1. QUESTION BANK
Subject code: 151601
Subject Name: Computer Oriented Statistical Methods
1 If u =2v6 -5 , find the percentage error in u at v =1 if error in v is 0.05. 3 June11
2 Find the solution of the following equation using floating point arithmetic 3 June11
with 4-digit mantissa x2 -1000x +25 =0
3 Discuss the pitfalls in computing using normalize floating – point numbers. 3 Dec10
4 Explain Floating Point Representation of number with example. 3 June12
5 Explain different types of Errors with it’s propagation during computation & 6 June12
how to improve the accuracy of Numeric Computation.
6 Discuss briefly the different types of errors encountered in performing 3 Nov11
numerical calculations
7 Find the root of the equation x4 – x – 10 = 0 upto 3 decimal points using 7 June12
Bisection Method.
8 Find the root of the equation 2x-log10x-7 = 0 correct to three decimal places 3 June11
using iteration method.
9 Find the approximate root of the equation x3 ‐ 4x ‐ 9 = 0 by using False 7 June12
Position Method.
10 Use three iterations of Newton Raphson Method to solve the non-linear 6 Dec10
quations, x 2 − y 2 + 7 = 0, x − xy + 9 = 0 .Take ( x 0 , y 0 ) = (3.5,4.5) as the
initial approximation.
11 Find the real root of the equation x3 - 9x +1=0 by method of Newton Raphson 4 Dec 10
12 Explain Newton Raphson Method in detail 5 June12
13 Prove that Newton-Raphson procedure is second order convergent. 3 Nov11
14 If y(1) = 4, y(3) = 12, y(4) = 19 and y(x) = 7 then find x by Newton’s formula
15 Find the root of the equation by Secant method. 4 June11
16 Write an algorithm for the false position method to find root of the 3 Nov11
equation f ( x) = 0 .
17 Write an algorithm for the successive approximation method to find root of 2 Dec10
nonlinear equation.
18 Use the secant method to estimate the root of f ( x) = e − x − x correct to two 4 Nov 11
significant digits with initial estimate of x-1 =0 and x0 =1.0
19 Describe BAIRSTOW method in brief 5 Dec10
20 Find all roots of the equation x3 – 2x2 -5x + 6 = 0 using Graeffe`s method 5 Dec10,
squaring thrice. 7 Nov11
21 Use Lagrange’s formula to find third degree polynomial which fits into the 5 June11
data below
X 0 1 3 4
Y -12 0 12 24
Evaluate the polynomial for x = 4.
22 State Budan’s theorem. Apply it to find the number of roots of the equation June11
in the interval [-1, 0] and [0,1].
23 Find the root of the equation using Lin-Bairstow’s 4 June11
Method
24 Compute f '(0.75) , from the following table 3 June11
x 0.50 0.75 1.00 1.25 1.50
f(x) 0.13 0.42 1.00 1.95 2.35
Prepared by Dr. Shailja Sharma

2. QUESTION BANK
Subject code: 151601
Subject Name: Computer Oriented Statistical Methods
25 Evaluate by (i) Trapezoidal rule (ii) Simpson’s 1/3 rule 4 June 11
26 Represent the function f(x) = 3 in factorial notation and hence 5 June11
show that f (x) =18.
27 The distance, s(in km) covered by a car in a given time, t (min) is given in the 4 June11
following table
Time(t) 0 1 2 3 4 5 6
Distance(s) 0 2.5 8.5 15.5 24.5 36.5 50
Estimate the speed and acceleration of the car at t = 5 minutes.
28 The distance (s) covered by a car in a given time (t) is given below 6 Dec10
Time(Minutes) : 10 12 16 17 22
Distance(Km.) : 12 15 20 22 32
Find the speed of car at time t =14 minutes
29 Obtain cubic spline for every subinterval from the following data 6 Dec10
x: 0 1 2 3
f(x) : 1 2 33 244
Hence an estimate f(2.5)
30 Fit cubic splines for first two subintervals from the following data. Utilize the 7 Nov11
result to estimate the value at x=5.
x: 3 4.5 7 9
f(x) : 2.5 1 2.5 0.5
31 Estimate the function value f (7) using cubic splines from the following data 5 June11
given p0 =p2 =0
i 0 1 2
zi 4 9 16
fi 2 3 4
32 Prove the following (i) Δ∇ = ∇Δ = Δ − ∇ (ii) δ = ∇E 1 / 2 4 June11
33 Write an algorithm for Lagrange’s interpolation method to interpolate a value 2 Dec10
of dependent variable for given value of independent variable.
34 Differentiate Interpolation & Extrapolation. 3 June12
35 Estimate the value of f(22) and f(42) from the following data 5 June11
x: 20 25 30 35 40 45
f(x): 354 332 291 260 231 204
36 Explain Cubic Spline Interpolation with it’s conditions. 3 June12
37 Write Langrage Interpolation Algorithm & Solve the following using it: 8 June12
Find f(x) at x=4.
X : 1.5 3 6
f(x) : ‐0.25 2 20
38 Consider the following table: 8 June12
x : 20 25 30
f(x) : 0.342 0.423 0.500
Find the value of x where f(x) = 0.399 using Inverse Interpolation. Would
you use the difference method or Lagrangian Method?
39 Write an algorithm for Trapezoidal Rule to integrate a tabulated function. 3 Nov11
Prepared by Dr. Shailja Sharma

