GATE ME 2016 Set 3

## GATE ME

A real square matrix $$A$$ is called skew-symmetric if

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The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{
2 & 1 & 0 \cr
0 & 2 &

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$$\mathop {Lt}\limits_{x \to 0} {{{{\log }_e}\left( {1 + 4x} \right)} \over {{e^{3x}} - 1}}$$ is equal to

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$$\mathop {Lt}\limits_{x \to \infty } \left( {\sqrt {{x^2} + x - 1} - x} \right)$$ is

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The value of the line integral $$\,\,\oint\limits_C {\overrightarrow F .\overrightarrow r ds,\,\,\,} $$ where $$C$$ is a

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Three cards were drawn from a pack of $$52$$ cards. The probability that they are a king, a queen, and a jack is

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The area (in percentage) under standard normal distribution curve of variable $$Z$$ within limits from $$-3$$ to $$+3$$

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The root of the function $$f\left( x \right) = {x^3} + x - 1$$ obtained after first iteration on application of Newton-R

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Solutions of Laplace's equation having continuous second-order partial derivatives are called

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A force $$F$$ is acting on a bent bar which is clamped at one end as shown in the figure.
The CORRECT free body diag

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A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved pa

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An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two

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A rigid rod $$(AB)$$ of length $$L = \sqrt 2 $$ m is undergoing translational as well as rotational motion in the $$ x-

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For a certain two-dimensional incompressible flow, velocity field is given by $$2xy\widehat i - {y^2}\widehat j.$$ The s

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A channel of width $$450$$ $$mm$$ branches into two sub-channels having width $$300$$ $$mm$$ and $$200$$ $$mm$$ as shown

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For a two-dimensional flow, the velocity field is $$\overrightarrow u = {x \over {{x^2} + {y^2}}}\widehat i + {y \over

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The water jet exiting from a stationary tank through a circular opening of diameter $$300$$ $$mm$$ impinges on a rigid w

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Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $$\mu $$ through a circular pip

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Steady one-dimensional heat conduction takes place across the faces $$1$$ and $$3$$ of a composite slab consisting of sl

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A cylindrical steel rod, $$0.01$$ $$m$$ in diameter and $$0.2$$ $$m$$ in length is first heated to $${750^ \circ }C$$ an

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Grashof number signifies the ratio of

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Two large parallel plates having a gap of $$10$$ $$mm$$ in between them are maintained at temperatures $${T_1} = 1000\,\

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For a heat exchanger, $$\Delta {T_{\max }}$$ is the maximum temperature difference and $$\Delta {T_{\min }}$$ is the min

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In $$PERT$$ chart, the activity time distribution is

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The demand for a two-wheeler was $$900$$ units and $$1030$$ units in April $$2015$$ and May $$2015,$$ respectively. The

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A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the

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A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $$25\,m{m^2}.$$. A t

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Which of the bearings given below SHOULD NOT be subjected to a thrust load?

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Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum.

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Engineering strain of a mild steel sample is recorded as $$0.100\% .$$ The true strain is

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Spot welding of two steel sheets each $$2$$ $$mm$$ thick carried out successfully by passing $$4$$ $$kA$$ of current for

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For an orthogonal cutting operation, tool material is $$HSS,$$ rake angle is $${22^ \circ },$$ chip thickness is $$0.8$$

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In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor's expon

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Internal gears are manufactured by

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In a sheet metal of $$2$$ $$mm$$ thickness a hole of $$10$$ $$mm$$ diameter needs to be punched. The yield strength in t

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Match the following part programming codes with their respective functions

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Two optically flat plates of glass are kept at a small angle $$\theta $$ as shown in the figure. Monochromatic light is

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A point $$P\left( {1,\,\,\,3,\,\,\, - 5} \right)$$ is translated by $$2\widehat i + 3\widehat j - 4\widehat k$$ and then

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A square plate of dimension L $$ \times $$ L is subjected to a uniform pressure load P = 250 MPa on its edges as shown i

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The state of stress at a point on an element is shown in figure (a). The same state of stress is shownin another coordin

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The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has fle

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Two circular shafts made of same material, one solid $$(S)$$ and one hollow $$(H)$$, have the same length and polar mome

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A beam of length $$L$$ is carrying a uniformly distributed load $$w$$ per unit length. The flexural rigidity of the beam

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A rigid link $$PQ$$ is undergoing plane motion as shown in the figure ($${V_P}$$ and $${V_Q}$$ are non-zero). $${V_{QP}}

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The number of degrees of freedom in a planner mechanism having $$n$$ links and $$j$$ simple hinge joints is

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The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the accelerat

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A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation

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The INCORRECT statement about the characteristics of critical point of a pure substance is that

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Steam at an initial enthalpy of $$100$$ $$kJ/kg$$ and inlet velocity of $$100$$ $$m/s,$$ enters an insulated horizontal

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The blade and fluid velocities for an axial turbine are as shown in the figure.
The magnitude of absolute velocity at e

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