EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2019>Q 9

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IMPORTANT

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Simpson's rule for evaluation of $\int_{a}^{b} f (x) d x$ requires the interval $(a, b)$ to be divided into

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Important Questions on Numerical Methods

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CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2017>Q 1

One root of the equation

x^{3} - 4 x + 1 = 0

is between

1

and

2

. The value of this root using Newton-Raphson method will be

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2018>Q 2

One root of the equation,

x^{3} - 3 x - 5 = 0

lies between

2

and

2.5

. Using Newton-Raphson method, the value of that root will be

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2019>Q 3

For the solution of equation

f (x) = 0

by the Newton-Raphson method, the value of

x

tends to root of the equation highly when

f^{'} (x_{n})

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2017>Q 4

Dividing the interval

(1, 2)

into four equal parts and using Simpson's rule, the value of

\int_{1}^{2} \frac{d x}{x}

will be

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2017>Q 5

Taking four subintervals, the value of

\int_{0}^{1} \frac{d x}{1 + x}

by using trapezoidal rule will be

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2018>Q 6

Taking two sub-intervals and using Simpson's

\frac{1}{3}

rd rule, the value of

\int_{0}^{1} \frac{d x}{1 + x}

will be

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2018>Q 7

Using trapezoidal rule and taking

n = 4

, the approximate value of integral

\int_{1}^{9} x^{2} d x

is

2 [\frac{1}{2} (1 + 9^{2}) + α^{2} + β^{2} + 7^{2}]

, then

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Numerical Methods>CG PET 2019>Q 8

By Simpson's rule, the value of

\int_{1}^{2} \frac{d x}{x}

dividing the interval

(1, 2)

into four parts is