1
GATE ME 2017 Set 2
+2
-0.6
If $$f\left( z \right) = \left( {{x^2} + a{y^2}} \right) + ibxy$$ is a complex analytic function of $$z=x+iy,$$
where $${\rm I} = \sqrt { - 1} ,$$ then
A
$$a=-1,b=-1$$
B
$$a=-1, b=2$$
C
$$a=1, b=2$$
D
$$a=2, b=2$$
2
GATE ME 2017 Set 2
Numerical
+2
-0
The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s2 . The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML2 /12). At this instant, the magnitude of angular acceleration (in radian/s2 ) of the rod is ____________.
3
GATE ME 2017 Set 2
+2
-0.6
For the stability of a floating body the
A
centre of buoyancy must coincide with the centre of gravity
B
centre of buoyancy must be above the centre of gravity
C
centre of gravity must be above the centre of buoyancy
D
metacentre must be above the centre of gravity
4
GATE ME 2017 Set 2
Numerical
+2
-0
A $$60$$ $$mm$$ $$-$$ diameter water jet strikes a plate containing a hole of $$40mm$$ diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is $$1000$$ $$kg/{m^3}$$ . If velocities are as indicated in the figure, the magnitude of horizontal force (in $$N$$) required to hold the plate is _______________