1
GATE CE 2011
MCQ (Single Correct Answer)
+2
-0.6
The square root of a number $$N$$ is to be obtained by applying the Newton $$-$$ Raphson iteration to the equation $$\,{x^2} - N = 0.\,\,$$ If $$i$$ denotes the iteration index, the correct iterative scheme will be
A
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} + {N \over {{x_i}}}} \right]$$
B
$${x_{i + 1}} = {1 \over 2}\left[ {x_i^2 - {N \over {x_i^2}}} \right]$$
C
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} + {{{N^2}} \over {{x_i}}}} \right]$$
D
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} - {N \over {{x_i}}}} \right]$$
2
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exists for $$t>0$$ then the convolution $$z\left( t \right) = x\left( t \right) * y\left( t \right)$$ is ____________.
A
$${e^{ - t}} - {e^{ - 2t}}$$
B
$${e^{ - 2t}}$$
C
$${e^{ - t}}$$
D
$${e^{ - t}} + {e^{ - 3t}}$$
3
GATE CE 2011
MCQ (Single Correct Answer)
+2
-0.6
If $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of $$f(t)$$ are respectively
A
$$0,2$$ $$0,{2 \over 7}$$
B
$$2,0$$
C
$$0,{2 \over 7}$$
D
$${2 \over 7},\,0$$
4
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
For an analytic function $$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$ is given by $$u = 3{x^2} - 3{y^2}.$$ The expression for $$v,$$ considering $$k$$ is to be constant is
A
$$3{y^2} - 3{x^2} + k$$
B
$$6x - 6y + k$$
C
$$6y - 6x + k$$
D
$$6xy + k$$
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