At least one eigenvalue of a singular matrix is

At $$x=0,$$ the function $$f\left( x \right) = \left| x \right|$$ has

The surface integral $$\,\,\int {\int\limits_s {{1 \over \pi }} } \left( {9xi - 3yj} \right).n\,dS\,\,$$ over the spher

Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is

The chance of a student passing an exam is $$20$$% The chance of a student passing the exam and getting above $$90$$% ma

Consider the following differential equation $${{dy} \over {dt}} = - 5y;$$ initial condition: $$y=2$$ at $$t=0.$$ The

The values of function $$(x)$$ at $$5$$ discrete points are given below: Using Trapezodial rule with step size of $$0.

The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

Laplace transform of $$\cos \left( {\omega t} \right)$$ is

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of m

The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expressi

For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is

If the fluid velocity for a potential flow is given by $$V\left( {x,y} \right) = u\left( {x,y} \right)i + v\left( {x,y}

For a fully developed laminar flow of water (dynamic viscosity $$0.001$$ $$Pa$$-s) through a pipe of radius $$5$$ $$cm,$

The head loss for a laminar incompressible flow through a horizontal circular pipe is $${h_1}$$. Pipe length and fluid r

Within a boundary layer for a steady incompressible flow, the Bernoulli equation

If a foam insulation is added to a $$4cm$$ outer diameter pipe as shown as figure, the critical radius of insulation (i

A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of $$4 \times {10^7}\,

In the laminar flow of air $$(Pr=0.7)$$ over a heated plate, if $$\delta $$ and $${\delta _T}$$ denote, respectively the

The total emissive power of a surface is $$500$$ $$W/{m^2}$$ at a temperature $${T_1}$$ and $$1200$$ $$W/{m^2}$$ at a te

A balanced counter-flow heat exchanger has a surface area of $$20\,\,{m^2}$$ and overall heat transfer coefficient of $$

Annual demand of a product is $$50,000$$ units and the ordering cost is Rs. $$7,000$$ per order. Considering the basic e

A project consists of $$7$$ activities. The network along with the time durations (in days) for various activities is sh

Sales data of a product is given in the following table: Regarding forecast for the month of June, which one of the f

A manufacturer has the following data regarding a product: Fixed cost per month $$=$$ Rs. $$50,000$$ Variable cost per u

The uniaxial yield stress of a material is $$300$$ $$MPa.$$ According to Von mises criterion, the shear yield stress $$(

A cube and a sphere made of cast iron (each of volume $$1000\,\,c{m^3}$$) were cast under identical conditions. The time

In a two stage wire drawing operation, the fractional reduction (ratio of change in cross sectional area to initial cros

The flowing stress (in $$MPa$$) of a material is given by $$\sigma = 500{\varepsilon ^{0.1}},$$ When $$\varepsilon $$

During a $$TIG$$ welding process, the arc current and arc voltage were $$50$$ $$A$$ and $$60$$ $$V,$$ respectively, when

A single point cutting tool with $${0^0}$$ rake angle is used in an orthogonal machining process. At a cutting speed of

Which one of the following statements is TRUE?

During the development of a product, an entirely new process plan is made based on design logic, examination of geometry

A drill is positioned at point $$P$$ and it has to proceed to point $$Q.$$ The coordinates of point $$Q$$ in the increme

A rod is subjected to an uniaxial load within linear elastic limit. When the change in the stress is $$200$$ MPa, the ch

In a plane stress condition, the components of stress at a point are $${\sigma _x} = 20$$ MPa, $${\sigma _y} = 80$$ MPa

A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of $$10$$ kN is applied

The deflection of a spring with 20 active turns under a load of 1000 N is 10 mm. The spring is made into two pieces each

A hollow shaft (d0 = $$2$$di, where d0 and di are the outer and inner diameters respectively) needs to transmit $$20$$ k

A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the

A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible an

A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2kN normal to the top surface as show

A gas is stored in a cylindrical tank of inner radius $$7$$ m and wall thickness $$50$$ mm. The gage pressure of the gas

The number of degrees of freedom of the planetary gear train shown in the figure is

In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform

In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system i

A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\ome

The Vander-waals equation of state is $$\left( {p + {a \over {{v^2}}}} \right)\left( {v - b} \right) = RT,$$ where $$p$$

Work is done on an adiabatic system due to which its velocity changes from $$10$$ $$m/s$$ to $$20$$ $$m/s,$$ elevation i

The $$COP$$ of a Carnot heat pump operating between $${6^ \circ }C$$ and $${37^ \circ }C$$ is ____________

One kg of air ($${R = 287\,\,J/kg}$$-$$K$$) under goes irreversible process between equilibrium state $$1\,\,\left( {{{2

Which of the following statements regarding a Rankine cycle with reheating are TRUE? (i) increase in average temperature

In a Rankine cycle, the enthalpies at turbine entry and outlet are $$3159$$ $$kJ/kg$$ and $$2187$$ $$kJ/kg$$ respectivel