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

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)

View Question 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 $$100$$ $$N$$ is suspended with the help of a string. The ball is pulled by a horizontal force $$

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

View Question 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

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

View Question For a floating body, buoyant force acts at the

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

View Question 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 $$r = 0.5$$ $$mm$$) carrying electric current

View Question A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ 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 $$500$$ $$K$$ flows over a flat plate of $$1.5$$ $$m$$ length, maintained at $$300

View Question 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{
& 12{x_1} + 4{x_2} \ge 36 \cr
& 12{x_1}

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

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

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

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

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

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

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

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

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

View Question Match the following

View Question 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 $$3$$ $$MPa$$ and $

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

View Question