1
GATE ME 2014 Set 2
Numerical
+2
-0
Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such that each color appears only two times on the die. If the die is thrown thrice, the probability of obtaining red colour on top face of the die at least twice is ________.
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2
GATE ME 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = \cos \left( {x + y} \right),\,\,$$ with $$c$$ as a constant, is
A
$$y + \sin \left( {x + y} \right) = x + c$$
B
$$\tan \left( {{{x + y} \over 2}} \right) = y + c$$
C
$$\cos \left( {{{x + y} \over 2}} \right) = x + c$$
D
$$\tan \left( {{{x + y} \over 2}} \right) = x + c$$
3
GATE ME 2014 Set 2
Numerical
+2
-0
The value of $$\int\limits_{2.5}^4 {\ln \left( x \right)} $$ calculated using the Trapezoidal rule with five sub-intervals is
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4
GATE ME 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
An analytic function of a complex variable $$z=x+iy,$$ where $$i = \sqrt { - 1} $$ is expressed as
$$f\left( z \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right).\,$$ If $$u(x,y)=2xy,$$
then $$v(x,y)$$ must be
A
$${x^2} + {y^2} + $$ constant
B
$${x^2} - {y^2} + $$ constant
C
$$-{x^2} + {y^2} + $$ constant
D
$$-{x^2} - {y^2} + $$ constant
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