1
GATE ME 2013
MCQ (Single Correct Answer)
+2
-0.6
Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length $$3$$ $$m,$$ is subjected to a wall heat flux $${q_w}$$ in $$W/{m^2}:$$

If $${q_w}$$ $$=2500x,$$ where $$x$$ is $$m$$ and in the direction of flow ($$x=0$$ at the inlet), the bulk mean temperature of the water leaving the pipe in $$^ \circ C$$ is

A
$$42$$
B
$$62$$
C
$$74$$
D
$$104$$
2
GATE ME 2013
MCQ (Single Correct Answer)
+1
-0.3
In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to
A
$$-1$$
B
zero
C
$$0.5$$
D
$$1.0$$
3
GATE ME 2013
MCQ (Single Correct Answer)
+1
-0.3
Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is $$1$$ $$min.$$ Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in $$min$$ is
A
$$3$$
B
$$4$$
C
$$5$$
D
$$6$$
4
GATE ME 2013
MCQ (Single Correct Answer)
+2
-0.6
A linear programming problem is shown below.
$$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x + 6y \le 8 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x,\,\,y \ge 0 \cr} $$

It has ..............

A
an unbounded objective function
B
exactly one optimal solution
C
exactly two optimal solutions
D
infinitely many optimal solutions
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