Solve your IGNOU Doubts

Question:

Near what points may the surface $z^2 + xz + y = 0$ be represented uniquely as a graph of a differentiable function $z = k(x,y)$ ? Locate such a point.

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Question:

Let E be an open subset of $R^n$ and $f : E \rightarrow R^m$ be a function such that each of its components function $f_i$ are differentiable, then show that f is differentiable. Is the converse of this result true? Justify your answer.

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Question:

Find the first derivative $f'(a)$ of the function f defined by $f : R^3 \rightarrow R^2$ given by $f(x,y,z) = (xyz, x + y+z^2)$ where $a = (1. -1,2)$ .

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Question:

Show that an infinite discrete metric space X is bounded but not totally bounded.

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Question:

Let $(X_1,d_1)$ and $(X_2,d_2)$ be metric spaces. Show that $f : X \rightarrow Y$ is continuous if and only if $f (\overline{A}) \subseteq \overline{f(A)}$ where A is any subset of X

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Question:

Find the interior, boundary and closure of the following sets A in $\mathbb{R}$ with the usual metric and discrete metric.

i) A = $\mathbb{Q}$ , the set of rationals in $\mathbb{R}$

ii) $A = ]1,2] \cup ]2 ,4[$

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Question:

Let A and B be any two subsets of a metric space $(X, d)$ , then show that
i) int $A = \cup$ {E : is open and $E \subseteq A$ }
ii) int $(A \cap B)$ = int A $\cap$ int B
iii) int(A $\cup$ )B $\supseteq$ int A $\cap$ int B
iv) $\overline{A \cap B} \subseteq \overline{A} \cap \overline{B}$ .

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Question:

Let $(X, d)$ be a metric space and $a \in X$ be a fixed point of $X$ . Show that the function $f_a : X \rightarrow R$ given by $f_a (x) = d(x,a)$ is continuous. Is it uniformly continuous? Justify you answer

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Question:

Let $X = C[0, 1]$ . Define $d : X \times X \rightarrow R$ by $d(f,g) = \int_{0}^{1}\mid f(t) -g(t) \mid dt , f, g \in X$ where the integral is the Riemann integral. Show that d is a metric on X . Find $d(f,g)$ where $f(x) = 4x$ and $g(x) = x^3$ , $x \in [0,1]$

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Question:

What do you understand by file organisation? Explain the methods of file organisation.

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Question:

Explain the meaning of the terms garbage collection, fragmentation, relocation and compaction.

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Question:

Write a function that evaluates an expression in RPN that is given as a string.

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Question:

Define a structure of type hms containing three integer members, called hour, minute and second, respectively. Then define a union containing two members, each a structure of type hms. Call the union members local and home, respectively. Declare a pointer variable called time that points to this union.

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Question:

Write the inorder, preorder and postorder traversals of the following binary search tree

Image ignouassignments-ignouacademy-com--p-your-60801

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Question:

Write a C program which reads a line of text from keyboard, and writes the line to a file with lower case letters converted to upper case and vice-versa

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Question:

Consider the following structure declaration of a doubly linked list:
struct dlink
{
int nodeid;
dlink *next;
dlink *prev;
} dlink t;
A pointer of the head of the linked list is maintained as a global variable, whose
definition is
dlink t *head;
The function remove element(dlink t *rp) defined below needs to remove the
node pointed to rp and adjust the head. The first node’s prev and the last node’s
next are NULL.
remove element(dlink t *rp)
{
rp->prev->next = rp->next;
rp->next->prev = rp->prev;
if(head == rp)
head = rp->next;
}
Explain whether the function remove element() works properly or not.

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Question:

What do you understand by a nested structure? Explain with an example. Also, explain how would you access the members of a structure or a nested structure using pointers?

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Question:

What does the following C function compute? Discover.
int some fun(int n)
{
if(n%2 == 0)
return 2;
int d, s = sqrt(n);
2
for(d = 3; d <= s; d = d+2)
if(n%d == 0)
return d;
return n;
}

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Question:

How would you differentiate between the terms pointer to an array and array of pointers? Give proper examples.

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Question:

A C program contains the following statements:
char u, v = ‘A’;
char *pu, *pv = &v;
*pv = v+1;
u = *pv + 1;
pu = &u;

Suppose each character occupies one byte of memory. If the value assigned to u is stored in (hexadecimal) address F8C and the value assigned to v is stored in the address F8D, then
i) What value is represented by &v?
ii) What value is assigned to pv?
iii) What value is represented by *pv?
iv) What value is assigned to u?
v) What value is represented by &u?
vi) What value is assigned to pu?

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