$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$

If $${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$ and $$y(1)=0$$ then what is $$y(e)$$?

Starting from $$\,{x_0} = 1,\,\,$$ one step of Newton - Raphson method in solving the equation $${x^3} + 3x - 7 = 0$$ gi

Which of the following is a solution of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \

The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0$

Using given data points tabulated below, a straight line passing through the origin is fitted using least squares method

A single die is thrown two times. What is the probability that the sum is neither $$8$$ nor $$9?$$

A lot had $$10$$% defective items. Ten items are chosen randomly from this lot. The probability that exactly $$2$$ of th

Stokes theorem connects

Changing the order of integration in the double integral $${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{$\

By a change of variables $$x(u, v) = uv,$$ $$\,\,y\left( {u,v} \right) = {v \over u}$$ in a double integral, the integr

$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$ is equal to

Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 &

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has

Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contac

An elevator (lift) consists of the elevator cage and a counter weight, of mass m each. The cage and the counterweight ar

A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the

The time variation of the position of a particle in rectilinear motion is given by $$x = 2{t^3} + {t^2} + 2t$$. If 'V' i

A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean pos

A $$U$$-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two lo

A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$

A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the w

The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respe

The following figure was generated from experimental data relating spectral black body emissive power to wave length at

Hot oil is cooled from $${80^ \circ }C$$ to $${50^ \circ }C$$ in an oil cooler which uses air as the coolant. The air te

A solid cylinder (surface $$2$$) is located at the center of a hollow sphere (surface $$1$$). The diameter of the sphere

An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \times 0.5\,m,$$ carrying air at $${20^ \cir

An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \times 0.5\,m,$$ carrying air at $${20^ \cir

A small copper ball of $$5$$ $$mm$$ diameter at $$500$$ $$K$$ is dropped into an oil bath whose temperature is $$300$$ $

Heat flows through a composite slab, as shown below. The depth of the slab is $$1$$ $$m.$$ the $$k$$ values are in $$W/m

In case of one dimensional heat conduction in a medium with constant properties, $$T$$ is the temperature at position $$

A company has two factories $${S_1},$$ $${S_2}$$ and two warehouses $${D_1},$$ $${D_2}$$ . the supplies from $${S_1}$$ a

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1

Consider a single server queuing model with Poisson arrivals $$\left( {\lambda = 4/hour} \right)$$ and exponential serv

The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth

A project has six activities $$(A$$ to $$F)$$ with respective activity durations $$7,5,6,6,8,4$$ days. The network has t

The distribution of lead-time demand fro an item is as follows: The reorder level is $$1.25$$ times the expected valu

A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The

A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The

Which one of the following is criterion in the design of hydrodynamic journal bearings?

A mould has a downsprue whose length is $$20$$ $$cm$$ and the cross sectional area at the base of the down sprue is $$1\

Which among the $$NC$$ operations given below are continuous path operations? Arc Welding $$(A$$ $$W)$$, Milling $$(M),

The tool of an $$NC$$ machine has to move along a circular arc from $$(5,5)$$ to $$(10,10)$$ while performing an operati

In order to have interference fit, it is essential that the lower limit of the shaft should be

A $$2$$ $$mm$$ thick metal sheet is to be bent at an angle of one radian with a bend radius of $$100$$ $$mm.$$ If the st

A $$600$$ $$mm$$ $$ \times \,\,30\,\,mm$$ flat surface of a plate is to be finish machined on a shaper. The plate has b

Two tools $$P$$ and $$Q$$ have signature $${5^ \circ } - {5^ \circ } - {6^ \circ } - {6^ \circ } - {8^ \circ } - {30^ \c

The figure below shows a graph, which qualitatively relates cutting speed and cost per piece produced. The three curve

Spot welding of two $$1$$ $$mm$$ thick sheets of steel (density $$ = 8000kg/{m^3}$$ ) is carried out successfully by pas

The strength of a brazed joint

Match List - $${\rm I}$$ (products) with List - $${\rm II}$$ (casting process) and select the correct answer using the c

A weighing machine consists of a 2 kg pan resting on a spring in this condition, with the pan resting on the spring, the

Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the

The two shafts $$AB$$ and $$BC$$, of equal length and diameters $$d$$ and $$2d$$, are made of the same material. They ar

A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm a

A cantilever beam has the square cross section of 10 mm $$ \times $$ 10 mm. It carries a transverse load of 10 N. Consid

A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm a

A beam is made up of two identical bars AB and BC, by hinging them together at B. The end A is built-in (cantilevered) a

A cantilever beam carries the anti-symmetric load shown, where wo is the peak intensity of the distributed load. Qualita

An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this

An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this

An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this

The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is

In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the freq

There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. There are mounted o

In the velocity diagram shown below, $$u=$$ blade velocity, $$C=$$ absolute fluid velocity and $$W = $$ relative veloci

A vapor absorption refrigeration system is a heat pump with three thermal reservoirs as shown in the figure. A refrigera

The following four figures have been drawn to represent a fictitious thermodynamic cycle, on the $$P$$-$$v$$ and $$T$$-$

Nitrogen at an initial state of $$10$$ bar, $$1{m^3}$$ and $$300$$ $$K$$ is expanded isothermally to a final volume of $

The following table of properties was printed out for saturated liquid and saturated vapour of ammonia. The titles for o

The following table of properties was printed out for saturated liquid and saturated vapour of ammonia. The titles for o