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Explanation:

The concept of raising the outer edge above the inner edge in horizontal curves is known as super-elevation (cant or banking) and is primarily used in:

1. Highways – To counteract centrifugal force on vehicles, reducing the risk of skidding and overturning.
2. Railways – To provide a smooth transition for trains on curves, reducing lateral forces and rail wear.

However, taxiways generally do not require super-elevation because aircraft move at lower speeds on taxiways, and the main concern is ensuring smooth, level surfaces for ground maneuvering rather than counteracting lateral forces.

Thus, the correct choice is Highways and Railways only

Explanation:

• P. NO₂ → iv. NH₃ injection

(Selective catalytic reduction (SCR) or selective non-catalytic reduction (SNCR) involves NH₃ injection to reduce NO₂ emissions.)

• Q. SO₂ → iii. Lime scrubbing

(Lime scrubbing is used in flue gas desulfurization (FGD) to remove SO₂ from emissions.)

• R. CO → i. Flaring

(Flaring is used to burn off excess CO and other hydrocarbons in industrial processes.)

• S. Particles → ii. Cyclonic separator

(Cyclonic separators help in removing particulate matter from air streams.)

Explanation:

According to the properties of a matrix

(i) (A + B)T = AT + BT

The sum of the transpose of matrices is equal to the transpose of the sum of two matrices.

(ii) (AB)T = AT BT

The product of the transpose of two matrices in reverse order is equal to the transpose of the product of them.

Explanation:

• P. Bubble tube → iv. Levelling

(The bubble tube is used in leveling instruments to check and adjust the horizontal level.)

• Q. Plumb bob → iii. Centering

(A plumb bob helps in centering the instrument precisely over a survey point.)

• R. Tangent screw → ii. Minor movements

(Tangent screws allow fine adjustments and minor movements for precise alignment.)

• S. Stadia cross-wire → i. Tacheometry

(Stadia cross-wires are used in tacheometry for measuring distances using a theodolite or level.)

Explanation:

Statement P: "In a Pure project organization, the project manager maintains complete authority and has maximum control over the project."

True

• A pure project organization (also called a projectized organization) gives the project manager full authority over project execution, decision-making, and resources.
• The project team reports directly to the project manager, as confirmed by standard project management literature.

Statement Q: "A matrix organization structure facilitates quick response to changes, conflicts, and project needs."

True

• As per the matrix organization structure description in the images, one of its advantages is:
• "The structure facilitates quick response to changes, conflicts, and project needs."
• The matrix structure combines functional and project-based management, ensuring efficient adaptability to project demands and conflicts.

Explanation:

Discharge (Q) = 30 m³/s

Width of channel (B) = 2m

Bed slope = 1 in 300

Energy correction factor (α) = 1.1

g = 10 m/s²

Discharge per unit width \((q)=\frac{Q}{B}\)

\(=\frac{30}{2}=15 \mathrm{~m}^3 / \mathrm{sec} / \mathrm{m}\)

Critical depth does not depend on slope or the roughness of channel.

Critical depth is given by

 \(\left(y_c\right)=\left(\frac{q^2 \cdot \alpha}{g}\right)^{1 / 3}\)

\(=\left(\frac{1.1 \times 15^2}{10}\right)^{1 / 3}=2.914 \mathrm{~m} \simeq 2.91 \mathrm{~m}\)

Additional InformationTotal energy \((E)=y+\frac{\alpha V^2}{2 g}\)

\(=y+\frac{\alpha q^2}{y^2 \times 2 g} \)

\(\frac{d E}{d y} =1+\frac{\alpha q^2}{2 g} \frac{(-2)}{y^3}\)

For critical low, putting \(\frac{d E}{d y}=0\)

\(\frac{\alpha q^2}{g y_c^3}=1\)

\(\therefore \quad y_c=\left(\frac{\alpha q^2}{g}\right)^{1 / 3}\)

Explanation:

For normally consolidated clays A = 0.5 - 1

• For OC clays, A = f (OCR), for heavily over consolidated clays, A < 0.

Additional Information

Pore Pressure Parameters:

(i) Sometimes it is not possible to determine pore pressure practically, then the theoretical approach given by skempton can be adopted.

(ii) Pore pressure parameters A and B are empirical coefficients that are used to express the response of pore pressure to changes in vertical pressure and lateral pressure under "undrained condition".

Parameter B:

(i) This parameter is defined under cell pressure stage and represents the ratio of change in pore pressure to the change in cell pressure.

B = ΔUc/Δσc

(ii) B varies from o to 1 depending on the degree of saturation. "B" is zero for dry soil and is equals unity for fully saturated soil.

Parameter A:

(i) This parameter is valid in deviator stage and is defined in terms of another parameter A̅, such that

A̅ = A.B

(ii) The parameter A̅ represents the ratio of change in pore pressure to change in deviator stress during shear stage.

\(\bar A = \dfrac{{\Delta {U_d}}}{{\Delta {\sigma _d}}} = \dfrac{{\Delta {U_d}}}{{\Delta ({\sigma _1} - {\sigma _3})}} = \dfrac{{\Delta {U_d}}}{{\Delta {\sigma _1} - \Delta {\sigma _3}}}\)

(iii) The parameter depends upon strain in soil, degree of saturation, over consolidated ratio, stratification of soil, sample disturbance, etc. Its value may be as low as -0.5 for over consolidated soil with high O.C.R. to as high as 3 or loose saturated sand.

Explanation:

Given Data:

• Required scale of aerial photograph = 1 : 13,000
• Permissible flying height above datum = 3000 m
• Average terrain elevation above datum = 1050 m

Now,

Scale  \(=\frac{1}{13000}\)

Hence, 

\(\mathrm{S} =\frac{\mathrm{f}}{\mathrm{H}-\mathrm{h}} \)

\(\frac{1}{13000} =\frac{\mathrm{f}}{3000-1050} \)

∴   f = 0.15 m = 150 mm

Explanation:

As per given data:

• Budgeted Cost of Work Scheduled (BCWS) = Rs. 200
• Budgeted Cost of Work Performed (BCWP) = Rs. 150
• Actual Cost of Work Performed (ACWP) = Rs. 190

Schedule Variance is given by

= BCWP - BCWS 

= 150 - 200

= -50

Explanation:

Grashoff method is used to determine the bending moment in two way RCC slab. It is used for load distribution when the slab is simply supported on all four edges and the corners are not held down.

As per Rankine Grashoff method

\(M_{u x}=\frac{r^4}{8\left(1+r^4\right)} w \epsilon_x^2\)

\(M_{u y}=\frac{r^2}{8\left(1+r^4\right)} w \epsilon_x^2\)

Here \(r=\frac{\ell_y}{\ell_x} \)

\(\Rightarrow \quad \frac{\mathrm{M}_{\mathrm{ux}}}{\mathrm{M}_{\mathrm{uy}}}=\mathrm{r}^2=\left(\frac{\ell_{\mathrm{y}}}{\ell_{\mathrm{x}}}\right)^2\)