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Question:

Explain the impact of the modern information technology on our life style and society.

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Question:

Mention four ways in which our societyhas benefitted from the artificial satellite programme

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Question:

Explain how the recent technological advances have benefitted the modern education system.Give suitable examples.

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Question:

Discuss in detail the evidences of human evolution giving suitable examples.

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Question:

Distinguish between nuclear fusion and nuclear fission and discuss briefly the working of a nuclear reactor.

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Question:

List the major endocrine glands and add a note on their functions.

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Question:

Draw a well labelled diagram of human brain cut along the medial plane.

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Question:

List and describe the developments in medicine during the Iron Age.

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Question:

Give an account of the scientific revolution during post renaissance period.

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Question:

a) For the set of keys {3, 7, 9, 4, 6, 8, 12} draw binary search trees of height 2, 3, 4, 5 and 6.
b) Using Fig. 6.3 in page 134 of the book as a model, illustrate the operation of Build-Max-Heap on the array See Answer →

Question:

a) Let Image ignouassignments-ignouacademy-com--p-ignou-22747 and be cyclic codes over $F_{q}$ with generator polynomials $g_{1}(x)$ and $g_{2(x),}$ respectively. Prove that

$\subseteq$ Image ignouassignments-ignouacademy-com--p-ignou-81648 if and only if $g_{2(x)} |g_{1}(x).$

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Question:

a) The maximum subsequence sum problem is defined as follows: If $a_1,a_2,...,a_n$ are in Z, find the maximum value $\sum_{k=i}^{j}a_i,$ for all $i,\, j,1\leq i\leq j\leq n.$ We assume that the answer is 0 if all the $a_i$ are negative or if the sum is empty. The following algorithm finds a solution to the problem. Here, we assume that $a_i$ s are stored in the array A.

Maximum-Subsequence $(A,MaxSum)$

1 $Sum\leftarrow 0,MaxSum\leftarrow0$

2 $for\, i\leftarrow1\: to\: n$

3 $do$

4 $Sum=Sum+A[i]$

5 $if$ $Sum>MaxSum$

6 $then$ $MaxSum\leftarrow\, Sum$

7 $else\: if\, Sum<0$

8 $then\, Sum=0$

State precisely a loop invariant for the for loop in line 2–8. Prove that your loop invariant holds and hence conclude that the algorithm works.

b) Analyse the algorithm and find an upper bound for the run time of the above algorithm.

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Question:

Let α be a root of $x^{2}+1=0$ in $F_{9.}$

a) Check whether α is a primitive element of $F_{9.}$ If it is not a primitive element in $F_{9.}$ find a primitive element γ in $F_{9.}$ in terms of α. b) Make a table similiar to Table 5.1 on page 184 for $F_{9.}$ with the primitive element γ

c) Factorise $X^{8}- 1$ over $F_{3.}$

d) Find all the possible generator polynomials of a [8,6] cyclic code.

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Question:

d) The aim of this exercise is to show that every binary repetition code of odd length is perfect

i) Find the value of t and d for a perfect code of length 2m+1, m $\epsilon$

ii) Show that

$\sum_{i=0}^{m\binom{2m+1}{i=2^{2m}$ $\sum _{i=0}^{m}\binom{2m+1}{i}=2^{2m}$

(Hint: Start with the relation

$2^{2m+1}=\sum _{i=0}^{2m+1}\binom{2m+1} )$

iii) Deduce that every repetiition code of odd length is perfect.

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Question:

Show that, if $x\epsilon F_{2}^{N,}$

$wt(x)\equiv x.x$ (mod 3)

Deduce that, if Image ignouassignments-ignouacademy-com--p-doubts-59731 is a ternary self orthogonal code, the weight of each codeword is divisible by 3.

(Hint: Observe that $x^{2}=1for all x$ Image ignouassignments-ignouacademy-com--p-ignou-59647 $0\epsilon F_{3} )$

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Question:

Let Image ignouassignments-ignouacademy-com--p-ignou-51375 be a binary code with a generator matrix each of whose rows has even weight. Show that, every codeword of has even weight ( Hint: Why is it enough to prove that sum of vectors of even weight in $F_{2}^{n}$ is a vector of even weight? )

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Question:

b) Using Fig. 7.1 in page 147 of the book as the model, illustrate the operation of Partition on the array See Answer →

Question:

a) With the help of an example, explain the following:
i) Algorithm.
ii) Input and output for an algorithm.
iii) Running time of an algorithm.

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Question:

a) $If x,y\in F_{2,}^{n}$ show that

$wt(x+y)=wt(y)-2wt(x\cap y)$

where $x\cap y$ is the vector in $F_{2}^{n}$ which has 1s precisely at those positions where x and y have 1s.

(Hint: Let $x=(x_1,x_2,.....,x-n)\, and\, y=(y_1,y_2,....,y_n). Suppose$ Image ignouassignments-ignouacademy-com--p-solve-53747 Observe that $wt(x)=n_1+n_2 \: and \: wt (y)=n_1+n_3.$