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

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

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

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

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

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

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

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

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

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.

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 $$M$$ $$25.$$

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

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

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

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

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

The order for the flexibility matrix for a structure is,

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

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