GATE ME 2016 Set 2

## GATE ME

The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{
2 & 1 \cr
1 & k \cr
} }

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The values of $$x$$ for which the function $$f\left( x \right) = {{{x^2} - 3x - 4} \over {{x^2} + 3x - 4}}$$ is NOT con

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A scalar potential $$\,\,\varphi \,\,$$ has the following gradient: $$\,\,\nabla \varphi = yz\widehat i + xz\widehat j

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The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets con

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Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

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The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,} $$

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The value of $$\oint\limits_\Gamma {{{3z - 5} \over {\left( {z - 1} \right)\left( {z - 2} \right)}}dz} $$ along a close

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A function $$f$$ of the complex variable $$z=x+iy,$$ is given as $$f(x,y)=u(x,y)+iv(x,y),$$
Where $$u(x,y)=2kxy$$ and $

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A point mass having mass $$M$$ is moving with a velocity $$V$$ at an angle $$\mathop \theta \limits^ \cdot $$ to the wa

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A system of particles in motion has mass center $$G$$ as shown in the figure. The particle $$i$$ has mass $${m_i}$$ and

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Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height ca

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Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $$50$$ $$mm$$)

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The volume tric flow rate (per unit depth) between two streamlines having stream functions $${\psi _1}$$ & $${\psi _

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The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such

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Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $$2R \times L$$ at the

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A hollow cylinder has length $$L,$$ inner radius $${{r_1}}$$, outer radius $${{r_2}}$$, and thermal conductivity $$k.$$

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Two cylindrical shafts $$A$$ and $$B$$ at the same initial temperature are simultaneously placed in a furnace. The surfa

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Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the out

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Consider a parallel-flow heat exchanger with area $${A_p}$$ and a counter-flow heat exchanger with area $${A_c}.$$ In bo

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A food processing company uses $$25,000$$ $$kg$$ of corn flour every year. The quantity-discount price of corn flour is

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A project consists of $$14$$ activities, $$A$$ to $$N$$. The duration of these activities (in days) are shown in bracket

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In a single-channel queuing model, the customer arrival rate is $$12$$ per hour and the serving rate is $$24$$ per hour.

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A machine element $$XY,$$ fixed at end $$X,$$ is subjected to an axial load $$P,$$ transverse load $$F,$$ and a twisting

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In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $$50$

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The force $${F_1}$$ and $${F_2}$$ in a brake band and the direction of rotation of the drum are as shown in the figure.

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For the brake shown in the figure, which one of the following is TRUE?

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A mass of $$2000$$ kg is currently being lowered at a velocity of $$2$$ $$m/s$$ from the drum as shown in the figure. Th

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The welding process which uses a blanket of fusible granular flux is

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Gray cast iron blocks of size $$100\,\,mm \times 50\,\,mm \times 10\,\,mm$$ with a central spherical cavity of diameter

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The value of true strain produced in compressing a cylinder to half its original length is

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The voltage - length characteristic of a direct current arc in an arc welding process is $$V=$$ $$(100+40l),$$ where $$l

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For a certain job, the cost of metal cutting is $$Rs.18C/V$$ and the cost of tooling is Rs.$$270C/(TV).$$ Where $$C$$ is

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The following data is applicable for a turning operation. The length of job is $$900$$ $$mm,$$ diameter of job is $$200$

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For the situation shown in the figure below the expression for $$H$$ in terms of $$r, R$$ and $$D$$ is

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In the figure, the load P = 1 N, length L = 1 m, Young’s modulus E = 70 GPa, and the cross-section of the links is a squ

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A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is

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A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the

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A rigid horizontal rod of length $$2L$$ is fixed to a circular cylinder of radius $$R$$ as shown in the figure. Vertical

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A simply supported beam of length $$2L$$ is subjected to a moment $$M$$ at the mid-point $$x = 0$$ as shown in the figur

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A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoo

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A single degree of freedom mass-spring - viscous damper system with mass $$m,$$ spring constant $$k$$ and viscous dampin

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The rod AB, of length 1 m, shown in the figure is connected to two sliders at each end through pins. The sliders can sli

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The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing ov

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The internal energy of an ideal gas is a function of

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A piston-cylinder device initially contains $$0.4\,{m^3}$$ of air (to be treated as an ideal gas) at $$100$$ $$kPa$$ and

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The heat removal rate from a refrigerated space and the power input to the compressor are $$7.2$$ $$kW$$ and $$1.8$$ $$k

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A reversible cycle receives $$40$$ $$kJ$$ of heat from one heat source at a temperature of $${127^ \circ }C$$ and $$37$$

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