GATE 2022 ME (Set 2) question paper PDF and answer key

A person was born on the fifth Monday of February in a particular year.

Which one of the following statements is correct based on the above information?

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).

A massive uniform rigid circular disc is mounted on a frictionless bearing at the end E of a massive uniform rigid shaft AE which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings AB and CD as shown, where G is the center of mass of the shaft-disc assembly and $g$ is the acceleration due to gravity. The disc is then given a rapid spin $\omega$ about its axis in the positive x-axis direction as shown, while the shaft remains at rest. The direction of rotation is defined by using the right-hand thumb rule. If the string AB is suddenly cut, assuming negligible energy dissipation, the shaft AE will

A square plate is supported in four different ways (configurations (P) to (S) as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to be frictionless. All support links of the plate are identical.

The square plate can remain in equilibrium in its initial state for which one or more of the following support configurations?

A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20$ N each can be placed on the platforms. The number of discs placed on the left side platform is $n$ and that on the right side platform is $m$.

It is found that for $n=5$ and $m=0$, a force $F=200$ N (refer to part (i) of the figure) is just sufficient to initiate upward motion of the left side platform. If the force $F$ is removed then the minimum value of $m$ (refer to part (ii) of the figure) required to prevent downward motion of the left side platform is______ (in integer).