If $$F(s)$$ is the Laplace transform of the function $$f(t)$$ then Laplace transform of $$\int\limits_0^t {f\left( x \ri

The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is

Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ varianc

The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $

$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$

If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________.

The minimum value of function $$\,\,y = {x^2}\,\,$$ in the interval $$\,\,\left[ {1,5} \right]\,\,$$ is

The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 & 1 \cr 0 & 2 \cr } } \righ

If a square matrix $$A$$ is real and symmetric then the eigen values

The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\pa

If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$

A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in

During inelastic collision of two particles, which one of the following is conserved?

Consider a steady incompressible flow through a channel as shown below. The velocity profile is uniform with a value o

Consider a steady incompressible flow through a channel as shown below. The velocity profile is uniform with a value o

Consider an incompressible laminar boundary layer flow over a flat plate of length $$L$$, aligned with the direction of

Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction factor, $$f=0.0225$$) of length $$500m.$$ The

Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of co

Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stres

In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by $$u = {u_0}\left( {1 + 3x/L} \right)

Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $$1.96{m^3}$$. If the pressure of oil in

Newton's law of viscosity states that the shear stress in a fluid is proportional to :

The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by $$\left

In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass

The average heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observa

Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ }C$$ (wet bulb). The dew point temp und

Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3

Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3

Capacities of production of an item over $$3$$ consecutive months in regular time are $$100,$$ $$100$$ and $$80$$ and in

In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ per month and the same is consumed at a

The maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory be

A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p

A block brake shows below has a free width of $$300$$ $$mm$$ and a mean coefficient of friction of $$0.25$$. For an acti

A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operating at $$20$$ revolutions/sec carries a lo

A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of the bearing, in hours, when the load is

A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p

A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p

A bolted joint in shown below. The maximum shear stress, in $$MPa,$$ in bolts $$A$$ and $$B$$ respectively are

A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is subjected to an internal pressure varyin

Which of the following engineering materials is the most suitable candidate for hot chamber die casting

If a particular $$Fe$$-$$C$$ alloy contains less than $$0.83$$% carbon, it is called

A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide in

Which type of motor is used in axial or spindle drives of $$CNC$$ m/c tools

A hole is specified as $${40^{\matrix{ {0.050} \cr {0.000} \cr } }}\,\,mm.$$ The mating shaft has a clearanc

The force requirement in a blanking operation of low carbon steel sheet is $$5.0$$ $$kN.$$ The thickness of the sheet is

In orthogonal turning of low carbon steel pipe with principal cutting edge angle of $$90,$$ the main cutting force is $$

In orthogonal turning of medium carbon steel, the specific machining energy is $$2$$ $$kJ/m{m^3},$$ the cutting velocity

In orthogonal turning of a low carbon steel bar of diameter $$150mm$$ with uncoated carbide tool, the cutting velocity i

A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide in

Two metallic sheets, each of $$2.0$$ $$mm$$ thickness are welded in lap joint configuration by resistance spot welding

A $$DC$$ welding machine with a linear power source characteristic provides open circuit voltage of $$80V$$ and short ci

Which of the following is a solid state welding process.

Match the correct combination for following metal working processes.

In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed without any barreling effect. The final

The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to a final value of $$10mm$$ in one single

A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2}$$ where the pouring basin meets the do

Volume of a cube of a side $$''l''$$ and volume of sphere of radius $$' r '$$ are equal. Both the cube and the sphere ar

A stepped steel shaft shown below is subjected to $$10$$ N-m torque. If the modulus of rigidity is $$80$$ GPa, the strai

A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are

A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-directio

A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-directio

A disc of radius' r 'has a hole of radius 'r/2' cut-out as shown. The centroid of the remaining disc (shaded portion) at

In a simply-supported beam loaded as shown below, the maximum bending moment in N-m is

A steel rod of length $$L$$ and diameter $$D$$, fixed at both ends, is uniformly heated to a temperature rise of $$\Delt

The input link Q2P of a four bar linkage is rotated at $$2$$ rad/s counter clockwise direction as shown below. The angul

A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction The ang

A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction If the

The natural frequency of the system shown below is

The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {d

For an under damped harmonic oscillator, resonance

The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to

Which combination of the following statements is correct? The incorporation of re-heater in a steam power plant. $$P:$$

Which of the following relationships is valid only for reversible process undergone by a closed system of simple compres

An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a si

A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediate temperature, to a hi

Water has a critical specific volume of $$0.003155$$ $${m^3}/kg.$$ A closed and rigid steel tank of volume $$0.025{m^3}$

Match the items in columns $$I$$ and $$II$$. Column $$I$$ $$P:$$ Centrifugal compressor $$Q:$$ Centrifugal pump $$R:$$ P

A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. T

The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential compon