Which of the following integrals is unbounded?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

For generating coon's surface we require

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

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

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

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

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

Internal gear cutting operation can be performed by

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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