Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$ given th

The Laplace transform of the following function is $$$f\left( t \right) = \left\{ {\matrix{ {\sin t} & {for\,\,0

The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y}

The value of the following definite integral in $$\int\limits_{{\raise0.5ex\hbox{$\scriptstyle { - \pi }$} \kern-0.1em/\

The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.$$

Limit of the following sequence as $$n \to \infty $$ $$\,\,\,$$ is $$\,\,\,$$ $${x_n} = {n^{{1 \over n}}}$$

The following function has local minima at which value of $$x,$$ $$f\left( x \right) = x\sqrt {5 - {x^2}} $$

Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right

In natural water, hardness is mainly caused by

During a 6-hour storm the rainfall intensity was 0.8 cm/hr on a catchment of area 8.6 km2. The measured runoff volume du

A $$10m$$ long prestressing bed is used to cast $$4$$ (pretensioned) prestressed concrete beams of $$2.3$$ $$m$$ each. A

As per provision of $$IS$$ $$456$$-$$2000$$, in the limit state method for design of beams, the limiting value of the de

Read the following two statements $${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Maximum strain in concrete at the outermost compr

Modulus of elasticity of M25 grade concrete in MPa is

An $$ISMB$$ $$500$$ is used as a beam in a multi-storey construction. From the view point of structural design, it can b

When designing steel structures, one must ensure that local buckling in webs does not take place. This check may not be

Given reason for the following is not more than $$20$$ words (a) A maximum permissible distance between lacing and batte

$$ISA$$ $$100 \times 100 \times 10mm$$ (cross sectional area $$ = 1903\,\,m{m^2}$$) is welded along $$A$$ and $$B$$ (Ref

$$ISA$$ $$100 \times 100 \times 10\,\,mm$$ (Cross sectional area $$ = 1903\,\,m{m^2})$$ serves as tensile member. This a

For the loading given in the figure below, two statements ( $${\rm I}$$ and $${\rm II}$$ ) are made. $${\rm I}.$$ $$\,

In the propped cantilever beam carrying a uniformly distributed load of $$w$$-$$kN/m,$$ shown in the following figure, t

The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio ($$\mu$$) of a material are related as

Calculate the shape factor for the $$T$$-section shown in the following figure made up of two plates $$100\,\,mm \times

A steel beam (with a constant $$EI,$$ and span $$L$$) is fixed at both ends and carries a uniformly distributed load ($$

A propped cantilever beam of span $$'L'$$ is loaded with $$u.d.l$$ of intensity $$w$$/unit length, all through the span.

SSD and Friction coefficients are