Given the matrices $$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \c

The sum of Eigen values of the matrix, $$\left[ M \right]$$ is where $$\left[ M \right] = \left[ {\matrix{ {215} &am

$$\,\,\mathop {Lim}\limits_{x \to \infty } \left( {{{x + \sin x} \over x}} \right)\,\,$$ equal to

With reference to the conventional Cartesian $$(x,y)$$ coordinate system, the vertices of a triangle have the following

A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water trea

Some of the nontoxic metals normally found in natural water are

For a sample of water with the ionic composition shown in the figure below, the carbonate and noncarbonate hardness conc

The dimension for kinematic viscosity is

Three rigid buckets, shown as in the figures (1), (2) and (3), are of identical heights and base areas. Further, assume

For a beam of cross-section, width $$= 230$$ $$mm$$ and effective depth $$= 500$$ $$mm,$$ the number of rebars of $$12$$

In a reinforced concrete section, the stress at the extreme fibre in compression is $$5.80$$ $$MPa.$$ The depth of neutr

A rectangular beam of width $$(b)$$ $$230$$ $$mm$$ and effective depth $$(d)$$ $$450$$ $$mm$$ is reinforced with four ba

While designing, for a steel column of $$Fe250$$ grade, a base plate resting on a concrete pedestal of $$M20$$ grade, th

The tension and shear force (both in $$kN$$) in each bolt of the joint, as shown below, respectively are

A steel section is subjected to a combination of shear and bending actions. The applied shear force is $$V$$ and the she

A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude a

The possible location of shear center of the channel section, shown below, is

For the cantilever beam of span $$3$$ $$m$$ (shown below), a concentrated load of $$20$$ $$kN$$ applied at the free end

If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown i

The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is

In a beam of length $$L,$$ four possible influence line diagrams for shear force at a section located at a distance of $

For the truss shown below, the member $$PQ$$ is short by $$3$$ $$mm.$$ The magnitude of vertical displacement of joint $

The ultimate collapse load $$(P)$$ in terms of plastic moment $${M_P}$$ by kinematic approach for a propped cantilever o

Match the information given in Group $$-$$ $${\rm I}$$ with those in Group $$-$$ $${\rm II}.$$

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $

The perception-reaction time for a vehicle travelling at 90 km/h, given the coefficient of longitudinal friction of 0.35