The Optimistic Time (O), most likely Time (M) and Pessimistic Time (P) (in days) of the activities in the critical path are given below in the format O-M-P. The expected completion time (in days) of the project is _______.

The compound which is largely responsible for initial setting and early strength gain of Ordinary Portland Cement is

Bull's trench kiln is used in the manufacturing of

The type of partial differential equation $${{{\partial ^2}p} \over {\partial {x^2}}} + {{{\partial ^2}p} \over {\partial {y^2}}} + 3{{{\partial ^2}p} \over {\partial x\partial y}} + 2{{\partial p} \over {\partial x}} - {{\partial p} \over {\partial y}} = 0$$ is

Newton-Raphson method is to be used to find root of equation $$\,3x - {e^x} + \sin \,x = 0.\,\,$$ If the initial trial value for the root is taken as $$0.333,$$ the next approximation for the root would be _________ (note: answer up to three decimal)

The solution of the partial differential equation $${{\partial u} \over {\partial t}} = \alpha {{{\partial ^2}u} \over {\partial {x^2}}}$$ is of the form

Type $${\rm I}{\rm I}$$ error in hypothesis testing is

If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is

The magnitudes of vectors P, Q and R are 100 kN, 250 kN and 150 kN, respectively as shown in the figure. The respective values of the magnitude (in kN) and the direction (with respect to the x-axis) of the resultant vector are

A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force P acts at C as shown. Let R_Ah and R_Bh be the horizontal reactions at supports A and B, respectively, and R_Av be the vertical reaction at support A. Self- weight of the member may be ignored. Which one of the following sets gives the correct magnitudes of R_Av, R_Bh and R_Ah ?

Effluent from an industry 'A' has a pH of 4.2. The effluent from another industry 'B' has double the hydroxyl (OH^-) ion concentration than the effluent from industry 'A'. pH of effluent from the industry 'B' will be _______.

A sector gate is provided on a spillway as shown in the figure. Assuming g = 10 m/s², the resultant force per meter length (expressed in kN/m) on the gate will be __________

The porosity (n) and the degree of saturation (S) of a soil sample are 0.7 and 40%, respectively. In a 100 $$m^3$$ volume of the soil, the volume (expressed in $$m^3$$) of air is _____.

A concrete gravity dam section is shown in the figure. Assuming unit weight of water as 10$$kN/m^3$$ and unit weight of concrete as 24$$kN/m^3$$, the uplift force per unit length of the dam (expressed in kN/m) at PQ is____.

For $$M25$$ concrete with creep coefficient of $$1.5,$$ the long-term static modulus of elasticity (expressed in $$MPa$$) as per provisions of $$IS:$$ $$456-2000$$ is ______________

In shear design of an $$RC$$ beam, other than the allowable shear strength of concrete $$\left( {{\tau _c}} \right),$$there is also an additional check suggested in $$IS$$ $$456$$-$$2000$$ with respect to the maximum permissible shear stress $$\left( {{\tau _{c\,\,\max }}} \right).$$ The check for $${{\tau _{c\,\,\max }}}$$ is required to take care of

A reinforced concrete $$(RC)$$ beam with width of $$250$$ $$mm$$ and effective depth of $$400$$ $$mm$$ is reinforced with $$Fe415$$ steel. As per the provisions of $$IS$$ $$456$$ - $$2000,$$ the minimum and maximum amount of tensile reinforcement (expressed in $$m{m^2}$$ ) for the section are, respectively

The semi-compact section of a laterally unsupported steel beam has an elastic section modulus, plastic section modulus and design bending compressive stress of $$500\,\,c{m^3},\,\,650\,\,c{m^3}$$ and $$200$$ $$MPa,$$ respectively. The design flexural capacity (expressed in $$kNm$$) of the section is ___________________

Two plates are connected by fillet welds of size $$10$$ $$mm$$ and subjected to tension, as shown in the sketch. The thickness of each plate is $$12$$ $$mm.$$ The yield stress and the ultimate tensile stress of steel are $$250$$ $$MPa$$ and $$410$$ $$MPa,$$ respectively. The welding is done in the workshop $$\left( {{\gamma _{mw}} = 1.25} \right).$$

As per the Limit State Method of $$IS$$ $$800:2007,$$ the minimum length (rounded off to the nearest higher multiple of $$5$$ $$mm$$) of each weld to transmit a force $$P$$ equal to $$270$$ $$kN$$ (factored) is

A $$3$$ $$m$$ long simply supported beam of uniform cross section is subjected to a uniformly distributed load of $$w = 20$$ $$kN/m$$ in the central $$1$$ $$m$$ as shown in the figure.

If the flexural rrigidity $$(EI)$$ of the beam is $$30 \times {10^6}\,\,N$$ - $${m^2},$$ the maximum slope (expressed in radians) of the deformed beam is

Consider the plane truss with load $$P$$ as shown in the figure. Let the horizontal and vertical reactions at the joint $$B$$ be $$HB$$ and $${V_B},$$ respectively and $${V_C}$$ be the vertical reaction at the joint $$C.$$

Which one of the following sets gives the correct values of $${V_B},\,\,{H_B}$$ and $${V_C}$$?

A plane truss with applied loads is shown in the figure.

The members which do not carry any force are

A propped cantilever of span $$L$$ carries a vertical concentrated load at the mid-span. If the plastic moment capacity of the section is $${M_P}$$, the magnitude of the collapse load is

Two beams $$PQ$$ (fixed at $$P$$ and with a roller support at $$Q,$$ as shown in Figure $$I,$$ which allows vertical movement) and $$XZ$$ (with a hinge at $$Y$$) are shown in the Figures $$I$$ and $$II$$ respectively. The spans of $$PQ$$ and $$XZ$$ are L and $$2L$$ respectively. Both the beams are under the action of uniformly distributed load $$(W)$$ and have the same flexural stiffness, $$EI$$ (where, $$E$$ and $$I$$ respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be $${\delta _{\max 1}}$$ and $${\theta _{\max 1}},$$ respectively, in the case of beam $$PQ$$ and the corresponding quantities for the beam $$XZ$$ be $${\delta _{\max 2}}$$ and $${\theta _{\max 2}},$$ respectively.

Which one of the following relationships is true?