This document contains a question bank with 62 questions related to the subject of Computer Oriented Statistical Methods. The questions cover various topics including numerical methods, interpolation, integration, solving differential equations, and error analysis. The questions vary in difficulty level from 2 to 7 and include calculating derivatives and integrals, fitting data to functions, and using numerical techniques like Newton-Raphson, Runge-Kutta, and Taylor Series. For each question, the document provides the difficulty level and the month/year the question was added.

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