Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$

If a function is continuous at a point,

Divergence of the vector field $${x^2}z\widehat i + xy\widehat j - y{z^2}\widehat k\,\,$$ at $$(1, -1, 1)$$ is

A group consists of equal number of men and women. Of this group $$20$$% of the men and $$50$$% of the women are unemplo

A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3}$

Consider two solutions $$\,x\left( t \right)\,\,\,\, = \,\,\,{x_1}\left( t \right)\,\,$$ and $$x\left( t \right)\,\,\

The definite integral $$\,\int\limits_1^3 {{1 \over x}} dx\,\,$$ is evaluated using Trapezoidal rule with a step size of

The real root of the equation $$5x-2cosx=0$$ (up to two decimal accuracy) is

An analytic function of a complex variable $$z = x + iy$$ is expressed as $$f\left( z \right) = u\left( {x + y} \right)

A mass m1 of 100kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000kg

A body of mass (m) 10kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic f

An annular disc has a mass m, inner radius R and outer radius $$2R$$. The disc rolls on a flat surface without slipping.

A four-wheel vehicle of mass 1000kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheel

A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is mainta

A fluid of dynamic viscosity $$2 \times {10^{ - 5}}\,\,kg/m.s$$ and density $$1kg/{m^3}$$ flows with an average velocity

Consider the turbulent flow of a fluid through a circular pipe of diameter, $$D.$$ Identify the correct pair of statemen

Consider a long cylindrical tube of inner and outer radii, $${r_i}$$ and $${r_0}$$ , respectively, length, $$L$$ and the

Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness $$\left( \

A solid sphere of radius$${r_1} = 20\,\,mm$$ is placed concentrically inside a hollow sphere of radius $${r_2} = 30\,\,m

A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at $$19$$ liter/s is

A manufacturer can produce $$12000$$ bearings per day. The manufacturer received an order of $$8000$$ bearings per day

Consider the given project network, where numbers along various activities represent the normal time. The free float on

The actual sales of a product in different months of a particular year are given below: The forecast of the sales, usi

Consider an objective function $$Z\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$ and the constraints $$\eqalign{ &a

Which one of the following is NOT correct?

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stre

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction betwee

Match the casting defects (Group A) with the probable causes (Group B):

The hot tearing in a metal casting is due to

A cylindrical blind riser with diameter $$d$$ and height $$h,$$ is placed on the top of the mold cavity of a closed type

For spot welding of two steel sheets (base metal) each of $$3$$ $$mm$$ thickness, welding current of $$10000$$ $$A$$ is

A straight turning operation is carried out using a single point cutting tool on an $$AISI$$ $$1020$$ steel rod. The fee

Cutting tool is much harder than the work piece. Yet the tool wears out during the tool-work interaction, because

Which pair of following statement is correct for orthogonal cutting using a single-point cutting tool? $$P.$$ reduction

The diameter of a recessed ring was measured by using two spherical balls of diameter $${d_2} = 60mm$$ and $${d_1} = 40m

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both f

Consider a simply supported beam of length $$50$$h, with a rectangular cross-section of depth h, and width $$2$$h. The b

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses develo

A force $$P$$ is applied at a distance $$x$$ from the end of the beam as shown in the figure. What would be the value of

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase ang

The damping ratio of a single degree of freedom spring-mass-damper system with mass of $$1$$ kg, stiffness $$100 N/m$$ a

A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10

A certain amount of an ideal gas is initially at a pressure $${p_1}$$ and temperature $${T_1}$$. First, it undergoes a c

Which one of the following pairs of equations describes an irreversible heat engine?

An amount of $$100$$ $$kW$$ of heat is transferred through a wall in steady state. One side of the wall is maintained at

A source at temperature of $$500K$$ provides $$1000$$ $$kJ$$ of heat. The temperature of environment is $${27^ \circ }C.

At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of absolute velocity is