GATE CE 2007 | GATE CE Year Wise Previous Years Questions

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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 $$-3$$

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

A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^ \circ }$$c. What will be the temperature of the body at the and of $$30$$ minutes?

$${35.2^ \circ }C$$

$${31.5^ \circ }C$$

$${28.7^ \circ }C$$

$${15^ \circ }C$$

GATE CE 2007

MCQ (Single Correct Answer)

-0.6

The inverse of $$2 \times 2$$ matrix $$\left[ {\matrix{ 1 & 2 \cr 5 & 7 \cr } } \right]$$ is

$${1 \over 3}\left[ {\matrix{ { - 7} & 2 \cr 5 & { - 1} \cr } } \right]$$

$${1 \over 3}\left[ {\matrix{ { 7} & 2 \cr 5 & { 1} \cr } } \right]$$

$${1 \over 3}\left[ {\matrix{ { 7} &- 2 \cr - 5 & { 1} \cr } } \right]$$

$${1 \over 3}\left[ {\matrix{ { - 7} & - 2 \cr - 5 & { - 1} \cr } } \right]$$

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