GATE 2021 ME (Set 1) question paper PDF and answer key

Ms. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing _________

Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.

The number of distinct seating arrangements possible is:

An uninsulated cylindrical wire of radius $1.0\ \mathrm{mm}$ produces electric heating at the rate of $5.0\ \mathrm{W/m}$. The temperature of the surface of the wire is $75\ ^\circ\mathrm{C}$ when placed in air at $25\ ^\circ\mathrm{C}$. When the wire is coated with PVC of thickness $1.0\ \mathrm{mm}$, the temperature of the surface of the wire reduces to $55\ ^\circ\mathrm{C}$. Assume that the heat generation rate from the wire and the convective heat transfer coefficient are same for both uninsulated wire and the coated wire. The thermal conductivity of PVC is __________ $\mathrm{W/(m\,K)}$ (round off to two decimal places).

A solid sphere of radius $10\ \mathrm{mm}$ is placed at the centroid of a hollow cubical enclosure of side length $30\ \mathrm{mm}$. The outer surface of the sphere is denoted by $1$ and the inner surface of the cube is denoted by $2$. The view factor $F_{22}$ for radiation heat transfer is __________ (rounded off to two decimal places).

A cylindrical jet of water (density $=1000\ \mathrm{kg/m^3}$) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a linear spring with a spring constant $k=1\ \mathrm{kN/m}$. The incoming jet diameter is $D=1\ \mathrm{cm}$.

If the spring shows a steady deflection of $1\ \mathrm{cm}$ upon impingement of jet, then the velocity of the incoming jet is __________ $\mathrm{m/s}$ (round off to one decimal place).