1. Which of the following statements applies to the bisection method used for finding roots of functions?
A. B. C. D.
Converges within a few iterations Guaranteed to work for all continuous functions Is faster than the Newton-Raphson method Requires that there be no error in determining the sign of the function 2. The convergence of which of the following method is sensitive to starting value?
A. B. C. D.
False position Gauss seidal method Newton-Raphson method All of these 3. We wish to solve
by Newton Raphson technique. If initial guess is x0 = 1.0,
subsequent estimate of x (i.e. x1) will be A. B. C.
1.414 1.5 2.0 None of these
D. 4. Newton-Raphson method of solution of numerical equation is not preferred when A. B. C. D.
Graph of A(B) is vertical Graph of x(y) is not parallel The graph of f(x) is nearly horizontal-where it crosses the x-axis. None of these 5. Newton-Raphson method is applicable to the solution of
A. B. C. D.
Both algebraic and transcendental Equations Both algebraic and transcendental and also used when the roots are complex Algebraic equations only Transcendental equations only 6. In which of the following methods proper choice of initial value is very important?
A.
Bisection method
B.
False position
C.
Newton-Raphson
D.
Bairsto method 7. Let f(x) be an equation such that f(a) f(b) > 0 for two real numbers a and b. Then at least one root of f(x) = 0 lies in (a, b) no root lies in (a, b) either no root or an even number of roots lie in (a, b) None of these. 8. Order of convergence of Newton-Raphson method is 1 1.618 2 None of these 9. In Regular-falsi method, the first approximation is given by a) x1
x1
af (b) bf (a ) f (b) f (a )
b) x1
bf (b) af (a ) f (b) f (a )
c) x1
bf (a ) af (b) f (a ) f (b)
af (a ) bf (b) f (a ) f (b)
10. The Newton-Raphson method fails when a) f ' x is negative
Discrete Mathematics MCQ
b) f ' x is too large c) f ' x is zero d) Never fails.
d)
a) K4 is planar while Q3 is not b) Both K4 and Q3 are planar c) Q3 is planar while K4 is not d) Neither K4 nor Q3 are planar
2. What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle? Assume n >= 2. a) 2 b) 3 C c) n-1 d) n D 3. Let G be the non-planar graph with the minimum possible number of edges. Then G has
A 9 edges and 5 vertices B 9 edges and 6 vertices C 10 edges and 5 vertices 10 edges and 6 vertices
4. Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces D
in the planar embedding of the graph is
a) 6 b) 8 c) 9 d) 13
5. Which one of the Following is not Planer graph a) G1 b) G2 c)G3 d)G4 6. The minimum number of colours required to colour the following graph,
a)2 b) 3 c)4 d)5 7. What is the chromatic number of the following graph?
a) 2 b)3 c)4 d) 5 8. The maximum number of edges in a bipartite graph on 12 vertices is_ a)34 b)3 c)36 d)30 9. Let G be the non-planar graph with the minimum possible number of vertices. Then G has
A B C
9 edges and 5 vertices 9 edges and 6 vertices 10 edges and 5 vertices e) 10 Vertices and 10 Edges
