GATE CE 2012 | Numerical Methods Question 14 | Engineering Mathematics

The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point function evaluation exceeds the exact value by

$$0.235$$

$$0.068$$

$$0.024$$

$$0.012$$

GATE CE 2008

MCQ (Single Correct Answer)

-0.3

The Newton-Raphson iteration $${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {R \over {{x_n}}}} \right)$$ can be used to compute

square of $$R$$

reciprocal of $$R$$

square root of $$R$$

logarithm of $$R$$

GATE CE 2007

MCQ (Single Correct Answer)

-0.3

The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ The iterative equation for this purpose is ($$k$$ indicates the iteration level)

$${X_{k + 1}} = {{2X_k^3 + 9} \over {3X_k^2 + 4}}$$

$${X_{k + 1}} = {{3X_k^3 + 9} \over {2X_k^2 + 9}}$$

$${X_{k + 1}} = {X_k} - 3_k^2 + 4$$

$${X_{k + 1}} = {{4X_k^2 + 3} \over {9X_k^2 + 2}}$$

GATE CE 2007

MCQ (Single Correct Answer)

-0.3

Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are

$$2$$ and $$3$$

$$2$$ and $$4$$

$$3$$ and $$4$$

$$-2$$ and $$-3$$

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Reinforced Cement Concrete

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