A scalar potential $$\,\,\varphi \,\,$$ has the following gradient: $$\,\,\nabla \varphi = yz\widehat i + xz\widehat j

The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & k \cr } }

The values of $$x$$ for which the function $$f\left( x \right) = {{{x^2} - 3x - 4} \over {{x^2} + 3x - 4}}$$ is NOT con

The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets con

Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,} $$

The value of $$\oint\limits_\Gamma {{{3z - 5} \over {\left( {z - 1} \right)\left( {z - 2} \right)}}dz} $$ along a close

A function $$f$$ of the complex variable $$z=x+iy,$$ is given as $$f(x,y)=u(x,y)+iv(x,y),$$ Where $$u(x,y)=2kxy$$ and $

A system of particles in motion has mass center $$G$$ as shown in the figure. The particle $$i$$ has mass $${m_i}$$ and

A point mass having mass $$M$$ is moving with a velocity $$V$$ at an angle $$\mathop \theta \limits^ \cdot $$ to the wa

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height ca

Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $$50$$ $$mm$$)

The volume tric flow rate (per unit depth) between two streamlines having stream functions $${\psi _1}$$ & $${\psi _

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $$2R \times L$$ at the

A hollow cylinder has length $$L,$$ inner radius $${{r_1}}$$, outer radius $${{r_2}}$$, and thermal conductivity $$k.$$

Two cylindrical shafts $$A$$ and $$B$$ at the same initial temperature are simultaneously placed in a furnace. The surfa

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the out

Consider a parallel-flow heat exchanger with area $${A_p}$$ and a counter-flow heat exchanger with area $${A_c}.$$ In bo

A food processing company uses $$25,000$$ $$kg$$ of corn flour every year. The quantity-discount price of corn flour is

A project consists of $$14$$ activities, $$A$$ to $$N$$. The duration of these activities (in days) are shown in bracket

In a single-channel queuing model, the customer arrival rate is $$12$$ per hour and the serving rate is $$24$$ per hour.

A mass of $$2000$$ kg is currently being lowered at a velocity of $$2$$ $$m/s$$ from the drum as shown in the figure. Th

A machine element $$XY,$$ fixed at end $$X,$$ is subjected to an axial load $$P,$$ transverse load $$F,$$ and a twisting

In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $$50$

For the brake shown in the figure, which one of the following is TRUE?

The force $${F_1}$$ and $${F_2}$$ in a brake band and the direction of rotation of the drum are as shown in the figure.

The welding process which uses a blanket of fusible granular flux is

Gray cast iron blocks of size $$100\,\,mm \times 50\,\,mm \times 10\,\,mm$$ with a central spherical cavity of diameter

The value of true strain produced in compressing a cylinder to half its original length is

The voltage - length characteristic of a direct current arc in an arc welding process is $$V=$$ $$(100+40l),$$ where $$l

For a certain job, the cost of metal cutting is $$Rs.18C/V$$ and the cost of tooling is Rs.$$270C/(TV).$$ Where $$C$$ is

The following data is applicable for a turning operation. The length of job is $$900$$ $$mm,$$ diameter of job is $$200$

For the situation shown in the figure below the expression for $$H$$ in terms of $$r, R$$ and $$D$$ is

In the figure, the load P = 1 N, length L = 1 m, Young’s modulus E = 70 GPa, and the cross-section of the links is a squ

A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is

A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the

A rigid horizontal rod of length $$2L$$ is fixed to a circular cylinder of radius $$R$$ as shown in the figure. Vertical

A simply supported beam of length $$2L$$ is subjected to a moment $$M$$ at the mid-point $$x = 0$$ as shown in the figur

A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoo

A single degree of freedom mass-spring - viscous damper system with mass $$m,$$ spring constant $$k$$ and viscous dampin

The rod AB, of length 1 m, shown in the figure is connected to two sliders at each end through pins. The sliders can sli

The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing ov

The heat removal rate from a refrigerated space and the power input to the compressor are $$7.2$$ $$kW$$ and $$1.8$$ $$k

The internal energy of an ideal gas is a function of

A piston-cylinder device initially contains $$0.4\,{m^3}$$ of air (to be treated as an ideal gas) at $$100$$ $$kPa$$ and

A reversible cycle receives $$40$$ $$kJ$$ of heat from one heat source at a temperature of $${127^ \circ }C$$ and $$37$$