For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________.

Consider the following statements:
P. Walls of one brick thick are measured in square meters.
Q. Walls of one brick thick are measured in cubic meters.
R. No deduction in the brickwork quantity is made for openings in walls up to 0.1 $$m^2$$ area.
S. For the measurement of excavation from the borrow pit in a fairly uniform ground, dead men are left at suitable intervals.
For the above statements, the correct option is

Given that the scope of the construction work is well-defined with all its drawings, specifications, quantities and estimates, which one of the following types of contract would be most preferred?

Let $$\,\,W = f\left( {x,y} \right),\,\,$$ where $$x$$ and $$y$$ are functions of $$t.$$ Then, according to the chain rule, $${{dw} \over {dt}}$$ is equal to

A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following outcomes: $$H, H,H.$$ If the coin is tossed one more time, the probability (up to one decimal place ) of obtaining $$H$$ again, given the previous realizations of $$H, H$$ and $$H$$, would be _____.

The divergence of the vector field $$\,V = {x^2}i + 2{y^3}j + {z^4}k\,\,$$ at $$x=1, y=2, z=3$$ is ________.

Consider the following definite integral $$${\rm I} = \int\limits_0^1 {{{{{\left( {{{\sin }^{ - 1}}x} \right)}^2}} \over {\sqrt {1 - {x^2}} }}dx} $$$
The value of the integral is

The tangent to the curve represented by $$y=x$$ $$ln$$ $$x$$ is required to have $${45^ \circ }$$ inclination with the $$x-$$axis. The coordinates of the tangent point would be

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

If $$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8 & 4 \cr } } \right]A{B^T}$$ is equal to

The analysis of a water sample produces the following results: The total hardness (in mg/L as $${\mathrm{CaCO}}_3$$) of the water sample is ______.

The figure shows a U-tube having a 5 mm × 5 mm square cross-section filled with mercury (specific gravity = 13.6) up to a height of 20 cm in each limb (open to the atmosphere).

If 5cm³ of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be______

A catchment is idealized as a 25 km × 25 km square. It has five rain gauges, one at each corner and one at the center, as shown in the figure. During a month, the precipitation at these gauges is measured as G₁ = 300 mm, G₂ = 285 mm, G₃ = 272 mm, G₄ = 290 mm and G₅ = 288 mm. The average precipitation (in mm, up to one decimal place) over the catchment during this month by using the Thiessen polygon method is_______ .

The culturable command area of a canal is 10,000 ha. The area grows only two crops-rice in the Kharif season and wheat in the Rabi season. The design discharge of the canal is based on the rice requirements, which has an irrigated area of 2500 ha, base period of 150 days and delta of 130 cm. The maximum permissible irrigated area (in ha) for wheat, with a base period of 120 days and delta of 50 cm, is_______.

A simply supported rectangular concrete beam of span $$8$$ $$m$$ has to be prestressed with a force of $$1600$$ $$kN.$$ The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity $$30$$ $$kN/m.$$ Neglecting the self - weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be _______________

Let the characteristic strength be defined as that value, below which not more than 50% of the results are expected to fall. Assuming a standard deviation of 4 MPa, the target mean strength (in MPa) to be considered in the mix design of a M25 concrete would be

Two plates of $$8$$ $$mm$$ thickness each are connected by a fillet weld of $$6$$ $$mm$$ thickness as shown in the figure.

The permissible stresses in the plate and the weld are $$150$$ $$MPa$$ and $$110$$ $$MP,$$ respectively. Assuming the length of the weld shown in the figure to be the effective length, the permissible load $$P$$ (in $$kN$$) is _____________.

Two prismatic beams having the same flexural rigidity of $$1000\,kN$$-$${m^2}$$ are shown in the figures.

If the mid-span deflections of these beams are denoted by $${\delta _1}$$ and $${\delta _2}$$ (as indicated in the figures), the correct option is

A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and inner diameter of $$50mm.$$ If the allowable shear stress is $$125$$ $$MPa$$, the maximum torque (in $$kN$$-$$m$$) that the shaft can resist is ___________

Consider the three prismatic beams with the clamped supports $$P,Q$$ and $$R$$ as shown in the figures.

Given that the modulus of elasticity, $$E$$ is $$2.5 \times {10^4}\,\,MPa;$$ and the moment of inertia, $${\rm I}$$ is $$8 \times {10^3}\,\,m{m^4},$$ the correct comparison of the magnitudes of the shear force $$S$$ and the bending moment $$M$$ developed at the supports is

In a material under a state of plane strain, a 10×10 mm square centered at a point gets deformed as shown in the figure. If the shear strain $$\gamma_{xy}$$ at this point is expressed as 0.001k (in rad), the value of k is

Consider the portal frame shown in the figure and assume the modulus of elasticity, $$E = \,2.5 \times {10^4}\,\,MPa$$ and the moment of inertia, $${\rm I} = 8 \times {10^8}\,\,m{m^4}$$ for all the members of the frame.

The rotation (in degrees, up to decimal place) at the rigid joint $$Q$$ would be ____________

Consider the frame shown in the figure.

If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to

While aligning a hill road with a ruling gradient of 6%, a horizontal curve of radius 50 m is encountered. The grade compensation (in percentage, up to two decimal places) to be provided for this case would be ______.