GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

The Dirac delta Function $$\delta \left( t \right)$$ is defined as

$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,{\,^,}} & {otherwise} \cr } } \right.$$

$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$

$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1} $$

$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1} $$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

In what range should $$Re(s)$$ remain so that the laplace transform of the function $${e^{\left( {a + 2} \right)t + 5}}$$ exists?

$${\mathop{\rm Re}\nolimits} \left( s \right) > a + 2$$

$${\mathop{\rm Re}\nolimits} \left( s \right) > a + 7$$

$${\mathop{\rm Re}\nolimits} \left( s \right) < 2$$

$${\mathop{\rm Re}\nolimits} \left( s \right) > a + 5$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

Match the following and choose the correct combination

Group $$-$$ $${\rm I}$$
$$E.$$ Newton $$-$$ Raphson method
$$F.$$ Runge-Kutta method
$$G.$$ Simpson's Rule
$$H.$$ Gauss elimination

Group $$-$$ $${\rm II}$$
$$(1)$$ Solving non-linear equations
$$(2)$$ Solving linear simultaneous equations
$$(3)$$ Solving ordinary differential equations
$$(4)$$ Numerical integration method
$$(5)$$ Interpolation
$$(6)$$ Calculation of eigen values

$$E - 6,\,\,F - 1,\,\,G - 5,\,\,H - 3$$

$$E - 1,\,\,F - 6,\,\,G - 4,\,\,H - 3$$

$$E - 1,\,\,F - 3,\,\,G - 4,\,\,H - 2$$

$$E - 5,\,\,F - 3,\,\,G - 4,\,\,H - 1$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

The following differential equation has $$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} + 2 = x$$

degree $$=2,$$ order $$=1$$

degree $$=1,$$ order $$=2$$

degree $$=4,$$ order $$=3$$

degree $$=2,$$ order $$=3$$

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