The matrix form of the linear system $${{dx} \over {dt}} = 3x - 5y$$ and $$\,{{dy} \over {dt}} = 4x + 8y\,\,$$ is

Given that the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 0 \cr 2 & 6 & 4 \cr { -

Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\

$$\mathop {Lt}\limits_{x \to 0} {{x - \sin x} \over {1 - \cos x}}$$ is

The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,} $$ is evaluated along the circle $${x^2} + {y^2} = {1

In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard devia

If $$\,y = f\left( x \right)\,\,$$ is the solution of $${{{d^2}y} \over {d{x^2}}} = 0$$ with the boundary conditions $

Using the trapezoidal rule, and dividing the interval of integration into three equal sub-intervals, the definite integ

The argument of the complex number $${{1 + i} \over {1 - i}},$$ where $$i = \sqrt { - 1} ,$$ is

A block weighing 200N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2

A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a

A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s2 . When th

A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity $$V$. T

Water flows through a pipe having an inner radius of $$10$$ $$mm$$ at the rate of $$36$$ $$kg/hr$$ at $${25^ \circ }C$$.

For a fully developed flow of water in a pipe having diameter $$10$$ $$cm,$$ velocity $$0.1$$ $$m/s$$ and kinematic visc

An ideal water jet with volume flow rate of $$0.05{m^3}/s$$ strikes a flat plane placed normal to its path and exerts a

In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the

For a completely submerged body with center of gravity $$'G'$$ and center of buoyancy $$'B',$$ the condition of stabilit

Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $$30$$ $$mm$

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $${{{T_w}

In exponential smoothening method, which one of the following is true?

The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jo

Jobs arrive at a facility at an average rate of $$5$$ in an $$8$$ hour shift. The arrival of the jobs follows Poisson di

The state of stress at a point is given by $$\,\,{\sigma _x} = - 6\,MPa,\,\,{\sigma _y} = 4\,\,MPa,$$ and $${\tau _{xy}

A pair of spur gears with module $$5$$ $$mm$$ and a center distance of $$450mm$$ is used for a speed reduction of $$5:1$

A hydrodynamic journal bearing is subject to $$2000$$ $$N$$ load at a rotational speed of $$2000$$ $$rpm.$$ Both bearing

In solid-state welding, the contamination layers between the surfaces to be welded are removed by

An aluminium alloy (density $$2600$$ $$kg/{m^3}$$ ) casting is to be produced. A cylindrical hole of $$100$$ $$mm$$ diam

A metal rod of initial length $${L_0}$$ is subjected to a drawing process. The length of the rod at any instant is given

The major difficulty during welding of aluminium is due to its

If the Taylor's tool life exponent $$n$$ is $$0.2,$$ and the tool changing time is $$1.5$$ $$min,$$ then the tool life (

The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is $$400N.$$ The tu

During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produc

Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during

For machining a rectangular island represented by coordinates $$P(0,0), Q(100,0), R(100,50)$$ and $$S(0,50)$$ on a cast

For the given assembly : $$25$$ $$H7/g8,$$ match Group $$A$$ with Group $$B$$

A metallic rod of $$500$$mm length and $$50$$mm diameter, when subjected to a tensile force of $$100$$kN at the ends, ex

A metallic rod of $$500$$mm length and $$50$$mm diameter, when subjected to a tensile force of $$100$$kN at the ends, ex

A circular rod of length $$‘L’$$ and area of cross-section $$‘A’$$ has a modulus of elasticity $$‘E’$$ and coefficient o

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency

A rigid uniform rod $$AB$$ of length $$L$$ and mass $$m$$ is hinged at $$C$$ such that $$AC = L/3, CB = 2L/3.$$ Ends $$A

$$1.5$$ $$kg$$ of water is in saturated liquid state at $$2$$ bar $$\left( {{v_f} = 0.001061\,\,{m^3}/kg,\,\,{u_f} = 50

A reversible heat engine receives $$2$$ $$kJ$$ of heat from a reservoir at $$1000$$ $$K$$ and a certain amount of heat f

The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called

In a power plant, water (density $$ = 1000\,\,kg/{m^3}$$ ) is pumped from $$80$$ $$kPa$$ to $$3$$ $$MPa$$. The pump has

An ideal reheat Rankine cycle operates between the pressure limits of $$10$$ $$kPa$$ and $$8$$ $$MPa,$$ with reheat bein