31.
Consider a full binary tree with n internal
nodes, internal path length i, and external path length e. The internal path
length of a full binary tree is the sum, taken over all nodes of the tree, of
the depth of each node. Similarly, the external path length is the sum, taken
over all leaves of the tree, of the depth of each leaf.

Which of the
following is correct for the full binary tree?

(1) e = i + n

(2) e = i + 2n

(3) e = 2i +
n

(4) e = 2

^{n }+ i
Answer: 2

32. You
are given a sequence of n elements to sort. The input sequence consists of n/k subsequences,
each containing k elements. The elements in a given subsequence are all smaller
than the elements in the succeeding subsequence and larger than the elements in
the preceding subsequence. Thus, all that is needed to sort the whole sequence
of length n is to sort the k elements in each of the n/k subsequences.

The lower
bound on the number of comparisons needed to solve this variant of the sorting
problem is:

(1) â„¦(n)

(2) â„¦(n/k)

(3) â„¦(n lg
k)

(4) â„¦(n/k lg
n/k)

Answer: 3

33. Consider
the recurrence relation:

T (n) =
8T(n/2) + Cn, if n > 1

= b, if n =1

Where b and
c are constants.

The order of
the algorithm corresponding to above recurrence relation is:

(1) n

(2) n

^{2}
(3) n lg n

(4) n

^{3}
Answer: 4

34. Consider
the following two sequences :

X = <B,
C, D, C, A, B, C>

and Y =
<C, A, D, B, C, B>

The length
of longest common subsequence of X and Y is:

(1) 5

(2) 3

(3) 4

(4) 2

Answer: 3

35. A
text is made up of the characters a, b, c, d, e each occurring with the
probability 0.11, 0.40, 0.16, 0.09 and 0.24 respectively. The optimal Huffman
coding technique will have the average length of:

(1) 2.40

(2) 2.16

(3) 2.26

(4) 2.15

Answer: 2

36. An
undirected graph G (V, E) contains n (n > 2) nodes named v

_{1}, v_{2},...,v_{n}. Two nodes v_{i}and v_{j}are connected if and only if 0 < | i – j | ≤ 2. Each edge (v_{i}, v_{j}) is assigned a weight i+j.
The cost of
the minimum spanning tree of such a graph with 10 nodes is :

(1) 88

(2) 91

(3) 49

(4) 21

Answer: 2

37. An
XML document that adheres to syntax rules specified by XML 1.0 specification in
that it must satisfy both physical and logical structured, is called :

(1) Well -
formed

(2)
Reasonable

(3) Valid

(4)
Sophisticated

Answer: 1

38. Which
of the following statement(s) is/are TRUE regarding Java Servelets?

(a) A Java
Servelet is a server-side component that runs on the web server and extends the
capabilities of a server.

(b) A
Servelet can use the user interface classes like AWT or Swing.

**Code :**

(1) Only (a)
is TRUE.

(2) Only (b)
is TRUE.

(3) Both (a)
and (b) are TRUE.

(4) Neither
(a) nor (b) is TRUE.

Answer: 1

39. Consider
the following HTML table definition :

<table
border=1>

<tr>

<td
colspan=2> Text A </td>

</tr>

<tr>

<td>
Text B </td>

<td>
Text C </td>

</tr>

<tr>

<td
rowspan=2> Text D </td>

<td>
Text E </td>

</tr>

<tr>

<td>
Text F </td>

</tr>

</table>

The above
HTML code would render on screen as :

Answer: 3

40. Which
of the following statements is/are TRUE?

(a) In HTML,
character entities are used to incorporate external content into a web page, such
as images.

(b) Once a
web server returns a cookie to a browser, the cookie will be included in all future
requests from the browser to the same server.

**Code :**

(1) Only (a)
is TRUE.

(2) Only (b)
is TRUE.

(3) Both (a)
and (b) are TRUE.

(4) Neither
(a) nor (b) is TRUE.

Answer: 4

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