GATE 2016 Mechanical Engineering

A cylindrical job with diameter of $$200$$ $$mm$$ and height of $$100$$ $$mm$$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical ris...

A $$300$$ $$mm$$ thick slab is being cold rolled ussing roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _...

A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a water environment at $$300$$ $$K.$$ The convective heat tran...

$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$ is an analytic function of complex variable $$z=x+iy$$ , where $$i = \sqrt { - 1} $$ If $$u(x,y)=2xy,...

The instantaneous stream-wise velocity of a turbulent flow is given as follows: $$$u\left( {x,y,z,t} \right) = \overline u \left( {x,y,z} \right) + \mu '\left( {x,y,z,t} \right)$$$...

The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$ evaluated using contour integration and the residue theorem is

The annual demand for an item is $$10,000$$ units. The unit cost is Rs. $$100$$ and inventory carrying charges are $$14.4\% $$ of the unit cost per annum. The cost of one procureme...

The solution to the system of equations is $$\left[ {\matrix{ 2 & 5 \cr { - 4} & 3 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\} = \left\{ {\matrix{ 2 \cr { - 30} \cr }...

If $$y = f(x)$$ satiesfies the boundary value problem $$\,\,y''\,\,\, + \,\,\,9y\,\,\, = \,\,\,0,\,\,\,y\left( 0 \right)\,\,\, = \,\,\,0,\,$$ $$\,\,y\left( {{\pi \over 2}} \right)...

The too life equation for $$HSS$$ tool is $$V{T^{0.14}}\,\,{f^{0.7}}\,\,{d^{0.4}} = $$ Constant. The tool life $$(T)$$ of $$30$$ $$min$$ is obtained using the following cutting con...

For a floating body, buoyant force acts at the

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $$1$$) and at the end (subscript $$2$$) of the...

Which of the following statements are TRUE with respect to heat and work? $$(i)$$ They are boundary phenomena $$(ii)$$ They are exact differentials $$(iii)$$ They are path function...

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

In a steam power plant operating on an ideal Rankine cycle, super-heated steam enters the turbine at $$3$$ $$MPa$$ and $${350^ \circ }C.$$ The condenser pressure is $$75$$ $$kPa.$$...

The INCORRECT statement about regeneration in vapor power cycle is that

Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first...

Under optimal conditions of the process the temperatures experienced by a copper work piece in fusion welding, brazing and soldering are such that

Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$ Subject to $$\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$ The...

Gauss-Seidel method is used to solve the following equations (as per the given order). $$${x_1} + 2{x_2} + 3{x_3} = 5$$$ $$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$$\,3{x_1} + 2{x_2} + {x...

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu $$. The standard deviation for this distribution is given by

The principal stresses at a point inside a solid object are $${\sigma _1} = 100\,\,MPa,\,\,{\sigma _2} = 100\,\,MPa$$ and $${\sigma _3} = 0\,\,MPa.$$ The yield strength of the mate...

A fluid (Prandtl number, $$Pr=1$$) at $$500$$ $$K$$ flows over a flat plate of $$1.5$$ $$m$$ length, maintained at $$300$$ $$K.$$ The velocity of the fluid is $$10\,\,m/s.$$ Assumi...

A $$300$$ $$mm$$ thick slab is being cold rolled using roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is __...

A plastic sleeve of outer radius $${r_0} = 1\,\,mm$$ covers a wire (radius $$r = 0.5$$ $$mm$$) carrying electric current. Thermal conductivity of the plastic is $$0.15\,\,W/m$$-$$K...

Consider the function $$f\left( x \right) = 2{x^3} - 3{x^2}\,\,$$ in the domain $$\,\left[ { - 1,2} \right].$$ The global minimum of $$f(x)$$ is _________.

In an orthogonal cutting process the tool used has rake angle of zero degree. The measured cutting force and thrust force are $$500$$ $$N$$ and $$250$$ $$N,$$ respectively. The coe...

A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, the tip deflection decreases approximately by

The spring constant of a helical compression spring DOES NOT depend on

A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping...

Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $$50$$ $$mm$$). The top plate is sliding parallel to the stationary bottom...

In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $$50$$ $$MPa$$ and $$150$$ $$MPa,$$ respectively. The endurance,...

A hollow cylinder has length $$L,$$ inner radius $${{r_1}}$$, outer radius $${{r_2}}$$, and thermal conductivity $$k.$$ The thermal resistance of the cylinder for radial conduction...

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

The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & k \cr } } \right]$$ are positive, is

In a single-channel queuing model, the customer arrival rate is $$12$$ per hour and the serving rate is $$24$$ per hour. The expected time that a customer is in queue is _______ mi...

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is $${R_0}$$ and that of the inner cylinder is $...

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

Consider a parallel-flow heat exchanger with area $${A_p}$$ and a counter-flow heat exchanger with area $${A_c}.$$ In both the heat exchangers, the hot stream flowing at $$1$$ $$kg...

