GATE ME 2008

## GATE ME

The matrix $$\left[ {\matrix{
1 & 2 & 4 \cr
3 & 0 & 6 \cr
1 & 1 & P \cr
} } \ri

View Question The eigen vectors of the matrix $$\left[ {\matrix{
1 & 2 \cr
0 & 2 \cr
} } \right]$$ are written in

View Question For what values of 'a' if any will the following system of equations in $$x, y$$ and $$z$$ have a solution?
$$$2x+3y=4,$

View Question Consider the shaded triangular region $$P$$ shown in the figure. What is $$\int\!\!\!\int\limits_p {xy\,dx\,dy\,?} $$

View Question In the Taylor series expansion of $${e^x}$$ about $$x=2,$$ the coefficient of $$\,\,{\left( {x - 2} \right)^4}\,\,$$ is

View Question The value of $$\,\,\mathop {Lim}\limits_{x \to 8} {{{x^{1/3}} - 2} \over {x - 8}}\,\,$$ is

View Question Which of the following integrals is unbounded?

View Question The length of the curve $$\,y = {2 \over 3}{x^{3/2}}$$ between $$x=0$$ & $$x=1$$ is

View Question Let $$\,\,f = {y^x}.$$ What is $$\,\,{{{\partial ^2}f} \over {\partial x\partial y}}\,\,$$ at $$x=2,$$ $$y=1$$?

View Question The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y

View Question The directional derivative of the scalar function $$f(x, y, z)$$$$ = {x^2} + 2{y^2} + z\,\,$$ at the point $$P = \left(

View Question A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?

View Question It is given that $$y'' + 2y' + y = 0,\,\,\,\,y\left( 0 \right) = 0,y\left( 1 \right) = 0.$$ What is $$y(0.5)$$?

View Question Given that $$\mathop x\limits^{ \bullet \bullet } + 3x = 0$$ and $$x\left( 0 \right) = 1,\,\,\mathop x\limits^ \bulle

View Question The integral $$\oint {f(z)dz} $$ evaluated around the unit circle on the complex plane for $$f(z) = {{\cos z} \over z}$$

View Question A straight rod length $$L(t),$$ hinged at one end freely extensible at the other end, roates through an angle $$\theta \

View Question Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is

View Question A circular disk of radius $$'R'$$ rolls without slipping at a velocity $$v$$. The magnitude of the velocity at point $$'

View Question A journal bearing has a shaft diameter of $$40$$ $$mm$$ and a length of $$40mm.$$ The shaft is rotating at $$20$$ $$rad/

View Question A cubic block of side $$'L'$$ and mass $$'M'$$ is dragged over an oil film across table by a string connects to a hangin

View Question For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, $$\overrightarrow V $$ where is the velo

View Question The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate co

View Question The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate co

View Question A two dimensional fluid element rotates like a rigid body. At a point with in the element, the pressure is $$1$$ unit. R

View Question Steady two dimensional heat conduction takes place in the body shown in the fig below. The normal temperature gradients

View Question For the three dimensional object shown in the fig below. Five faces are insulated. The sixth face $$(PQRS),$$ which is n

View Question For flow of fluid over a heated plate, the following fluid properties are known: Viscosity $$=0.001Pa.s;$$ Specific heat

View Question A hollow enclosure is formed between two infinitely concentric cylinders of radii $$1m$$ and $$2m$$ respectively. Radiat

View Question The $$LMTD$$ of a counter flow heat exchanger is $${20^ \circ }C$$. The cold fluid enters at $${20^ \circ }C$$ and the h

View Question For the network below, the objective is to find the length of the shortest path from node $$P$$ to node $$G.$$ Let $${d_

View Question A moving average system is used for forecasting weekly demand. $${F_1}\left( t \right)$$ and $${F_2}\left( t \right)$$ a

View Question In an $$M/M/1$$ queuing system, the number of arrivals in an interval of length $$T$$ is a Poisson random variable (i.e.

