GATE 2022 ME (Set 1) question paper PDF and answer key

Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning Dutch and Japanese.

Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch is easier than Japanese, and Spanish is easier than French.

Based on the above information, which girl is learning the most difficult pair of languages?

A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above.

Which one of the following is the correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow in the above figure?

A uniform light slender beam AB of section modulus $EI$ is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight $W$ as shown. If the maximum value of $W$ to avoid buckling of the beam AB is obtained as $\beta\pi^2EI$, where $\pi$ is the ratio of circumference to diameter of a circle, then the value of $\beta$ is

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?

The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through O. Its mass moment of inertia is equal to $0.1\ \mathrm{kg}\cdot\mathrm{cm}^2$ about O. A point mass of $0.001$ kg hits it normally at $200$ cm/s at the location shown, and sticks to it. Immediately after the impact, the angular velocity of the rod is ___________ rad/s (in integer).