For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is

$${e^z}$$ is a periodic with a period of

The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,

If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then

If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$

If the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 2 \cr 0 & 5 & { - 6} \cr 2 & 7 & 8 \cr } } \right]$$ is $$26,$$ then the determinant of
the matrix $$\left[ {\matrix{ 2 & 7 & 8 \cr 0 & 5 & { - 6} \cr 1 & 3 & 2 \cr } } \right]$$ is

If $$A$$ and $$B$$ are two matrices and $$AB$$ exists then $$BA$$ exists,

Inverse of matrix $$\left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 1 & 0 & 0 \cr } } \right]$$ is

MPN index is measure of one of the following:

Alkalinity of water can be defined correctly in one of the following ways

If the porosity of a soil sample is 20%, the void ratio is

Lysimeter and Tensiometer are used to measure respectively, one of the following groups of quantities:

Hyetograph is a graph representing

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

A simply supported beam of a beam and slab system, rests on a support of width $$450$$ $$mm.$$ The clear span of the beam is $$10.0$$ $$m.$$ The thickness of the slab is $$120$$ $$mm.$$ The depth of the beam below the slab is $$480$$ $$mm$$ and the width of the beam is $$250$$ $$mm.$$ The beam is reinforced with one row of $$32$$ $$mm$$ diameter steel rods. The total load including the super imposed dead load, live load and its own weight is $$25.0$$ $$kN/m$$ at service stage. Compute the maximum nominal design shear stress in the concrete _______________

A hall is covered by a beam and slab system with beams placed at $$3.0$$ $$m$$ center. The effective span of the beam is $$8.35$$ $$m.$$ The thickness of the slab is $$120$$ $$mm.$$ The size of the beam below the slab is $$230$$ $$mm$$ width and $$380$$ $$mm$$ depth. The beam is reinforced with two numbers of $$32$$ $$mm$$ diameter steel rods of grade $$415\,\,N/m{m^2}.$$ Compute the Maximum total load/$$m$$ run, the beam can carry, including its own weight at service stage. Grade of concrete is $$M$$ $$25.$$

Design a square $$R.C$$ column to resist an axial load of $$400$$ $$kN$$ due to dead load and $$240$$ $$kN$$ due to live load at service stage. Design the section as a short axially loaded column. Use $$M25$$ concrete and steel of grade $$415$$ $$N/m{m^2}.$$ Give a near sketch of the cross section.

The cylinder strength of the concrete is less than the cube strength because of

The permissible tensile stress in concrete made of M 25 concrete is

Allowable average shear stress in an unstiffened web for beams made of steel of grade $$250\,\,N/m{m^2}$$ is

Maximum size of a fillet weld for a plate of square edge is

A compound steel column consisting of $$2$$ $$ISHB$$ $$400$$ placed at $$320$$ $$mm$$ centers, carries a total axial load of $$2500$$ $$kN.$$ Minimum slenderness ratio of the compound column is $$30.$$ Width of the flange of one $$ISHB$$ section is $$250$$ $$mm$$ and its minimum radius of gyration is $$51.6$$ $$mm$$. Design a suitable single flat lacing. $$20$$ $$mm$$ diameter single rivet is used to connect the lacings to the column. Rivet capacity need not be calculated. The following table may be used.

Factor of safety adopted by IS: 800-1984 while arriving at the permissible stress in axial compression is

A small element at the critical section of component is in a state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa$$ . The maximum shear stress is

A cantilever beam of span $$'L'$$ is loaded with a concentrated load $$'P'$$ at the free end. Deflection of the beam at the free end is

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

The force in the member $$DE$$ of the truss shown in the fig. is,

The order for the flexibility matrix for a structure is,

For the frame shown in the Fig. the maximum bending moment in the column is,

The degree of Kinematic Indeterminacy of the rigid frame with clamped ends at $$A$$ and $$D$$ shown in the fig. is

The value of camber recommended for CC roads in area of heavy rainfall is