GATE ME 2017 Set 2

## GATE ME

The determinant of a $$2 \times 2$$ matrix is $$50.$$ If one eigenvalue of the matrix is $$10,$$ the other eigenvalue is

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Consider the matrix $$A = \left[ {\matrix{
{50} & {70} \cr
{70} & {80} \cr
} } \right]$$ whose eigen

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The surface integral $$\int {\int\limits_s {F.ndS} } $$ over the surface $$S$$ of the sphere $${x^2} + {y^2} + {z^2} =

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Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is

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A simple of $$15$$ data is as follows; $$17,18,17,17,13,18,5,5,6,7,8,9,20,17,3.$$ The mode of the data is

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Consider the differential equation $$\,\,3y''\left( x \right) + 27y\left( x \right) = 0\,\,$$ with initial conditions $$

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If $$f\left( z \right) = \left( {{x^2} + a{y^2}} \right) + ibxy$$ is a complex analytic function of $$z=x+iy,$$
where $

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The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown i

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For the stability of a floating body the

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A $$60$$ $$mm$$ $$-$$ diameter water jet strikes a plate containing a hole of $$40mm$$ diameter as shown in the figure.

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The arrangement shown in the figure measures the velocity $$V$$ of a gas of density $$1kg/{m^3}$$ flowing through a pipe

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Consider a laminar flow at zero over a flat plate . The shear stress at the wall is denoted by $${\tau _w}.$$ The axial

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The heat loss from a fin is $$6W.$$ The effectiveness of the fin are $$3$$ and $$0.75,$$ respectively. The heat loss (in

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A metal ball of diameter $$60mm$$ is initially at $${220^ \circ }C.$$ The ball is suddenly cooled by an air jet of $${20

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The emissive power of a blackbody is $$P.$$ If its absolute temperature is doubled, the emissive power becomes

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In a counter-flow heat exchanger, water is heated at the rate of $$1.5kg/s$$ from $$\,40{}^ \circ C\,$$ to $$\,80{}^ \ci

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The standard deviation of linear dimensions $$P$$ and $$Q$$ are $$3\mu m$$ and $$4\mu m$$, respectively. When assembled,

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A project starts with activity $$A$$ and ends with activity $$F.$$ The precedence relation and durations of the activiti

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For a single server with Poisson arrival and exponential service time, the arrival rate is $$12$$ per hour. Which one of

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Maximize $$\,\,\,\,\,\,\,\,\,Z = 5{x_1} + 3{x_2}$$
Subject to $$\,\,\,\,\,\,\,\,\,\,{x_1} + 2{x_2} \le 10,$$
$$\eqalign

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A product made in two factories $$P$$ and $$Q,$$ is transported to two destinations, $$R$$ and $$S.$$ The per unit costs

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The principal stresses at a point in a critical section of a machine component are $${\sigma _1} = 60\,\,MPa,\,\,{\sigma

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A machine component made of a ductile material is subjected to a variable loading with $${\sigma _{\min }} = - 50MPa$$

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A steel plate, connected to a fixed channel using three identical bolts $$A, B$$ and $$C,$$ carries a load of $$6kN$$ as

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A single – plate clutch has a friction disc with inner and outer radii of $$20mm$$ and $$40$$ $$mm,$$ respectively. The

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It is desired to make a product having T-shaped cross - section from a rectangular aluminium block. Which one of the fol

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A strip of $$120mm$$ width and $$8mm$$ thickness is rolled between two $$300$$ $$mm$$-diameter rolls to get a strip of $

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A rod of length $$20$$ $$mm$$ is stretched to make a rod of length $$40$$ $$mm.$$ Subsequently, it is compressed to make

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In an orthogonal machining with a tool of $${9^ \circ }$$ orthogonal rake angle, the uncut chip thickness is $$0.2$$ $$m

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During the turning of a $$20$$ $$mm-$$diameter steel bar at a spindle speed of $$400$$ $$rpm,$$ a tool life of $$20$$ mi

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A cylindrical pin $$25_{ + 0.010}^{ + 0.020}\,\,mm$$ diameter is electroplated. Plating thickness is
$${2.0^{ \pm 0.0

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A steel bar is held by two fixed supports as shown in the figure and is subjected to an increases of temperature $$\Delt

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The state of stress at a point is $${\sigma _x} = {\sigma _y} = {\sigma _z} = {\tau _{xz}} = {\tau _{zx}} = {\tau _{yz}}

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For a loaded cantilever beam of uniform cross-section, the bending moment (in N-mm) along the length is M(x) = 5x2+10x,

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A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shea

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A cantilever beam of length $$L$$ and flexural modulus $$EI$$ is subjected to a point load $$P$$ at the free end. The el

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In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100mm and 160mm, respectively. The cran

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Block 2 slides outward on link 1 at a uniform velocity of 6m/s as shown in the figure. Link 1 is rotating at a constant

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A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All t

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A mass $$m$$ is attached to two identical springs having spring constant $$k$$ as shown in the figure. The natural frequ

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The radius of gyration of a compound pendulum about the point of suspension is $$100$$ mm. The distance between the poin

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The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is $$2.87{m^3}$$ and $$300$$ $$K,$$ re

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A calorically perfect gas (specific heat at constant pressure $$1000$$$$J/kg.K$$) enters and leaves a gas turbine with t

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A mass $$m$$ of a perfect gas at pressure $${p_1}$$ and volume $${V_1}$$ undergoes an isothermal process. The final pres

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One $$kg$$ of an ideal gas (gas constant $$R=287$$ $$J/kg$$-$$K$$) undergoes an irreversible process from state- $${\rm

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In the Rankine cycle for a system power plant the turbine entry and exit enthalpies are $$2803$$ $$kJ/kg$$ and $$1800$$

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Which one of the following statement is TRUE?

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