln2,3 )$

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Question:

Obtain the unit tangent vector for a vector function

$\vec{a}(t)=( 2t+5 )\hat{i}+ ( t^{2}+1 )\hat{j}+(1-t^{3} )\hat{k}at \: \: t=1 .$

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Question:

Using Green’s theorem evaluate the integral: $\int_{C}^{}\left ( y^{3}dx+3x^{3} dx\right )$ where C is the contour along the circle x² + y² = 1 taken counter clockwise.