GATE ME 2016 Set 1
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## GATE ME

The solution to the system of equations is $$\left[ {\matrix{ 2 &amp; 5 \cr { - 4} &amp; 3 \cr } } \right]\l View Question Consider the function$$f\left( x \right) = 2{x^3} - 3{x^2}\,\,$$in the domain$$\,\left[ { - 1,2} \right].$$The globa View Question Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is$$\mu $$. The standa View Question If$$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 $$x = {\pi View Question Gauss-Seidel method is used to solve the following equations (as per the given order).$$\${x_1} + 2{x_2} + 3{x_3} = 5$$View Question$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$is an analytic function of complex varia View Question The value of the integral$$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$evaluated using c View Question A rigid ball of weight$$100N$$is suspended with the help of a string. The ball is pulled by a horizontal force$$
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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: $$u\left( {x,y,z,t} \right) = \overline View Question A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the flui View Question A plastic sleeve of outer radius$${r_0} = 1\,\,mm$$covers a wire (radius$$r = 0.5mm$$) carrying electric current View Question A steel ball of$$10mm$$diameter at$$1000K$$is required to be cooled to$$350K$$by immersing it in a View Question An infinitely long furnace of$$0.5m \times 0.4m$$cross-section is shown in the figure below. Consider all surfaces of View Question A fluid (Prandtl number,$$Pr=1$$) at$$500K$$flows over a flat plate of$$1.5m$$length, maintained at$$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 $$14. View Question Maximize$$\,\,\,\,Z = 15{x_1} + 20{x_2}$$Subject to$$\eqalign{ &amp; 12{x_1} + 4{x_2} \ge 36 \cr &amp; 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 $$View Question A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s modules for t View Question A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR, RS with coordinates View Question The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in mm4) of this cross-section View Question A simply-supported beam of length$$3L$$is subjected to the loading shown in the figure. It is given that$$P = 1$$View Question The spring constant of a helical compression spring DOES NOT depend on View Question The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is giv View Question A cantilever beam having square cross-section of side$$a$$is subjected to an end load. If a is increases by$$19$$%, t View Question In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2 View Question A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excit View Question A solid disc with radius a is connected to a spring at a point$$d$$above the center of the disc. The other end of the View Question Which of the following statements are TRUE with respect to heat and work?$$(i)$$They are boundary phenomena$$(ii)$$View Question An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the sta View Question The INCORRECT statement about regeneration in vapor power cycle is that View Question In a steam power plant operating on an ideal Rankine cycle, super-heated steam enters the turbine at$$3MPa$$and  View Question Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio$$\l
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