Objective Type Questions
Multiple Choice Questions
Indicate the correct answer for each question by writing the corresponding letter from
(a), (b), (c) and (d).
I . a is a root of the equation f (x) =0 if and only if
2.
3.
4.
0
(a) f la) =0
(b) f (a) *
(c) f '(a) =0
(d) f '(a) #0
An algebraic equation of degree n, where n is a positive integer, has
(a) n roots
(b) n
(c)
(d) none of these
roots
roots
The real roots of the equation f () =0 are the abscissae ofthe points where
the graph crosses the
(a) y-axis
(b) x-axis
(c) line y =x
(d) line y =-x
In Regula-Falsi method if a root of f (x) =0 lies between x and x2 then the
approximate value of the desired root is x +h where h is
(a)
(a)
(c)
5.
2)lyl
(b
Dl+12l
(
Iil+21
(d)
(2)J2l
(d)
2) 2l
l+l2l
Let the equation f
2-X)Jl
Iil+l2l
(r) 0be expressed in the formx
=
¢ (x).If xo be an initial
approximation to the solution of x = ¢ (x), then in Iteration
method the
successive approximations are
=
given by In+1
(b) " (x,)
(d) (*)-Xo
=
(a) o(x)
(c) ()-Xo
6.
Letxo
Then
be an approximate value of the desired
root of the equation
f (t)
by Newton-Raphson method the improved value of the root is
xo
where h is
(a)o)
(a)xo
(b)-o)
(c)
(d)-r)
f xo)
(b)
o
=
0.
+h
Solution
7.
8.
8.
of
Algebraic
and
Transcendental Equations
Newton's iterative formula for obtaining a
is
(a) +l=X, (2 + ar,)
(b) + 1 = *, (2 - ax,)
(c)
(d) x+
= *, (1+ar,)
*, (1- ax,)
Newton's iterative formula for obtaining the square root of a is
(a) u+l
(b)
(c) +1
9.
N-177
Xt
(d) n+l
-
The method which does not require any prior information of the roots such
as approximate value of the root etc. is
(a) Bisection method
(b) Iteration method
(c) Secant method
(d) Graeffe's root squaring method
10. One root of the equation r
11.
- x- l=0 lies between
(a) 1 and 2
(b) 0 and l
(c) 2 and 3
(d) none of these
The exact roots of the equation r
(a) 1, 2, 3
(c) 2, 3, 5
- 8x
+17x - 10 = 0 are
(b) 1, 2, 5
(d) 1, 3, 5.
12. Newton-Raphson method is suitable for:
(a) f'(x) is small
(c)
13.
f'()
is
(b) f"(«) is large
negative
(d) f (*) is positive
(Rohilkhand 2011)
Which method is not applicable for finding roots ?
(a) Secant
(b) Bisection
(c) Langrange's
(d) Newton's
Fill in the
(Rohilkhand 2008)
Blank(s)
Fill in the blanks " . . " so that the following statements are complete and correct.
lta+ib is a root of f (r) = 0,then ... is also a root of the equation.
2.
Every equation of odd degree has at least ... real root.
.
lfr = ais a root of the equation f
4
1f f a) and f (b) are of opposite signs then at least... or an ... number of real
() = 0,thenf (r) is exactly divisible by..
rots of the equationf (x) = 0 lie between a and b.
. I n iteration method for finding the roots of the equation
() =0 it is
expressed in the form...
6
Let o
denote an approximate value of the root of the equation f
(r) = 0. In
Newton-Raphson method successive approximations are givenby y+l = ..
Kaiskra's T.B. Numerical Analysis (Unified)
178
7.
7
I fthe equation y
cquation r
"
+
ay
" + b h y + b z y 1-2
"-
+
agx " 2 + . . +
= 0 is obtained from the
d,
=
0
after squaring then the roots
of the equation in y are the ... of the roots of the equation in x.
True or False
Write
Tfor true and "F" for false statement.
1.
If f
2.
In
0, with real coefficients the number of
positive roots cannot exceed the number of changes of signs from positive to
negative and from negative to positive inf (r).
3.
An
equation
of odd
4.
If
function
f (x) is continuous betweena and b, and f (a) and f (b) areof
a
(r) is exactly divisible by (r
an
algebraic equation f (x)
degree
has
a), a
-
is
a
root
of the
equation f (r)
=
0.
=
real
no
root.
opposite signs, then there exists at least one root between a and b.
5.
Newton-Raphson
method is suitable in
cases
nearly horizontal where it crosses the x-axis.
6.
7.
when the
graph
of
By Newton's method, the iterative formula
x,P +a
n+1
ne] P+)
for
computing p"
root
Px
Answers
Multiple Choice Questions
1.
(a)
6.
11.
(b)
2.
7.
12.
(b)
Fill in the
4.
a - ib
(a)
3.
(b)
(b)
(b)
8.
13.
(a)
(c)
2.
one
5.
x
4.
9.
(b)
5.
(a)
(d)
10.
(a)
Blank(s)
one;odd
=
3.
)
x-a
6. X
f')
T
5.
7. squares
True or false
1.
6.
is
Newton-Raphson method cannot be used when the roots are complex.
=
1.
f (t)
T
F
27.
T
F
3.
F
4.
F
of a is