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

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

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

A scalar potential $$\,\,\varphi \,\,$$ has the following gradient: $$\,\,\nabla \varphi = yz\widehat i + xz\widehat j + xy\widehat k.\,\,$$ Consider the integral $$\,\,\int_C {\na...

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 a constant, $$V$$ is the cutting speed in $$m/min$$ and $$T...

The volume tric flow rate (per unit depth) between two streamlines having stream functions $${\psi _1}$$ & $${\psi _2}$$ is

The internal energy of an ideal gas is a function of

The heat removal rate from a refrigerated space and the power input to the compressor are $$7.2$$ $$kW$$ and $$1.8$$ $$kW$$, respectively. The coefficient of performance $$(COP)$$...

A reversible cycle receives $$40$$ $$kJ$$ of heat from one heat source at a temperature of $${127^ \circ }C$$ and $$37$$ $$kJ$$ from another heat source at $${97^ \circ }C.$$ The h...

A piston-cylinder device initially contains $$0.4\,{m^3}$$ of air (to be treated as an ideal gas) at $$100$$ $$kPa$$ and $${80^ \circ }C.$$ The air is now isothermally compressed t...

Gray cast iron blocks of size $$100\,\,mm \times 50\,\,mm \times 10\,\,mm$$ with a central spherical cavity of diameter $$4$$ mm are sand cast. The shrinkage allowance for the patt...

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 $$v(x,y)$$ $$ = {x^2} - {y^2}.$$ The value of $$k,$$ for which...

The value of $$\oint\limits_\Gamma {{{3z - 5} \over {\left( {z - 1} \right)\left( {z - 2} \right)}}dz} $$ along a closed path $$\Gamma $$ is equal to $$\left( {4\pi i} \right),$$ w...

The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets containing $$5$$ screws and gives a guarantee of replacement if...

The following data is applicable for a turning operation. The length of job is $$900$$ $$mm,$$ diameter of job is $$200$$ $$mm,$$ feed rate is $$0.25$$ $$mm/rev$$ and optimum cutti...

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is

The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,} $$ using the trapezoidal rule with three intervals of equal len...

A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is

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

For an orthogonal cutting operation, tool material is $$HSS,$$ rake angle is $${22^ \circ },$$ chip thickness is $$0.8$$ $$mm,$$ speed is $$48$$ $$m/min$$ and feed is $$0.4$$ $$mm/...

Grashof number signifies the ratio of

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

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

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

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

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

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $$\mu $$ through a circular pipe of radius $$R.$$ Given that the velocity at a radial locat...

Two large parallel plates having a gap of $$10$$ $$mm$$ in between them are maintained at temperatures $${T_1} = 1000\,\,K$$ and $${T_2} = 400\,\,K$$ Given emissivity values, $${\v...

In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor's exponent is $$0.25.$$ If the cutting speed is reduced by $$50\% $...

A point $$P\left( {1,\,\,\,3,\,\,\, - 5} \right)$$ is translated by $$2\widehat i + 3\widehat j - 4\widehat k$$ and then rotated counter clockwise by $${90^ \circ }$$ about the $$z...

In a sheet metal of $$2$$ $$mm$$ thickness a hole of $$10$$ $$mm$$ diameter needs to be punched. The yield strength in tension of the sheet material is $$100$$ $$MPa$$ and its ulti...

For a certain two-dimensional incompressible flow, velocity field is given by $$2xy\widehat i - {y^2}\widehat j.$$ The streamlines for this flow are given by the family of curves

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

Steam at an initial enthalpy of $$100$$ $$kJ/kg$$ and inlet velocity of $$100$$ $$m/s,$$ enters an insulated horizontal nozzle. It leaves the nozzle at $$200$$ $$m/s.$$ The exit en...

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

The root of the function $$f\left( x \right) = {x^3} + x - 1$$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $${x_0} = 1$$ is

The demand for a two-wheeler was $$900$$ units and $$1030$$ units in April $$2015$$ and May $$2015,$$ respectively. The forecast for the month of April $$2015$$ was $$850$$ units....

For a heat exchanger, $$\Delta {T_{\max }}$$ is the maximum temperature difference and $$\Delta {T_{\min }}$$ is the minimum temperature difference between the two fluids. $$LMTD$$...

Internal gears are manufactured by

A cylindrical steel rod, $$0.01$$ $$m$$ in diameter and $$0.2$$ $$m$$ in length is first heated to $${750^ \circ }C$$ and then immersed in a water bath at $${100^ \circ }C.$$ The h...

The value of the line integral $$\,\,\oint\limits_C {\overrightarrow F .\overrightarrow r ds,\,\,\,} $$ where $$C$$ is a circle of radius $${4 \over {\sqrt \pi }}\,\,$$ units is __...

The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr 0 & 0 & 3 \cr } } \right]$$ is ________.

Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum. The shape of the cavity is a cylinder with $$15$$ $$mm$$ di...

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

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

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

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

Two circular shafts made of same material, one solid $$(S)$$ and one hollow $$(H)$$, have the same length and polar moment of inertia. Both are subjected to same torque. Here. $${\...

The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s 2 . The natural frequency of th...