Multiple Choice Questions (MCQ) and answers on Numerical Methods
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c. d.
(Ans:b)
a. b. c. d.
a. b. c. d.
a. b. c. d.
a. b. c. d.
a. b. c. d.
a. b. c. d.
a. b. c. d.
a. b. c. d.
a. b.
In which of the following method, we approximate the curve of solution by the tangent in each interval Picard’s method Euler’s method Newton’s method Runge Kutta method (Ans:b) !acobi"s method is also #nown as Displacement method Simultaneous displacement method Simultaneous method Diagonal method (Ans:b)
a. b. c. d.
$he expected value of the random variable 8ill also be the most li2el5 9alue o* the random 9ariable 0s another term *or the mean 9alue 0s also called the 9ariance 3annot be greater than % (Ans:b)
1: The convergence of which of the following method is sensitive to starting value?
$he number of signi%cant digits in the number &''&''' is ! " # (Ans:d)
A.
False position
B.
Gauss seidal method
C.
Newton-Raphson method
In general the ratio of truncation er ror to that of round o* error is $:% %:% %:$ %:& (Ans:a)
. All of these !: Newton-Raphson method is used to find the root of the e"uation #! - ! $ %. &f iterations iterations are started from - 1' then iterations iterations will (e
$he convergence of which of the following method is sensitive to starting value+ 'alse position auss seidal method NewtonRaphson method All o* these (Ans:c) $o perform a Chis-uare test Data con*orm to a normal d istribution Data be measured on a nominal scale Each cell has e+ual number o* *re+uencies All o* these (Ans:d) In the .auss elimination method for solving a system of linear algebraic e-uations, triangular/ation leads to Diagonal matri, -ower triangular matri, .pper triangular matri, Singular matri, (Ans:c) Match the following0 A/ NewtonRaphson %/ 0ntegration 1/ Runge2utta $/ Root *inding 3/ aussseidel &/ 4rdinar5 Di**erential E+uations D/ Simpson’s Rule 6/ Solution o* s5stem o* -inear E+uations 7he correct se+uence is A$1&36D% A&1$3%D6 A%163$D& A61%3$D& (Ans:a) 1rder of convergence of 2egula3alsi method is %/&$% %/!%"
A.
converge to -1
B.
converge to √2
C.
converge to -)!
.
no coverage
*: +hich of the following statements applies to the (isection method used for finding roots of functions? A.Converges A. Converges within a few iterations B.,uaranteed B. ,uaranteed to wor for all continuous functions C.Is C. Is faster than the Newton-Raphson method .Reuires . Reuires that there !e no error in determining the sign of the function : +e wish to solve #! - ! $ % (/ Newton Raphson techni"ue. &f initial guess is #% $ 1.%' su(se"uent estimate of # 0i.e. # 1 will (e A.
1"#1#
B.
1.2
C.
2"$
.
None of these
5: 3sing Bisection method' negative root of #* - # 9 5 $ % correct to three decimal places is
2: 3sing Newton-Raphson method' find a root correct to three decimal places of the e"uation #* - *# - 2 $ %
A.
-2"&$/
B.
-!.4%6
A.
2"2%&
C.
- 2"#$/
B.
!.!45
.
None of these
C.
2"222
.
None of these
1%: ;our ar(itrar/ points 0#1' /1' 0#!' /!' 0#*' /*'0# ' / are given in the #' /-plane. 3sing the method of least s"uares' if regressing /
6:
upon # gives the fitted line / $ a# 9 (< and regressing / upon #
&n the ,auss elimination method for solving a s/stem of linear
gives the fitted line / 9 a# 9 (< and regressing # upon / gives the
alge(raic e"uations'triangular7ation e"uations'triangular7ation leads to
fitted line # $ c/ 9 d' then
A.
'iagonal matri( A. 0wo fitted lines must coincide
B.
)ower triangular matri( B. 0wo fitted lines need not coincide
C.
3pper triangular matri# C. It is possi!le that ac $
.
*ingular matri( . A must (e 1=c
4: &f 8f0# $ f0#9h - f0#' then a constant ' 8 8 e"uals
11: The root of #* - !# - 2 $ % correct to three decimal places (/ using
A.
1
Newton-Raphson method is
B.
%
A.
2"$#/
C.
f+,- f+$
B.
1"$#$#
.
f+( . , - f+(
C.
1"%321
.
$"%$11
: ou(le 0Repeated root of #*- #!- *# 9 5 $ % (/ ( / Newton-raphson method is
1!: Newton-Raphson method of solution of numerical e"uation is not
A.
1"#
preferred when
B.
1.2
A.Graph A. Graph of A+4 is vertical
C.
1"/
B.Graph B. Graph of (+5 is not parallel
.
1"&&
C.The C. The graph of f0# is nearl/ hori7ontal-where it crosses the #-
a#is. .None . None of these 1*:
C.
h3
.
h#
;ollowing are the values of a function /0# : /0-1 $ 2' /0%' /01 $ d/=d# at # $ % as per Newton>s central difference scheme is A.
$
B.
1.2
C.
2"$
.
3"$
14: &n which of the following methods proper choice of initial value is ver/ important?
1: A root of the e"uation #* - # - 11 $ % correct to four decimals using (isection method is A.
2"3%3%
B.
2"3636
C.
!.*4*6
.
None of these
A.
4isection method
B.
False position
C.
Newton-Raphson
.
4airsto method
1: 3sing Newton-Raphson method' find a root correct to three decimal places of the e"uation sin # $ 1 - #
Newton-Raphson method is applica(le to the solution of A Both alge(raic and transcendental "uations . B 4oth alge!raic and transcendental and also used when the roots are
A.
%.211
B.
$"&$$
C.
$"&&&
.
None of these
. comple( 15: C Alge!raic euations onl5
rrors ma/ occur in performing numerical computation on the
.
computer due to
0ranscende 0ranscendental ntal euations onl5 .
A.
Rounding errors
B.
7ower fluctuation
C.
8perator fatigue
.
All of these
16: The order of error s the @impson>s rule for numercal integration with a step si7e h is A.
