1
GATE ME 2016 Set 2
Numerical
+2
-0
The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,} $$ using the trapezoidal rule with three intervals of equal length between $$0$$ and $$\pi $$ is _________.
Your input ____
2
GATE ME 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The value of $$\oint\limits_\Gamma {{{3z - 5} \over {\left( {z - 1} \right)\left( {z - 2} \right)}}dz} $$ along a closed path $$\Gamma $$ is equal to $$\left( {4\pi i} \right),$$ where $$z=x+iy$$ and $$i = \sqrt { - 1} .$$ The correct path $$\Gamma $$ is
A
GATE ME 2016 Set 2 Engineering Mathematics - Complex Variable Question 8 English Option 1
B
GATE ME 2016 Set 2 Engineering Mathematics - Complex Variable Question 8 English Option 2
C
GATE ME 2016 Set 2 Engineering Mathematics - Complex Variable Question 8 English Option 3
D
GATE ME 2016 Set 2 Engineering Mathematics - Complex Variable Question 8 English Option 4
3
GATE ME 2016 Set 2
Numerical
+2
-0
A function $$f$$ of the complex variable $$z=x+iy,$$ is given as $$f(x,y)=u(x,y)+iv(x,y),$$
Where $$u(x,y)=2kxy$$ and $$v(x,y)$$ $$ = {x^2} - {y^2}.$$
The value of $$k,$$ for which the function is analytic, is __________.
Your input ____
4
GATE ME 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
A point mass having mass $$M$$ is moving with a velocity $$V$$ at an angle $$\mathop \theta \limits^ \cdot $$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is GATE ME 2016 Set 2 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 54 English
A
$$ - 2MV\cos \theta \widehat j$$
B
$$ 2MV\sin \theta \widehat j$$
C
$$ 2MV\cos \theta \widehat j$$
D
$$ - 2MV\sin \theta \widehat j$$
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