Solve the system $$2x+3y+z=9,$$ $$4x+y=7,$$ $$x-3y-7z=6$$

Among the following, the pair of vectors orthogonal to each other is

The area bounded by the parabola $$2y = {x^2}$$ and the lines $$x=y-4$$ is equal to _________.

If $$\overrightarrow V $$ is a differentiable vector function and $$f$$ is sufficienty differentiable scalar function then curl $$\left( {f\overrightarrow V } \right) = $$ _______.

The solution to the differential equation $$\,{f^{11}}\left( x \right) + 4{f^1}\left( x \right) + 4f\left( x \right) = 0$$

A differential equation of the form $${{dy} \over {dx}} = f\left( {x,y} \right)\,\,$$ is homogeneous if the function $$f(x,y)$$ depends only on the ratio $${y \over x}$$ (or) $${x \over y}$$

A spring scale indicates a tension $$T$$ in the right hand cable of the pulley system shown in figure below. Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass $$m$$ is

A fluid is said to be Newtonian fluid when the shear stress is

The velocity components in the $$x$$ and $$y$$ directions are given by $$u = \lambda x{y^3} - {x^2}y,$$ $$v = x{y^2} - {3 \over 4}{y^4}.$$ The value of $$\lambda $$ for a possible flow field involving an incompressible fluid is

The force $$F$$ needed to support the liquid of density $$d$$ and the vessel on top (fig) is

In fully developed laminar flow in the circular pipe, the head loss due to friction is directly proportional to ....... (Mean velocity/square of the mean velocity)

Consider two large parallel plates, one at $${T_1} = {727^ \circ }C$$ with emissivity $${\varepsilon _1} = 0.8$$ and the other at $${T_2} = {227^ \circ }C\,$$ with emissivity $${\varepsilon _2} = 0.4.$$ An aluminium radiation shield with an emissivity, $${\varepsilon _s} = 0.05$$ on both sides is placed between the plates. Calculate the percentage reduction in heat transfer rate between the two plates as a result of the shield.
Use $$\sigma = 5.67 \times {10^{ - 8}}W/\left( {{m^2}{K^4}} \right)$$

A counter flow heat exchanger is to heat air entering at $${400^ \circ }C$$ with a flow rate of $$6$$ $$kg/s$$ by the exhaust gas entering at $${800^ \circ }C$$ with a flow rate of $$4$$ $$kg/s$$. The overall heat transfer coefficient is $${100^ \circ }C$$ $$W/\left( {{m^2}K} \right)$$ and the outlet temperature of the air is $${551.5^ \circ }C.$$ Specific heat at constant pressure for both air and the exhaust gas can be taken as $$1100$$ $$J/(kgK).$$ Calculate the heat transfer area needed and the number of transfer units.

If the demand for an item is doubled and the ordering cost halved, the economic order quantity

Consider the following data for a product:
Demand $$=1000$$ units/year
Order cost $$=$$ Rs.$$40$$/order
Holding cost $$ = 10\% $$ of the unit cost / unit-year
Unit cost $$=$$ Rs.$$500$$

(a) What is the economic order quantity?
(b) Under the $$EOQ$$ what is the number of annual orders?
(c) With a policy of ordering every month what would be the total annual cost as a percentage of the cost at $$EOQ$$?

In $$PERT,$$ the distribution of activity times is assumed to be

A project with the following data is to be implemented:

(a) What is the minimum duration of the project?
(b) Draw a Gantt chart for the early schedule
(c) Determine the peak requirement of money and the day on which it occurs in above schedule.

On the average $$100$$ customers arrive at a place each hour, and on the average the server can process $$120$$ customers per hour. What is the proportion of time the server is idle?

The manufacturing area of a plant is divided into four quadrants. Four machines have to located one in each quadrant. The total number of possible layouts is

Interference in a pair of gears is avoided, if the addendum circles of both the gears intersect common tangent to the base circles with in the points of tangency.

