GATE ME 2017 Set 1

## GATE ME

The product of eigenvalues of the matrix $$P$$ is $$P = \left[ {\matrix{
2 & 0 & 1 \cr
4 & { - 3} &a

View Question The value of $$\mathop {\lim }\limits_{x \to 0} \left( {{{{x^3} - \sin \left( x \right)} \over x}} \right)$$ is

View Question A parametric curve defined by $$x = \cos \left( {{{\pi u} \over 2}} \right),y = \sin \left( {{{\pi u} \over 2}} \right)\

View Question For the vector $$\overrightarrow V = 2yz\widehat i + 3xz\widehat j + 4xy\widehat k,$$ the value of $$\,\nabla .\left( {

View Question A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________.

View Question The differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 16y = 0$$ for $$y(x)$$ with the two boundary conditions $${\le

View Question Consider the following partial differential equation for $$u(x,y)$$ with the constant $$c>1:$$ $$\,{{\partial u} \ove

View Question $$\,\,P\,\,\,\left( {0,3} \right),\,\,Q\,\,\,\left( {0.5,4} \right),\,\,$$ and $$\,\,R\,\,\,\left( {1,5} \right)\,\,\,$

View Question A Particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $$r\left( t \right) = {t

View Question The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered

View Question Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical

View Question Consider the two-dimensional velocity field given by
$$\overrightarrow V = \left( {5 + {a_1}x + {b_1}y} \right)\wideha

View Question For a steady flow, the velocity field is $$\overrightarrow V = \left( { - {x^2} + 3y} \right)\widehat i + \left( {2xy}

View Question For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in

View Question Consider steady flow of an incompressible fluid through two long and straight pipes of diameters $${d_1}$$ and $${d_2}$$

View Question The velocity profile inside the boundary layer for flow over a flat plate is given as $${u \over {{U_\infty }}} = \sin \

View Question Heat is generated uniformly in a long solid cylindrical rod ( diameter $$ = 10\,\,mm$$) at the rate of $$4 \times {10^7}

View Question Two black surfaces, $$AB$$ and $$BC,$$ of lengths $$5m$$ and $$6m,$$ respectively, are oriented as shown. Both surfaces

View Question Saturated steam at $${100^ \circ }C$$ condenses on the outside of a tube. Cold fluid enters the tube at $${20^ \circ }C$

View Question Two models, $$P$$ and $$Q,$$ of a product earn profits of Rs. $$100$$ and Rs. $$80$$ per piece, respectively. Production

View Question Following data refers to the jobs $$(P, Q, R, S)$$ which have arrived at a machine for scheduling. The shortest possible

View Question Consider the schematic of a riveted lap joint subjected to tensile load $$F,$$ as shown below. Let $$d$$ be the diameter

View Question A machine element has an ultimate strength $$\left( {{\sigma _u}} \right)$$ of $$600\,\,N/m{m^2},$$ and endurance limit

View Question A sprue in a sand mould has a top diameter of $$20mm$$ and height of $$200mm.$$ The velocity of the molten metal at the

View Question In a metal forming operation when the material has just started yielding, the principal stresses are $${\sigma _1} = \,\

View Question In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sec

View Question Two cutting tools with tool life equations given below are being compared:
$$\eqalign{
& Tool\,\,1:\,\,\,\,\,\,\,

View Question Metric thread of $$0.8$$ $$mm$$ pitch is to be cut on a lathe. Pitch of the lead screw is $$1.5$$ $$mm.$$ If the spindle

View Question A block of length $$200$$ $$mm$$ is machined by a slab milling cutter $$34$$ $$mm$$ in diameter. The depth of cut and ta

View Question A $$10$$ $$mm$$ deep cylindrical cup with diameter of $$15$$ $$mm$$ is drawn from a circular blank. Neglecting the varia

View Question Cylindrical pins of diameter $${15^{ \pm 0.020}}\,\,mm$$ are being produced on a machine. Statistical quality control te

View Question Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley heig

View Question Circular arc on a part profile is being machined on a vertical $$CNC$$ milling machine. $$CNC$$ part program using metri

View Question In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength $$(UTS)$$ refers to

View Question The Poisson's ratio for a perfectly incompressible linear elastic material is

View Question A point mass of $$100$$ kg is dropped onto a massless elastic bar (cross-sectional area = $$100$$ $$mm$$2 ,length = $$1$

View Question A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm2. Its elastic modulu

View Question A rectangular region in a solid is in a state of plane strain. The $$(x,y)$$ coordinates of the corners of the undeforme

View Question Consider a beam with circular cross-section of diameter $$d.$$ The ratio of the second moment of area about the neutral

View Question A motor driving a solid circular steel shaft transmits $$40$$ $$kW$$ of power at $$500$$ $$rpm$$. If the diameter of the

View Question An initially stress-free massless elastic beam of length $$L$$ and circular cross-section with diameter $$d (d < <

View Question For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3 m and 4 m respectively. At the i

View Question In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwi

View Question The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}}

View Question A thin uniform rigid bar of length $$L$$ and mass $$M$$ is hinged at point $$O,$$ located at a distance of $${L \over 3}

View Question The molar specific heat at constant volume of an ideal gas is equal to $$2.5$$ times the universal gas constant ($$8.314

View Question Water (density $$ = 1000$$ $$kg/{m^3}$$) at ambient temperature flows through a horizontal pipe of uniform cross section

View Question One $$kg$$ of an ideal gas (gas constant, $$R = 400$$ $$J/kg.K;$$ specific heat at constant volume, $${c_v} = 1000\,J/kg

View Question A heat pump absorbs $$10$$ $$kW$$ of heat from outside environment at $$250$$ $$K$$ while absorbing $$15$$ $$kW$$ of wor

View Question Which one of the following is NOT a rotating machine?

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