Solve your IGNOU Doubts

Question:

How will you define a complete bipartite graph? Give an example of it. Is every complete bipartite graph complete? Justify.

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Question:

Using combinatorial arguments, prove that $(a+b+c)^{n}=\Sigma_{r+s+t=n}\left(\!\!\!\begin{array}{c}{{n}}\\ {{r\,,\,\,s,\,\,t}}\end{array}\!\!\right)a^{r}b^{s}c^{t}.$ What is the coefficient of $x^{50}y^{12}z^{38}\stackrel{.}{\mathrm{in}}(x-y+2z)^{100}?$

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Using the method of generating functions, solve the recurrence relation $a_{n}=2a_{n-1}+2^{n},~~n\geq1~,a_{0}=1.$

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Question:

Check whether the graphs in Fig. 2 are planar or not. If yes, give their plane drawing, otherwise give a $K_{3,3}$ or $K_{5}$ subdivision. Image ignouassignments-ignouacademy-com--p-doubts-70410

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Check wether the graph in Fig. 1 is Eulerian or not. Is it regular? Justify your answer. Image ignouassignments-ignouacademy-com--p-ignou-28036

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Question:

What is the probability that an integer between 1 and 9,999 has exactly one 8 and one 9 ?Justify your answer.

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Question:

Find the number of nonnegative integer solutions of the equation $x_1+x_2+x_3+x_4+x_5=12$ . And how many solutions in positive integers will it have? Justify.

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Question:

A Cantabil showroom offers 7 styles of pants. For each style, there are 10 different possible waist sizes, 6 pants lengths and 4 color choices. How many different types of pants could the showroom have?

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Question:

Obtain the CNF of the Boolean expression $X(x_1,x_2,x_3)=x_2\,\vee(x_1\,\wedge x^{'}_3).$

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Question:

Using the principle of mathematical induction show that the sum of the cubes of three successive positive integers is divisible by 9.

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Question:

Find out which of the following are propositions and which are not. Give reasons for your answers.

(i) There are a total of 8 questions in this assignment.
(ii) Wow, it’s a beautiful evening!
(iii) I am not sure whether I can run as fast as you can.
(iv) The set {2, −1, 2, −1, 2, −1, … } is unbounded.
(v) The set ℕ of natural numbers is equivalent to the set ℤ of integers.
(vi) Rajasthan is the largest state in area among the Indian states and union territories.

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Question:

Let $p,q$ and $r$ be the statements as defined below:

$p$ ∶ The Course is enjoyable.
q ∶ The presentation is stimulating.
r ∶ The material is significant.

Write each of the following in symbolic form.

(i) The material is significant and the presentation is stimulating, but the course is not enjoyable.
(ii) It is not the case that both the course is enjoyable and, at the same time,the presentation is not stimulating.

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Question:

For any propositions See Answer →

Question:

Give a direct proof of the following statement: “Every skew-symmetric matrix of odd order is singular”.

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Question:

Prove by contradiction that the inverse of a square matrix, if exists, is unique.

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Question:

.Solve the recurrence relation $a_{n+1}=a_n+n.2^n,(n\geq0),a_0=1,$ using the method of telescopic sums.

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Question:

Construct the logic circuit of the Boolean expression $(x^{'}_1\vee \,x^{'}_2\,\wedge x_3)\vee(x_2\,\wedge\,x^{'}_3 ),$ where $x_1,x_2,x_3$ are the inputs in that circuitry.