Match the following:
List-$${\rm I}$$
(A) Worm gears
(B) Cross helical gears
(C) Bevel gears
(D) Spur gears

List-$${\rm I}{\rm I}$$
1. Parallel shafts
2. Non-parallel, intersecting shafts
3. Non-parallel, non-intersecting shafts
4. Large speed ratios

Machine tool, structures are made ................. for high process capability (tough/ rigid/ strong)

A test specimen is stressed slightly beyond the yield point and then unloaded. Its yield strength

Cutting power consumption in turning can be signification reduced by

A single point turning tool is designated as $$${10^ \circ } - {12^ \circ } - {7^ \circ } - {5^ \circ } - {20^ \circ } - {50^ \circ } - {0^ \circ }\left( {ORS} \right)$$$
The values of normal rake and normal clearance of the above mentioned tool .............

If under a condition of plain turning the life of the cutting tool decreases by $$50\% $$ due to increase in the cutting velocity by $$20\% $$, then what is the $$\% $$ increase in tool life due to reduction in the cutting velocity by $$20%$$ from its original value.

While turning a $$C15$$ steel of $$160mm$$ diameter at $$215rpm,$$ $$2.5mm$$ depth of cut and feed of $$0.16mm/rev$$ by a tool of geometry $$0-10-8-9-15-75-0mm,$$ the following observations were made. Tangential component of the cutting force $$=500N,$$ axial component of the cutting force $$=200N,$$ chip thickness $$=0.48mm.$$ Determine the dynamic shear strength of the work piece material.

Diamond wheels should not be used for grinding steel components

Among the conventional machining processes, maximum specific energy is consumed in

Plain milling of mild steel plates produces

Determine the transformation ratio $$(TR)$$ of the gear train connecting the spindle and the lead screw of $$4TPI$$ required to cut $$1.0mm$$ pitch screw threads in a center lathe

Slip gauges are calibrated by outside micrometer

Checking the diameter of a hole using GO and NOGO gauges is an example of inspection by …………… (variables/attributes)

A free bar of length 1 m is uniformly heated from $${0^ \circ }C$$ to a temperature of $${t^ \circ }C$$. $$\alpha $$ is the coefficient if linear expansion and $$E$$ the modulus of elasticity. The stress in the bar is

Fig. shows a quick return mechanism. The crank $$OA$$ rotates clockwise uniformly. $$OA=2$$ cm, $$O{O^1} = 4$$ cm. The ratio of time for forward motion to that for return motion is

List $$I$$ (Gear types)
(a) Worm gears
(b) Cross helical gears
(c) Bevel gears
(d) Spur gears

List $$II$$ (Applications)
1. Parallel shafts
2. Non-parallel, intersecting shafts
3. Non-parallel, non intersecting shafts
4. Large speed ratios

The arm OA of an epicylic gear train shown in Fig. revolves counter clockwise about O with an angular velocity of 4 rad/sec. Both gears are of same size. The angular velocity of gear C, if the sun gear B is fixed, is

In adiabatic flow with friction, the stagnation temperature along a streamline ____________ (increase / remains constant)

Consider a Rankine cycle with superheat. If the maximum pressure in the cycle is increased without changing the maximum temperature and the minimum pressure, the dryness fraction of stream after the isentropic expansion will increase / decrease _____________

Dry saturated steam enters a friction-less adiabatic nozzle with negligible velocity at a temperature of $${300^ \circ }C.$$ It is expanded to a pressure of $$5000$$ $$kPa.$$ The mass flow rate is $$1$$ $$kg/s$$. Calculate the exit velocity of steam.

A heat reservoir at $$900$$ $$K$$ is brought into contact with the ambient at $$300$$ $$K$$ for a short time. During this period $$9000$$ $$kJ$$ of heat is lost by the heat reservoir. The total loss in availability due to this process is

Constant pressure lines in the super-heated region of the Mollier diagram will have

Consider a refrigerator and a heat pump working on the reversed Carnot cycle between the same temperature limits. Which of the following is correct?

In the case of a refrigeration system undergoing an irreversible cycle, $$\oint {{{SQ} \over T}} $$ is _____________$$\left( { < 0/ = 0/ > 0} \right)$$

One kilomole of an ideal gas is throttled from an initial pressure of $$0.5$$ $$MPa$$ to $$0.1$$ $$MPa.$$ The initial temperature is $$300$$ $$K.$$ The entropy change of the universe is: