GATE ME 2015 Set 2

## GATE ME

At least one eigenvalue of a singular matrix is

View Question At $$x=0,$$ the function $$f\left( x \right) = \left| x \right|$$ has

View Question The surface integral $$\,\,\int {\int\limits_s {{1 \over \pi }} } \left( {9xi - 3yj} \right).n\,dS\,\,$$ over the spher

View Question Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is

View Question The chance of a student passing an exam is $$20$$% The chance of a student passing the exam and getting above $$90$$% ma

View Question Consider the following differential equation $${{dy} \over {dt}} = - 5y;$$ initial condition: $$y=2$$ at $$t=0.$$
The

View Question The values of function $$(x)$$ at $$5$$ discrete points are given below:
Using Trapezodial rule with step size of $$0.

View Question The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

View Question Laplace transform of $$\cos \left( {\omega t} \right)$$ is

View Question A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of m

View Question The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expressi

View Question For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is

View Question If the fluid velocity for a potential flow is given by $$V\left( {x,y} \right) = u\left( {x,y} \right)i + v\left( {x,y}

View Question For a fully developed laminar flow of water (dynamic viscosity $$0.001$$ $$Pa$$-s) through a pipe of radius $$5$$ $$cm,$

View Question The head loss for a laminar incompressible flow through a horizontal circular pipe is $${h_1}$$. Pipe length and fluid r

View Question Within a boundary layer for a steady incompressible flow, the Bernoulli equation

View Question If a foam insulation is added to a $$4cm$$ outer diameter pipe as shown as figure, the critical radius of insulation (i

View Question A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of $$4 \times {10^7}\,

View Question In the laminar flow of air $$(Pr=0.7)$$ over a heated plate, if $$\delta $$ and $${\delta _T}$$ denote, respectively the

View Question The total emissive power of a surface is $$500$$ $$W/{m^2}$$ at a temperature $${T_1}$$ and $$1200$$ $$W/{m^2}$$ at a
te

View Question A balanced counter-flow heat exchanger has a surface area of $$20\,\,{m^2}$$ and overall heat transfer coefficient of $$

View Question Annual demand of a product is $$50,000$$ units and the ordering cost is Rs. $$7,000$$ per order. Considering the basic e

View Question A project consists of $$7$$ activities. The network along with the time durations (in days) for various activities is sh

View Question Sales data of a product is given in the following table:
Regarding forecast for the month of June, which one of the f

View Question A manufacturer has the following data regarding a product:
Fixed cost per month $$=$$ Rs. $$50,000$$
Variable cost per u

View Question The uniaxial yield stress of a material is $$300$$ $$MPa.$$ According to Von mises criterion, the shear yield stress $$(

View Question A cube and a sphere made of cast iron (each of volume $$1000\,\,c{m^3}$$) were cast under identical conditions. The time

View Question In a two stage wire drawing operation, the fractional reduction (ratio of change in cross sectional area to initial cros

View Question The flowing stress (in $$MPa$$) of a material is given by $$\sigma = 500{\varepsilon ^{0.1}},$$
When $$\varepsilon $$

View Question During a $$TIG$$ welding process, the arc current and arc voltage were $$50$$ $$A$$ and $$60$$ $$V,$$ respectively, when

View Question A single point cutting tool with $${0^0}$$ rake angle is used in an orthogonal machining process. At a cutting speed of

View Question Which one of the following statements is TRUE?

View Question During the development of a product, an entirely new process plan is made based on design logic, examination of geometry

View Question A drill is positioned at point $$P$$ and it has to proceed to point $$Q.$$ The coordinates of point $$Q$$ in the increme

View Question A rod is subjected to an uniaxial load within linear elastic limit. When the change in the stress is $$200$$ MPa, the ch

View Question In a plane stress condition, the components of stress at a point are $${\sigma _x} = 20$$ MPa, $${\sigma _y} = 80$$ MPa

View Question A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of $$10$$ kN is applied

View Question The deflection of a spring with 20 active turns under a load of 1000 N is 10 mm. The spring is made into two pieces each

View Question A hollow shaft (d0 = $$2$$di, where d0 and di are the outer and inner diameters respectively) needs to transmit $$20$$ k

View Question A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the

View Question A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible an

View Question A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2kN normal to the top surface as show

View Question A gas is stored in a cylindrical tank of inner radius $$7$$ m and wall thickness $$50$$ mm. The gage pressure of the gas

View Question The number of degrees of freedom of the planetary gear train shown in the figure is

View Question In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform

View Question In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system i

View Question A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\ome

View Question The Vander-waals equation of state is $$\left( {p + {a \over {{v^2}}}} \right)\left( {v - b} \right) = RT,$$ where $$p$$

View Question Work is done on an adiabatic system due to which its velocity changes from $$10$$ $$m/s$$ to $$20$$ $$m/s,$$ elevation i

View Question The $$COP$$ of a Carnot heat pump operating between $${6^ \circ }C$$ and $${37^ \circ }C$$ is ____________

View Question One kg of air ($${R = 287\,\,J/kg}$$-$$K$$) under goes irreversible process between equilibrium state $$1\,\,\left( {{{2

View Question Which of the following statements regarding a Rankine cycle with reheating are TRUE?
(i) increase in average temperature

View Question In a Rankine cycle, the enthalpies at turbine entry and outlet are $$3159$$ $$kJ/kg$$ and $$2187$$ $$kJ/kg$$ respectivel

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