GATE CE 2007 | GATE CE Year Wise Previous Years Questions

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)

-0.6

The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is

$$y = {e^{{1 \over {2x}}}}$$

$$\ln \left( y \right) = {{{x^3}} \over 3} + 4$$

$$\ln \left( y \right) = {{{x^2}} \over 2}$$

$$y = {e^{{{{x^3}} \over 3}}}$$

GATE CE 2007

MCQ (Single Correct Answer)

-0.6

For what values of $$\alpha $$ and $$\beta $$ the following simultaneous equations have an infinite number of solutions $$$x+y+z=5,$$$ $$$x+3y+3z=9,$$$ $$$x + 2y + \alpha z = \beta $$$

$$2,7$$

$$3,8$$

$$8,3$$

$$7,2$$

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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