# Numerical Analysis (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 7 of 21

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## Question number: 1

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2013

### Describe in Detail

Use Simpson’s one-third rule to estimate approximately the area of the cross section of a river 80 feet wide, the depth d (in feet) at a distance x from one bank being given by the following table. :

x | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |

d | 0 | 4 | 7 | 9 | 12 | 15 | 14 | 8 | 3 |

### Explanation

T he one-third rule of the integrand using Simpson’s rule is

The area of the cross section of a river 80 feet wide is

Here n = 8, b = 80, a = 0, h= (b-a) /n = 10

## Question number: 2

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2013

### Describe in Detail

Find the missing value in the table by assuming a polynomial form for y:

X | 0 | 1 | 2 | 3 | 4 |

y | 1 | 2 | 4 | - | 16 |

### Explanation

we have given that there are four values of y is given, then find the missing value of y at x = 3 using Lagrange’s interpolation polynomial because the x values is not equal interval.

The table is

X | 0 | 1 | 2 | 4 |

y | 1 | 2 | 4 | 16 |

## Question number: 3

» Numerical Analysis » Numerical Integration

Appeared in Year: 2013

### Describe in Detail

Evaluate the following by taking seven ordinates of the integrand:

### Explanation

The seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y _{k} =f (a + kh) for k = 0, 1, 2, 3, 4, 5, 6

Here, b = 1, a = 0, h = 1/6, f (x) =

## Question number: 4

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2015

### Describe in Detail

By using Euler-Maclaurin formula, find the sum

### Explanation

The Euler-Maclaurin formula is

where

Given the equation

## Question number: 5

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2015

### Describe in Detail

Compute the value of by Simpson’s 1/3 ^{rd} rule. Given that ln4.0 = 1.39, ln4.2 = 1.43, ln4.4 = 1.48, ln4.6 = 1.53, ln4.8 = 1.57, ln5.0 = 1.61, ln5.2 = 1.65

### Explanation

So, the seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y _{k} =f (a + kh) for k = 0, 1, 2, 3, 4, 5, 6

Here, b = 5.2, a = 4, h = 0.2, f (x) = lnx

## Question number: 6

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2014

### Describe in Detail

Given the following values of the function y = f (x); evaluate f (4) and also find x for which f (x) = 25.

f (1) = 10, f (2) = 15, f (3) = 42.

### Explanation

Given that y = f (x), So

x 1 2 3 4

y 10 15 42?

To find the missing value, we use binomial expansion method. Here 3 values are known, we would take third order finite difference zero. Thus,

Second question is that if we

## Question number: 7

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

### Describe in Detail

The observed-values of a function are respectively 168, 120, 72 and 63 at the four positions 3, 7, 9 and 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable?

### Explanation

Using Lagrange’s formula

Given that a = 3, b = 7, c = 9, d = 10 and f (a) =168, f (b) =120, f (c) =72, f (d) =63

Find x = 6, the values of f (x) =?