# 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:

There are 5 questions to complete.