Eigen values of a real symmetric matrix are always

Consider the following system of equations $$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0

A series expansion for the function $$\sin \theta $$ is _______.

If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $

What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?

An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at le

Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with c

The integral $$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,} $$ when evaluated by using simpson's $$1/{3^{rd}}$$ rule on t

The product of two complex numbers $$1 + i\,\,\,\,\& \,\,\,\,2 - 5\,i$$ is

The coefficient of restitution of a perfectly plastic impact is

A stone with mass of $$0.1$$kg is catapulted as shown in the figure. The total force $${F_x}$$ (in N) exerted by the rub

A 1 kg block is resting on a surface with coefficient of friction $$\mu $$ $$=0.1.$$ A force of $$0.8$$ $$N$$ is applied

A streamline and an equipotential line in a flow field

Figure shows the schematic for the measurement of velocity of air (density $$ = 1.2\,\,kg/{m^3}$$ ) through a constant -

A pipe of $$25$$ $$mm$$ outer diameter carries steam. The heat transfer coefficient between the cylinder and surrounding

A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two flui

In a condenser of a power plant, the steam condenses at a temperature of $${60^ \circ }C.$$ The cooling water enters at

The word Kanban is most appropriately associated with

Cars arrive at a service station according to Poisson's distribution with a mean rate of $$5$$ per hour. The service tim

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One un

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One un

Match the following criteria of material failure, under biaxial stresses $${\sigma _1}$$and $${\sigma _2}$$ and yield st

Two identical ball bearings $$P$$ and $$Q$$ are operating at loads $$30kN$$ and $$45kN$$ respectively. The ratio of the

Green sand mould indicates that

A cubic casting of $$50mm$$ side undergoes volumetric solidification shrinkage and volumetric solid contraction of $$4\%

The maximum possible draft in cold rolling of sheet increases with the

Which one among the following welding processes uses non-consumable electrode?

A single-point cutting tool with $${12^0}$$ rake angle is used to machine a steel work-piece. The depth of cut, $$i.e$$

The shear strength of a sheet metal is $$300MPa.$$ The blanking force required to produce a blank of $$100$$ $$mm$$ diam

A hole is dimension $$\phi {9^{\matrix{ { + 0.015} \cr { + 0\,\,\,\,\,\,\,\,\,\,} \cr } }}\,mm.$$ The corres

A simply supported beam $$PQ$$ is loaded by a moment of $$1$$ $$kN-m$$ at the mid-span of the beam as shown in the figur

A torque $$T$$ is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear

A column has a rectangular cross-section of 10 mm $$ \times $$ 20 mm and a length of 1 m. The slenderness ratio of the c

A double - parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism

For the four - bar linkage shown in the figure, the angular velocity of link AB is $$1$$ rad/s. The length of link CD is

A disc of mass m is attached to a spring of stiffness $$k$$ as shown in the figure. The disc rolls without slipping on

A mass of $$1$$ kg is attached to two identical springs each with stiffness $$k=20kN/m$$ as shown in the figure. Under f

The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging dive

The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging dive

The contents of a well-insulated tank are heated by a resistor of $$23\Omega $$ in which $$10A$$ current is flowing. Con

A pump handling a liquid raises its pressure from $$1$$ bar to $$30$$ $$bar.$$ Take the density of the liquid as $$990$$

Heat and work are

In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends o

In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends o

The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are $$2800$$ $$kJ/kg$$ and