GATE 2020 ME (Set 1) question paper PDF and answer key

P, Q, R and S are to be uniquely coded using $\alpha$ and $\beta$. If P is coded as $\alpha\alpha$ and Q as $\alpha\beta$, then R and S, respectively, can be coded as _____.

Select the graph that schematically represents BOTH $y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq1$, for integer values of $m$, where $m>1$.

Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. $2,000$ per kg and Rs. $3,000$ per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much as B, and the upper limit for production of B is $10\ \mathrm{kg}$ per day, and ii) the respective state regulations restrict Shveta’s production of A to less than $20\ \mathrm{kg}$ per day, and Ashok’s production of A to less than $15\ \mathrm{kg}$ per day. The demand of both A and B in both the states is very high and everything produced is sold.

The absolute value of the difference in daily (optimal) revenue of Shveta and Ashok is ______________ thousand Rupees (round off to $2$ decimal places).

Consider two cases as below.

Case 1: A company buys $1000$ pieces per year of a certain part from vendor ‘X’. The changeover time is $2$ hours and the price is Rs. $10$ per piece. The holding cost rate per part is $10\%$ per year.

Case 2: For the same part, another vendor ‘Y’ offers a design where the changeover time is $6$ minutes, with a price of Rs. $5$ per piece, and a holding cost rate per part of $100\%$ per year. The order size is $800$ pieces per year from ‘X’ and $200$ pieces per year from ‘Y’.

Assume the cost of downtime as Rs. $200$ per hour. The percentage reduction in the annual cost for Case $2$, as compared to Case $1$ is __________ (round off to $2$ decimal places).

Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter $D$. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: $V=-C\left(r^2-\dfrac{D^2}{4}\right)\ \mathrm{m/s}$, where $C$ is a constant. The rate of kinetic energy (in $\mathrm{J/s}$) at the control surface A-B, as shown in the figure, is proportional to $D^n$. The value of $n$ is ______________.