# Numerical Method

 Question 1
Using Newton-Raphson method, a root correct to 3 decimal places of $x^{3}-3 x-5=0$
 A 2.222 B 2.275 C 2.279 D None of the above
ISRO CSE 2017   Engineering Mathematics
Question 1 Explanation:
 Question 2
What is the sum to infinity of the series,
$3+6 x^{2}+9 x^{4}+12 x^{6}+\ldots \text { given }|x| \lt 1$
 A $\frac{3}{(1+x^{2})}$ B $\frac{3}{(1+x^{2})^{2}}$ C $\frac{3}{(1-x^{2})^{2}}$ D $\frac{3}{(1-x^{2})}$
ISRO CSE 2016   Engineering Mathematics
Question 2 Explanation:
 Question 3
The velocity v (in kilometer/minute) of a motorbike which starts from rest, is given at fixed intervals of time t (in minutes) as follows:

The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is _______________.
 A 225 B 310 C 360 D 420
GATE CSE 2015 SET-3   Engineering Mathematics
Question 3 Explanation:
 Question 4
The secant method is used to find the root of an equation f(x)=0. It is started from two distinct estimates $x_{a}$ and $x_{b}$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_{b})$ is very small and then $x_{b}$ is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by ?. Which is the suitable expression that is to be put in place of ? so that it follows all steps of the secant method?
 A $x_{b}-(f_{b}-f(x_{a}))f_{b}/(x_{b}-x_{a})$ B $x_{a}-(f_{b}-f(x_{a}))f_{a}/(x_{b}-x_{a})$ C $x_{b}-(x_{b}-x_{a})f_{b}/(f_{b}-f(x_{a}))$ D $x_{a}-(x_{b}-x_{a})f_{a}/(f_{b}-f(x_{a}))$
GATE CSE 2015 SET-2   Engineering Mathematics
Question 4 Explanation:
 Question 5
With respect to the numerical evaluation of the definite integral,$K=\int_{a}^{b}x^{2}dx$ , where a and b are given, which of the following statements is/are TRUE?
(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
(II) The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
 A I only B II only C Both I and II D Neither I nor II
GATE CSE 2014 SET-3   Engineering Mathematics
Question 5 Explanation:
 Question 6
In the Newton-Raphson method, an initial guess of $x_{0}=2$ is made and the sequence $x_{0},x_{1},x_{2}...$ is obtained for the function
$0.75x^{3}-2x^{2}-2x+4=0$
Consider the statements
(I) $x_{3}$=0.
(II) The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?
 A Only I B Only II C Both I and II D Neither I nor II
GATE CSE 2014 SET-2   Engineering Mathematics
Question 6 Explanation:
 Question 7
The Guass-Seidal iterative method can be used to solve which of the following sets?
 A Linear algebraic equations B Linear and non-linear algebraic equations C Linear differential equations D Linear and non-linear differential equations
ISRO CSE 2013   Engineering Mathematics
Question 7 Explanation:
 Question 8
Function f is known at the following points:

The value of $\int_{0}^{3}f(x)dx$ computed using the trapezoidal rule is
 A 8.983 B 9.003 C 9.017 D 9.045
GATE CSE 2013   Engineering Mathematics
Question 8 Explanation:
 Question 9
Given
X: 0 10 16
Y: 6 16 28
The interpolated value X=4 using piecewise linear interpolation is
 A 11 B 4 C 22 D 10
ISRO CSE 2011   Engineering Mathematics
Question 9 Explanation:
 Question 10
Newton-Raphson method is used to compute a root of the equation $x^{2} -13=0$ with 3.5 as the initial value. The approximation after one iteration is
 A 3.575 B 3.676 C 3.667 D 3.607
GATE CSE 2010   Engineering Mathematics
Question 10 Explanation:
There are 10 questions to complete.