B.Sc. (E.C.S.) I (Semester (CBCS) Examination, 2018
Mathematics (Paper VII)
Numerical Methods
Day and Date Monday, 12-11-2018 Max. Marks 70
Time 10.30 a.m. to 1.00 p.m.
instructions All questions are compulsory.
Figures to the right indicate full marks.
Use of scientific calculator is allowed.
1. Choose the correct alternative for each of the following 14
In iteration method, the function is selected in such a way that
1 1
1 None of these
The equation xex tanx 0 is equation.
Linear Ordinary differential
Trigonometric Transcendental
Homogeneous system of linear equations is never
Inconsistent Consistent
Convergent None of these
One of the roots of the equation x3 3x 1 0 lies in the interval

If is a polynomial in x of degree then Δnf(x) is
Zero n
Constant
By putting n 2 in general quadrature formula, formula is
obtained.
Trapezoidal Simpson's 3
8 )th
Newton-Raphson None of these
In Runge-Kutta fourth order method, formula for K4 is
hf y0) f(x0 y0 k1)
hf(x0 y0 k3 f(x0 y0 k3)
While doing addition of two numbers in the normalised floating point notation,exponents are
Added Subtracted
Made equal Multiplied
While doing multiplication of two numbers in the normalised floating point
notation mantissa's should be
Multiplied Added
Divided Made equal
10) To find the numerical value of integration in the interval by taking
equidistant ordinates, the interval of integration is divided into
equal subintervals.
n
n 1 2n
11) Euler's method is used to solve equations.
Non linear Interpolating
Transcendental None of these
12) Process of estimating the value of dependent variable at an intermediate
value is called as
Extrapolation Extraction
Interpolation Intermediation
13) The first approximate value of a root of the equation ex 5x 0 by
Newton Raphson method taking initial approximation x0 0.26413 is
0.25917 0.26413
0.52197 0.26909
14) If in a system of 3 linear equations in 3 variables, two variables are leading and one variable is non leading variable then the system posses
solutions.
No Unique
Trivial Infinitely many
2. Answer the following (any four) 8
Prove that Δ ∇E.
State the formulae for K1 and K3, in Runge-Kutta fourth order method.
Write augmented matrix representing following system of linear equations
x 3y 2z 4w 6y w 3 x 3z 4.
Define absolute error and percentage error.
Define transcendental equation with suitable example.
Answer the following (any two) 6
Write an algorithm to find inverse of a square matrix by using row
reduction method.
Evaluate Δ2
. Take h 1.
Write an algorithm to find root of the equation 0 by using bisection
method.
3. Answer the following (any two) 8
Obtain the Taylor's series for and compute correct up to four
decimal places. Given that
xy, 1.
Define the operators Δ and ∇. Hence show that E Δ.
Evaluate x3 dx05
⋅ by using Trapezoidal rule. Take h 1.
Answer the following (any one) 6
Write an algorithm to solve system of m-linear equations in n-variables
by using Gauss Elimination Method.
Define relative error. Hence evaluate the following. Write the answers in
the normalized floating point form.
0.6928E6 5.4321E5
ii) 0.9871E4 0.5631E4
iii) 4.6512E5 × 3.5168E 2
iv) 0.8889E 3 ÷ 0.2121E 6
4. Answer the following (any two) 10
Evaluate cosx dx ⋅
0
2

by using Simpson's 1
3 )rd
rule, by dividing the
interval into 9 equal parts.
Find real root of the equation x2 x 3 in the interval by using
Regula-Falsi method. Perform only two iterations.
By using Lagrange's interpolation formula, find the value of from
the data given below.
x 6 7 9 12
y 2.556 2.690 2.908 3.158
Answer the following (any one) 4
Derive Newton-Raphson method formula to find root of the equation 0.
By using Euler's method, find y(1.6) by taking h 0.2. Given that
dy/dx=x+y2 with x0 1.2, y0 2.2.
5. Answer the following (any two) 14
Evaluate
Derive Newton's forward difference interpolation formula.
Solve the following system of linear equations by using Gauss-Elimination
method.
x y z 2w 2x y 4z w 3x y 5z 4w 3.