Solve your IGNOU Doubts

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.

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Question:

Look at the following pattern: Image ignouassignments-ignouacademy-com--p-ignou-24907

(i) How many ′ + ′ signs should be there in the box?

(ii) What are the smallest and largest integers in the box?

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Question:

Solve the recurrence relation $a_n=2a_{n-1}+n(n-1),n\geq 1,a_0=1,$ using the generating function technique.

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Question:

Let $a_n$ be the number of See Answer →

Question:

Find the number of integer solutions of the equation $x_1+x_2+x_3+x_4=0,x_1 \geq -4,\forall \,i$ using the generating function technique.

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Question:

State whether the following statements are true or false. Justify your answer with a short explanation or a counter-example. (2 × 10 = 20)
(i) The contra- positive of the statement $"x^2+y^2=0\Rightarrow x=0$ and $y=o"$ is $"x\neq 0$ and $"y\neq 0\Rightarrow x^2+y^2\neq 0"."$
(ii) $a^n=\frac{1}{9}[2^{n+1}+(-1)^n]^2$ is the solution of the recurrence relation
$\sqrt{a_n}=\sqrt{a_{n-1}}+2\sqrt{a_{n-2}},(n\geq 1),a_0=a_1=1.$
(iii) The number of integers between 1 and 360 which are relatively prime to 360 are
96.[ Note that 1 is relatively prime to every positive integer.]
(iv) The coefficient of $x^6y^5z^9$ in $(x+y+z)^{20}$ is $C(20,6).C(20,5).C(20,9).$
(v) If a graph has 6 vertices and 10 edges, then it can’t be regular.
(vi) Peterson graph is bipartite.
(vii) Every edge of a Tree is a bridge.
(viii) The independence number of $C_5,i.e.,\alpha (C_5)$ is $2.$
(ix) The DNF of the expression $p(x,y,z)=(x\wedge z)^{'}$ is $(x\vee y\,\vee z^{'})\vee(x\,\vee\,y^{'}\vee\,z^{'}).$
(x) The number 8 has atmost one self-conjugate partition.

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Question:

a) A marketing manager has 5 salespersons and 5 sales districts. Considering the capabilities of the salespersons and the nature of the districts, the marketing manager estimates the sales per month (in thousand ) for each salesperson in each distinct as follows

Salespersons

	Districts
	1	2	3	4	5
A	32	38	40	28	40
B	40	44	28	21	36
C	41	27	33	30	37
D	22	38	41	36	36
E	29	33	40	35	39

Find the assignment of sales persons to districts that will result in maximum sales.

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Question:

For 10 observations on price $(X)$ and supply $(Y)$ the following data were obtained (in appropriate units): $\sum X=130,\sum Y=200,\sum X^2=2288,\sum Y^2=5506 \,$ $\sum XY=3467.$

Obtain the line of regression of Y on X and estimate the supply when price is 16 units.

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Question:

a) A toy company manufactures two types of doll; a basic version-doll A and a deluxe version-doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum 2000 per day if it produce only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. The company makes profit of ₹3 and 5 per doll respectively on doll A and B. How many of each should be produced per day in order to maximize profit? Solve this problem by graphical method.a) A toy company manufactures two types of doll; a basic version-doll A and a deluxe version-doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum 2000 per day if it produce only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. The company makes profit of 3 and 5 per doll respectively on doll A and B. How many of each should be produced per day in order to maximize profit? Solve this problem by graphical method.

b) Find all the basic solutions of the following system: $x_1+2x_2+x_3=4$