View Question Consider the Linear programme $$(LP)$$
Max $$4x$$ + $$6y$$
Subject to
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,3x + 2

View Question Consider the Linear programme $$(LP)$$
Max $$4x$$ + $$6y$$
Subject to
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,3x + 2

View Question For the standard transportation linear programme with $$m$$ sources and $$n$$ destinations and total supply equaling tot

View Question A set of $$5$$ jobs is to be processed on a single machine. The processing time (in days) is given in the table below. T

View Question A steel bar of $$10$$ $$mm\,\, \times \,\,50\,\,mm$$ is cantilevered with two $$M12$$ bolts ($$P$$ and $$Q$$) to support

View Question A steel bar of $$10$$ $$mm\,\, \times \,\,50\,\,mm$$ is cantilevered with two $$M12$$ bolts ($$P$$ and $$Q$$) to support

View Question A spur gate has a module of $$3mm,$$ number of teeth $$16,$$ a face width of $$36mm$$ and a pressure angle of $${20^ \ci

View Question Match the type of gears with their most appropriate description
Type of gear
(P)$$\,\,\,\,\,$$ Helical
(Q)$$\,\,\,\,\,$

View Question A journal bearing has a shaft diameter of $$40mm$$ and a length of $$40mm.$$ The shaft is rotating at $$20$$ $$rad/s$$ a

View Question One tooth of gear having $$4$$ module and $$32$$ teeth is shown in the figure. Assume that the gear tooth and the corres

View Question A clutch has outer and inner diameters $$100mm$$ and $$40mm$$ respectively. Assuming a uniform pressure of $$2MPa$$ and

View Question While cooling, a cubical casting of side $$40mm$$ undergoes $$3\% ,\,\,4\% $$ and $$5\% $$ volume shrinkage during the l

View Question In a single pass rolling operation, a $$20mm$$ thick plate with plate width of $$100mm$$, is reduced to $$18mm$$ thick.

View Question In arc welding of a butt joint, the welding speed is to be selected such that highest cooling rate is achieved. Melting

View Question In a single point turning tool, the side rake angle and orthogonal rake angle are equal. $$\varphi $$ is the principle c

View Question Orthogonal turning is performed on a cylindrical work piece with shear strength of $$250Mpa.$$ The following conditions

View Question Orthogonal turning is performed on a cylindrical work piece with shear strength of $$250Mpa.$$ The following conditions

View Question Internal gear cutting operation can be performed by

View Question The figure shows an incomplete schematic of a conventional lathe to be used for cutting threads with different pitches.

View Question In the deep drawing of cups, blanks show a tendency to wrinkle up around the periphery (flange). The most likely cause

View Question A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel on the taper hole inside a drill

View Question For generating coon's surface we require

View Question In the feed drive of a point to point open loop $$CNC$$ drive, a stepper motor rotating at $$200steps/rev$$ drives a tab

View Question In the feed drive of a point to point open loop $$CNC$$ drive, a stepper motor rotating at $$200steps/rev$$ drives a tab

View Question A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is $$1$$ unit. Ra

View Question A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It further subjected to a torque of

View Question For the component loaded with a force $$F$$ as shown in the figure, the axial stress at the corner point $$P$$ is

View Question A compression spring is made of music wire of $$20$$ mm diameter having a shear strength and shear modulus of $$800$$ MP

View Question A cantilever type gate hinged at $$Q$$ is shown in the figure. $$P$$ and $$R$$ are the centers of gravity of the cantile

View Question The rod $$PQ$$ of length $$L$$ and with flexural rigidity $$EI$$ is hinged at both ends. For what minimum force $$F$$ is

View Question A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspe

View Question A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspe

View Question The strain energy stored in the beam with flexural rigidity $$EI$$ and loaded as shown in the figure is

View Question A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler's

View Question A uniform rigid rod of mass $$m =1kg$$ and length $$L=1$$ m is hinged at its centre & laterally supported at one e

View Question The natural frequency of the spring mass system shown in the figure is closest to

View Question In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a tw

View Question In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a tw

View Question In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a tw

View Question A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas

View Question A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air ( assumed to

View Question In a steady state steady flow process taking place in a device with a single inlet and a single outlet, the work done pe

View Question $$2$$ moles of oxygen are mixed adiabatically with another $$2$$ moles of oxygen in mixing chamber, so that the final to

View Question A cycle device operates between three thermal reservoirs, as shown in the figure. Heat is transferred to/from the cyclic

View Question $$A$$ gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by

View Question A thermal power plant operates on a regenerative cycle with a single open feed water heater, as shown in the figure. For

View Question Water having a density of $$1000\,\,kg/{m^3},$$ issues from a Nozzle with a velocity of $$10$$ $$m/s$$ and the jet strik

View Question