A construction project consists of twelve activities. The estimated duration (in days) required to complete each of the activities along with the corresponding network diagram is shown below. Total floats (in days) for the activities 5-7 and 11-12 for the project are, respectively,

The activity-on-arrow network of activities for a construction project is shown in the figure. The durations (expressed in days) of the activities are mentioned below the arrows. The critical duration for this construction project is

As per Indian standards for bricks, minimum acceptable compressive strength of any class of burnt clay bricks in dry state is

If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$$f\left( x \right) = \left\{ {\matrix{ {{x \over a} + 1} & : & { - a \le x < 0} \cr { - {x \over a} + 1} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$ $$$g\left( x \right) = \left\{ {\matrix{ { - {x \over a}} & : & { - a \le x < 0} \cr {{x \over a}} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$

Which of the following statements is true?

The quadratic approximation of $$f\left( x \right) = {x^3} - 3{x^2} - 5\,\,$$ at the point $$x=0$$ is

The spot speeds (expressed in km/hr) observed at a road section are $$66, 62, 45, 79, 32, 51, 56, 60, 53$$ and $$49.$$ The median speed (expressed in km/hr) is __________.

$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right) = 0.7.$$ Which one of the following is the value of $$P\left( {X \cup Y} \right)$$ $$?$$

Consider the following linear system $$$x+2y-3z=a$$$ $$$2x+3y+3z=b$$$ $$$5x+9y-6z=c$$$
This system is consistent if $$a,b$$ and $$c$$ satisfy the equation

An assembly made of a rigid arm A-B-C hinged at end A and supported by an elastic rope C-D at end C is shown in the figure. The members may be assumed to be weightless and the lengths of the respective members are as shown in the figure.

Under the action of a concentrated load P at C as shown, the magnitude of tension developed in the rope is

A sample of water has been analyzed for common ions and results are presented in the form of a bar diagram as shown. The non-carbonate hardness (expressed in mg/L as $${\mathrm{CaCO}}_3$$) of the sample is

The hardness of a ground water sample was found to be 420 mg/L as $$CaCO_3$$. A softener containing ion exchange resins was installed to reduce the total hardness to 75 mg/L as $$CaCO_3$$ before supplying to 4 households. Each household gets treated water at a rate of 540 L/day. If the efficiency of the softener is 100%, the bypass flow rate (expressed in L/day) is .

A launched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity $$10$$ $$kN/m.$$ The design shear force (expressed in $$kN$$) at the section $$X$$-$$X$$ of the beam is ____________

As per $$IS$$ $$456$$ - $$2000$$ for the design of reinforced concrete beam, the maximum allowable shear stress $$\left( {{\tau _{c\,\,\max }}} \right)$$ depends on the

Two bolted plates under tension with alternative arrangement of bolt holes are shown in figures $$1$$ and $$2.$$ The hole diameter, pitch, and gauge length are $$d, p$$ and $$g$$ respectively.

Which one of the following conditions must be ensured to have higher net tensile capacity of configuration shown in figure $$2$$ than that shown in figure $$1$$?

A $$450$$ $$mm$$ long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as $$150\,\,mm\,\, \times \,\,150\,\,mm.$$ Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in $$MPa$$) is ______________

For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.

The shear stress $$\tau $$ is

An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?

A fixed-end beam is subjected to a concentrated load $$(P)$$ as shown in the figure. The beam has two different segments having different plastic moment capacities $$\left( {{M_P},\,2{M_P}} \right)$$ as shown.

The minimum value of load $$(P)$$ at which the beam would collapse (ultimate load) is

The portal frame shown in the figure is subjected to a uniformly distributed vertical load $$w$$ (per unit length).

The bending moment in the beam at the joint $$'Q'$$ is

Consider the structural system shown in the figure under the action of weight $$W.$$ All the joints are hinged. The properties of the members in terms of length $$(L),$$ area $$(A)$$ and the modulus of elasticity $$(E)$$ are also given in the figure. Let $$L,A$$ and $$E$$ be $$1$$ $$m,$$ $$0.05$$ $${m^2}$$ and $$30 \times {10^6}\,\,N/{m^2},\,\,$$ respectively, and $$W$$ be $$100$$ $$kN.$$

Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member $$QR$$?

The kinematic indeterminacy of the plane truss shown in the figure is

A motorist traveling at 100 km/h on a highway needs to take the next exit, which has a speed limit of 50 km/h. The section of the roadway before the ramp entry has a downgrade of 3% and coefficient of friction ( f ) is 0.35. In order to enter the ramp at the maximum allowable speed limit, the braking distance (expressed in m) from the exit ramp is ______