GATE ME 2016 Set 1

## GATE ME

The solution to the system of equations is $$\left[ {\matrix{
2 & 5 \cr
{ - 4} & 3 \cr
} } \right]\l

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Consider the function $$f\left( x \right) = 2{x^3} - 3{x^2}\,\,$$ in the domain $$\,\left[ { - 1,2} \right].$$ The globa

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Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu $$.
The standa

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If $$y = f(x)$$ satiesfies the boundary value problem $$\,\,y''\,\,\, + \,\,\,9y\,\,\, = \,\,\,0,\,\,\,y\left( 0 \right)

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Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi

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Gauss-Seidel method is used to solve the following equations (as per the given order).
$$${x_1} + 2{x_2} + 3{x_3} = 5$$

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$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$ is an analytic function of complex varia

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The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$
evaluated using c

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A rigid ball of weight $$100$$ $$N$$ is suspended with the help of a string. The ball is pulled by a horizontal force $$

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A point mass $$M$$ is released from rest and slides down a spherical bowl (of radius $$R$$) from a height $$H$$ as shown

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A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coeffic

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A two-member truss $$PQR$$ is supporting a load W. The axial forces in members $$PQ$$ and $$QR$$ are respectively

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For a floating body, buoyant force acts at the

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An inverted U-tube manometer is used to measure the pressure difference between two pipes $$A$$ and $$B,$$ as shown in t

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The instantaneous stream-wise velocity of a turbulent flow is given as follows:
$$$u\left( {x,y,z,t} \right) = \overline

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A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the flui

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A plastic sleeve of outer radius $${r_0} = 1\,\,mm$$ covers a wire (radius $$r = 0.5$$ $$mm$$) carrying electric current

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A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a

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An infinitely long furnace of $$0.5m \times 0.4m$$ cross-section is shown in the figure below. Consider all surfaces of

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A fluid (Prandtl number, $$Pr=1$$) at $$500$$ $$K$$ flows over a flat plate of $$1.5$$ $$m$$ length, maintained at $$300

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The annual demand for an item is $$10,000$$ units. The unit cost is Rs. $$100$$ and inventory carrying charges are $$14.

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Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$
Subject to
$$\eqalign{
& 12{x_1} + 4{x_2} \ge 36 \cr
& 12{x_1}

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The principal stresses at a point inside a solid object are $${\sigma _1} = 100\,\,MPa,\,\,{\sigma _2} = 100\,\,MPa$$ an

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The part of a gating system which regulates the rate of pouring of molten metal is

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Heat is removed from a molten metal of mass $$2$$ $$kg$$ at a constant rate of $$10$$ $$kW$$ till it is completely solid

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A cylindrical job with diameter of $$200$$ $$mm$$ and height of $$100$$ $$mm$$ is to be cast using modulus method of ris

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A $$300$$ $$mm$$ thick slab is being cold rolled ussing roll of $$600$$ $$mm$$ diameter. If the coefficient of friction

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A $$300$$ $$mm$$ thick slab is being cold rolled using roll of $$600$$ $$mm$$ diameter. If the coefficient of friction i

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Under optimal conditions of the process the temperatures experienced by a copper work piece in fusion welding, brazing a

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In an orthogonal cutting process the tool used has rake angle of zero degree. The measured cutting force and thrust forc

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The too life equation for $$HSS$$ tool is $$V{T^{0.14}}\,\,{f^{0.7}}\,\,{d^{0.4}} = $$ Constant. The tool life $$(T)$$ o

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Match the following

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The figure below represents a triangle $$PQR$$ with initial coordinates of the vertices as $$P(1,3),$$ $$Q(4,5)$$ and $$

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A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s modules for t

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A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR, RS with coordinates

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The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in mm4) of this cross-section

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A simply-supported beam of length $$3L$$ is subjected to the loading shown in the figure.
It is given that $$P = 1$$ $

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The spring constant of a helical compression spring DOES NOT depend on

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The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is giv

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A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, t

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In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2

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A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excit

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A solid disc with radius a is connected to a spring at a point $$d$$ above the center of the disc. The other end of the

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Which of the following statements are TRUE with respect to heat and work?
$$(i)$$ They are boundary phenomena
$$(ii)$$

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An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the sta

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The INCORRECT statement about regeneration in vapor power cycle is that

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In a steam power plant operating on an ideal Rankine cycle, super-heated steam enters the turbine at $$3$$ $$MPa$$ and $

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Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio $$\l

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