For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{ 8 & x & 0 \cr 4

The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3

The volume of an object expressed in spherical co-ordinates is given by $$V = \int\limits_0^{2\pi } {\int\limits_0^{{\r

If $$\,\,\,x = a\left( {\theta + Sin\theta } \right)$$ and $$y = a\left( {1 - Cos\theta } \right)$$ then $$\,\,{{dy} \o

From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kin

The following data about the flow of liquid was observed in a continuous chemical process plant Mean flow rate of th

The figure below shown a pair of pin jointed gripper tongs holding an object weighing $$2000N$$. The coefficient of fric

A rigid body shown in the fig.(a) has a mass of 10kg. It rotates with a uniform angular velocity $$'\omega '$$ A balan

An ejector mechanism consists of a helical compression spring having a spring constant of k = 981 × 103 N/m. It is pre-c

The figure shows a pin-jointed plane truss loaded at the point M by hanging a mass of 100 kg. The member LN of the truss

For air flow over a flat plate, velocity $$(U)$$ and boundary layer thickness $$\left( \delta \right)$$ can be expresse

The pressure gauges $${G_1}$$ and $${G_2}$$ installed on the system show pressures of $${P_{G1}} = 5.00$$ bar and $${P_{

The pressure gauges $${G_1}$$ and $${G_2}$$ installed on the system shown pressures of $${P_{G1}} = 5.00$$ bar and $${P_

A closed cylinder having a radius $$R$$ and height $$H$$ is filled with oil of density $$\rho .$$ If the cylinder is rot

An incompressible fluid (kinematic viscosity $$ = 7.4 \times {10^{ - 7}}\,\,{m^2}/s,$$ specific gravity, $$0.88$$) is he

A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j

For a fluid flow through a divergent pipe of length $$L$$ having inlet and outlet radii of $${R_1}$$ and $${R_2}$$ respe

In a condenser, water enters at $${30^ \circ }C$$ and flows at the rate $$1500$$ $$Kg/hr.$$ The condensing steam is at a

A spherical thermocouple junction of diameter $$0.706 mm$$ is to be used for the measurement of temperature of a gas str

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate $$'{q_g}',$$ can be

A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company h

A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first com

An electronic equipment manufacturer has decided to add a component sub-assembly operation that can produce $$80$$ units

For a product, the forecast and the actual sales for December $$2002$$ were $$25$$ and $$20$$ respectively. If the expon

In $$PERT$$ analysis a critical activity has

A company has an annual demand of $$1000$$ units, ordering cost of Rs.$$100$$/order and carrying cost of Rs.$$100$$/unit

There are two products P and Q with the following characteristics The economic order quantity (EOQ) of products P and Q

Two mating spur gears have $$40$$ and $$120$$ teeth respectively. The pinion rotates at $$1200$$ $$rpm$$ and transmits a

A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arran

A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arran

Gray cast iron blocks $$200 \times 100 \times 10\,\,mm$$ are to be cast in sand moulds. Shrinkage allowance for pattern

Misrun is a casting defect which occurs due to

In a rolling process, sheet of $$25$$ $$mm$$ thickness is rolled to $$20$$ $$mm$$ thickness. Roll is of diameter $$600$$

During the execution of a CNC part program block $$NO20\,\,\,\,GO2\,\,\,\,X45.0\,\,\,\,Y25.0\,\,\,\,R5.0.$$ The type of

In a $$2-D$$ $$CAD$$ package, clockwise circular arc of radius, $$5,$$ specified from $${P_1}\left( {15,10} \right)$$ t

A hole of diameter $${25.00^{ + 0.01}}\,\,mm$$ is to be inspected by using GO / NO GO gages. The size of the GO plug gag

$$10$$ $$mm$$ diameter holes are to be punched in a steel sheet of $$3$$ $$mm$$ thickness. Shear strength of the materia

Through holes of $$10$$ $$mm$$ diameter are to be drilled in steel plate of $$20$$ $$mm$$ thickness. Drill spindle speed

In an orthogonal cutting test on mild steel, the following data were obtained Cutting speed: $$40$$ $$m/min,$$ Depth of

A standard machine tool and an automatic machine tool are being compared for the production of a component. Following da

In a machining operation, doubling the cutting speed reduces the tool life to $$1/{8^{th}}$$ of the original value. The

Two 1 mm thick steel sheets are to be spot welded at a current of $$5000$$ $$A.$$ Assuming effective resistance to be $

The Mohr's circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum s

A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 G

A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 G

A solid circular shaft of $$60$$ mm diameter transmits a torque of $$1600$$ N - m. The value of maximum shear developed

A torque of $$10$$ $$N-m$$ is transmitted through a stepped shaft as shown in figure. The torsional stiffnesses of indiv

The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the $$x

The figure below shows a steel rod of $$25$$ mm2 cross sectional area. It is loaded at four points, K, L, M and N. Assum

A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surf

In terms of Poisson's ratio $$\left( \mu \right)$$ the ratio of Young's Modulus $$(E)$$ to Shear Modulus $$(G)$$ of ela

Match the following with respect to spatial mechanism. Type of Joint $$P.$$ Revolute $$Q.$$ Cylindrical $$R.$$ Spherical

The figure below shows a planar mechanism with single degree of freedom. The instant center $${{\rm I}_{24}}$$ for the g

Match the following Type of Mechanism $$P.$$ Scott - Russel mechanism $$Q.$$ Geneva mechanism $$R.$$ Off-set slider- cr

For a mechanism shown below, the mechanical advantage for the given configuration is

In the figure shown, the relative velocity of link $$1$$ with respect to link $$2$$ is $$12$$ m/sec. Link $$2$$ rotates

A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machi

A uniform stiff rod of length $$300$$ $$mm$$ and having a weight of $$300$$ $$N$$ is pivoted at one end and connected to

A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25

Consider a steam power plant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at $$4$$ $$MP

Consider a steam power plant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at $$4$$ $$MP

A steel billet of $$2000$$ $$kg$$ mass is to be cooled from $$1250$$ $$K$$ to $$450$$ $$K.$$ The heat released during th

A solar collector receiving solar radiation at the rate of $$0.6$$$$kW/{m^2}$$ transforms it to the internal energy of a

A heat engine having an efficiency of $$70\% $$ is used to drive a refrigerator having a coefficient of performance of $

A gas contained in a cylinder is compressed, the work required for compression being $$5000$$ $$kJ.$$ During the process

A centrifugal pump is required to pump water to an open water tank situated $$4$$ $$km$$ away from the location of the p

At a hydro electric power plant site, available head and flow rate are $$24.5$$ $$m$$ and $$10.1{m^3}/s$$ respectively.