Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$

The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as wel

The quadratic equation $${x^2} - 4x + 4 = 0$$ is to be solved numerically, starting with the initial guess $${x_0} = 3.$

Consider the following differential equation $$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$ $$\

Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$$p\left( {x,q} \right) = \left\{

The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\wideh

For what value of $$'p'$$ the following set of equations will have no solutions? $$$2x+3y=5$$$ $$$3x+py=10$$$

The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr

In a catchment, there are four rain-gauge stations, P, Q, R, and S. Normal annual precipitation values at these stations

The two columns below show some parameters and their possible values. .tg {border-collapse:collapse;border-spacing:0;m

The development length of a deformed reinforcement bar can be expressed as $$\left( {1/k} \right)\left( {\phi {\sigma _s

Consider the singly reinforced beam shown in the figure below: At cross-section $$XX,$$ which of the following statem

Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section

Workability of concrete can be measured using slump, compaction factor and Vee bee time. Consider the following statemen

The composition of an air-entrained concrete is given below: Water : 184 kg /m3 Ordinary Portland Cement(OPC) : 368 kg

Consider the following statements for air-entrained concrete: (i) Air-entrainment reduces the water demand for a given l

A bracket plate connected to a column flange transmits a load of $$100$$ $$kN$$ as shown in the following figure. The ma

Two beams are connected by a linear spring as shown in the following figure. For a load $$P$$ as shown in the figure, th

A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter

Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, $$

For the beam shown below, the stiffness coefficient $${K_{22}}$$ can be written as

For formation of collapse mechanism in the following figure, the minimum value of $${{P_u}}$$ is $$c{M_P}/L.$$ $${M_P}$$

For the beam shown below, the value of the support moment $$M$$ is ____________ $$KN$$-$$m$$.

For the $$2D$$ truss with the applied loads shown below, the strain energy in the member $$XY$$ is _______________ $$kN$