# CSE - Questions and solutions set-12

Computer science and engineering(CSE) - Question & solution set-12
Question:-
Option (A)
1.4262
Option (B)
1.3571
Option (C)
1.4056
Option (D)
None of these
Correct Option:
B
Question Solution:
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By Simpson's rule
Question:-
Option (A)
1.8866
Option (B)
1.8899
Option (C)
1.8986
Option (D)
None of these
Correct Option:
C
Question Solution:
f(x) = sin x - x/2, f'(x) = cos x - 1/2.

This has three roots. One of them is at x = 0. The others are near x = ±2.

For this function, the Newton-Raphson method uses the iteration

If we start with x1 = 2, we quickly approach the rightmost root:

x1 = 2

x2 = 1.900995594

x3 = 1.898679953.

Question:-
Option (A)
1
Option (B)
5
Option (C)
2
Option (D)
None of these
Correct Option:
A
Question Solution:
First sort the degree vertex which gives us (5, 4, 3, 3, 2). Let label these vertices as (a, b, c, d, e) respectively and the new vertex (to be added) as ‘f'. The vertex ‘a' (degree 5) should be adjacent to 5 vertices. This means ‘f' vertex should have a degree of at least 1. The second vertex should be adjacent to another 3 vertices as vertex ‘a' is already adjacent to this contributing 1 degree. We will take these 3 vertices as (c, d, e). The vertex ‘c' should be adjacent to another vertex as ‘a' and ‘b' are already adjacent to this. This we can take as‘d'. With this all degrees are satisfied for all vertices. So the new vertex ‘f' should have a degree of 1.