# Numerical Analysis (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 8 - 13 of 21

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## Question number: 8

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2010

### Describe in Detail

If f (x) =1/x ^{2}, find the divided differences f (a, b) and f (a, b, c).

### Explanation

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## Question number: 9

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

Appeared in Year: 2014

### Describe in Detail

Using Euler’s method, compute the values of y correct upto 4 places of decimal for the differential equation with initial condition x _{0} = 0, y _{0} = 1, taking h = 0.05.

### Explanation

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## Question number: 10

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2011

### Describe in Detail

Use mathematical induction to prove

### Explanation

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## Question number: 11

» Numerical Analysis » Numerical Integration

Appeared in Year: 2012

### Describe in Detail

The speed y (in km/hr) of a car at different points of time x between 10: 00 a. m. and 10: 40 a. m. on some day was recorded as follows:

Time x (a. m. ) | 10.00 | 10.10 | 10.20 | 10.30 | 10.40 |

Speed y (in km/hr) | 24.2 | 35.0 | 41.3 | 42.8 | 39.2 |

Calculate the approximate distance covered by the car between 10: 00 a. m. and 10: 40 a. m. on that day using Simpson’s one-third formula for numerical integration.

### Explanation

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## Question number: 12

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

### Describe in Detail

The following values of the function f (x) for values of x are given:

f (l) = 4, f (2) = 5, f (7) = 5, f (8) = 4.

Find the value of f (6) and also the value of x for which f (x) is maximum or minimum.

### Explanation

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## Question number: 13

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2011

### Describe in Detail

Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x ^{2}) ^{-1} from 0 to 1.

### Explanation

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