The differential equation $${{{d^4}y} \over {d{x^4}}} + P{{{d^2}y} \over {d{x^2}}} + ky = 0\,\,$$ is

The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {x,y} \right)dy = 0\,\,$$ to be exact is

The value of $$\varepsilon $$ in the mean value theoram of $$f\left( b \right) - f\left( a \right) = \left( {b - a} \right)\,\,f'\left( \varepsilon \right)$$ for $$f\left( x \right) = A{x^2} + Bx + C$$ in $$(a, b)$$ is

The void ratio of a soil sample is 1. The corresponding porosity of the sample is _______.

A prestressed concrete rectangular beam of size $$300\,\,mm \times 900\,\,mm$$ is prestressed with an intial prestressing force of $$700$$ $$kN$$ at an eccentricity of $$350$$ $$mm$$ at midspan. Stress at top due to prestress alone, in $$N/m{m^2}$$ is

$$IS$$ $$456$$-$$2000$$ recommends providing certain minimum steel in a $$RCC$$ beam

Grading of aggregate in a concrete mix is necessary to achieve

A beam fixed at the ends and subjected to lateral loads only is statically indeterminate and the degree of indeterminacy is

The fixed end moment of a uniform beam of span $$l$$ fixed at the ends, subjected to a central point load $$P$$ is

When a column is fixed at both ends corresponding to Euler's criterion load is

A cantilever beam of span $$l$$ subjected to a uniformly distributed load $$'w'$$ per unit length resting on a rigid prop at the tip of cantilever. The magnitude of the reaction of at the prop is

For a given shear force across a symmetrical $${\rm I}$$-section, the intensity of shear is maximum at

A cantilever beam curved in plan and subjected to lateral loads will develop at any section

The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile stress, $${\sigma _x} = 1.5\,\,N/m{m^2},$$ and shear stress, $$\tau = 1.20\,N/m{m^2},$$ which cause cracking of concrete. Then the tensile strength of the concrete in $$N/m{m^2}$$ is

If $$'YY'$$ is the centroidal axis of a $$T$$-beam section, subjected to plastic moment, $${M_P},$$ the neutral axis lies

The ratio of the stiffness of a beam at the near end when the far end is hinged to the stiffness of the beam at the near end when the far end is fixed is

A single bay portal frame of height $$'h'$$ fixed at the base is subjected to a horizontal displacement $$'\delta '$$ at the top. The base moments developed is proportional to _____, where $$'{\rm I}'$$ is the moment of inertia of the cross section.

Which of the following statements is true with regard to the flexibility method of analysis.

Flexibility of a structure may be defined as the displacement caused by ----------------- force and stiffness of a structure may be defined as the force required for ----------------- displacement

In flexibility method the unknown quantities are ----------------- whereas in stiffness method the unknown quantities are --------------

The influence line diagram for the force in member $$'a'$$ of the truss shown below is given by

Influence line for redundant structures can be obtained by

The Kinematic Indeterminacy of plane frame shown below is

The kinematic indeterminacy of single bay portal frame fixed at the base is

A beam fixed at the ends and subjected to lateral loads only is statically indeterminate and the degree of indeterminacy is

Nagpur road plan is based on