GATE CE 1998 | GATE CE Year Wise Previous Years Questions

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GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The Taylor's series expansion of sin $$x$$ is ______.

$$1 - {{{x^2}} \over {2!}} + {{{x^4}} \over {4!}} - ......$$

$$1 + {{{x^2}} \over {4!}} + {{{x^4}} \over {4!}} + ......$$

$$x + {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} + ......$$

$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - ......$$

GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

$${f_x}\left( {a,\,b} \right) = {f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} > 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0,$$
$${f_{xx}}$$ and $${f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} = 0\,\,$$ at $$(a, b)$$

GATE CE 1998

Subjective

-0

Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$

GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as
$$\matrix{ {{u_a}\left( t \right) = 0} & {for\,\,\,t < a\,} \cr { = 1} & {for\,\,\,t > a,} \cr } $$ is

$${e^{ - as}}/s$$

$$s{e^{ - as}}$$

$$s - u\left( 0 \right)$$

$$s{e^{ - as}} - 1$$

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