3. QUESTION BANK
Subject code: 151601
Subject Name: Computer Oriented Statistical Methods
40 Evaluate ∫x2 dx using Trapezoidal Rule by taking h=1/8. 4 June12
41 5 6 Dec10
∫
Evaluate : log 10 xdx , taking 8 subintervals, correct to four decimal places by
1
Trapezoidal rule.
42 The table gives the distance in nautical miles of the visible horizon for the 4 Nov11
given heights in feet above the earth’s surface. Find the values of y when
x=390ft.
height(x): 100 150 200 250 300 350 400
Distance(y): 10.63 13.03 15.04 16.81 18.42 19.90 21.27
43 A train is moving at the speed of 30 m/sec. suddenly brakes are applied. The 4 Nov11
speed of the train per second after t seconds is given by the following table.
Time(t): 0 5 10 15 20 25 30
Speed(v): 30 24 19 16 13 11 10
Apply Simpson’s three-eighth rule to determine the distance moved by the
train in 30 seconds.
44 Explain Simpson 1/3 Rule in detail. 4 June12
45 Using Simpson’s rule, find the volume of the solid of revolution formed by
rotating about x-axis. The area between the x-axis, the lines x = 0 and x = 1
and a curve through the points (0,1), (0.25,0.9896), (0.50,0.9589),
(0.75,0.9089) and (1,0.8415).
46 A slider in a machine moves along a fixed straight rod. Its distance x cm. along 7 Nov11
the rod is given below for various values of the time t seconds. Find the
velocity of the slider when t = 0.1 second.
t: 0 0.1 0.2 0.3 0.4 0.5 0.6
x: 30.13 31.62 32.87 33.64 33.95 33.81 33.24
47 Write an algorithm for simpson`s three-eight rule to integrate a tabulated 2 Dec10
function.
48 Compute f’(0.75),from the following table 3 June11
X: 0.50 0.75 1.00 1.25 1.50
F(x):0.13 0.42 1.00 1.95 2.35
49 6
1 4 June11
Evaluate ∫ 1 + x 2 dx by (i)Trapezoidal rule (ii) Simpson’s 1/3 rule
0
50 The following data gives pressure and volume of superheated steam 6 Dec10
V: 2 4 6 8 10
P: 105 42.7 25.3 16.7 13
Find the rate of change of pressure w.r.t. volume when V=8
51 Following table shows speed in m/s and time in second of a car 6 Dec10
t : 0 12 24 36 48 60 72 84 96 108 120
v : 0 3.60 10.08 18.90 21.60 18.54 10.26 5.40 4.50 5.40 9.00
Using simpson`s one-third rule find the distance travelled by the car in 120
second
52 Given where y = 0 when x = 0 find y(0.2) and y(0.4) using 5 June11
Runga Kutta method
Prepared by Dr. Shailja Sharma

4. QUESTION BANK
Subject code: 151601
Subject Name: Computer Oriented Statistical Methods
53 Solve the dy/dx = x2– y, y(0) = 1. Find y(0.1) and y(0.2), h=0.1 using Runge 7 June 12
Kutta’s 2nd Order Method.
54 dy 6 Dec10
Given that = x + y 2 , y(0) = 1. Using Runge-kutta method find
dx
approximate value of y 0.2,take step size 0.1
55 dy 4 Nov11
Given that = x + y with initial condition y(0)=1.Use Runge-Kutta fourth
dx
order method to find y(0.1).
56 dy 2 Dec10
Write an algorithm for Euler`s method to solve ODE = f ( x, y )
dx
57 Solve dy/dx = 2x – y, y(0) = 2 in the range 0 ≤ x ≤ 0.3 by taking h=0.1 using 7 June12
Euler’s Method
58 Using Euler`s method, compute y(0.5) for differential equation 4 June11
dy
= y2 − x2
dx with y = 1 when x = 0(taking h = 0.1)
59 dy 4 June11
Solve the differential equation = x + y with y(0) = 1, x ∈ [0,1] by Taylor’s
dx
series expansion to obtain y for x = 0.
60 Use Taylor series to find approximate value of cos(-8 ) to 5 significant digits. 7 Nov11
61 dy 7 Nov11
Use Heun’s predictor-corrector method to integrate = 4e 0.8 x − 0.5 y from
dx
x= 0 to x = 3 with a step size of 1. The initial condition at x=0 is y=2.(Perform
only one iteration in corrector step)
62 4 3 June11
∫ ( x + 2 x)dx
2
Using Gauss’s quadrature formula, evaluate
2
Prepared by Dr. Shailja Sharma