All India Civil Engineering (CE) Group

If f(x) = 2x7+3x−5, which of the following is a factor of f(x)?
  • a)
    (x3+8)
  • b)
    (x-1)
  • c)
    (2x-5)
  • d)
    (x+1)
Correct answer is option 'B'. Can you explain this answer?

Anshu Kumar answered  •  9 hours ago
Understanding the Function f(x)
The function given is f(x) = 2x^7 + 3x - 5. To determine which of the options is a factor, we can use the Factor Theorem. This theorem states that if f(c) = 0 for some value c, then (x - c) is a factor of f(x).
Evaluating the Options
Let's evaluate each option by substituting the corresponding values into f(x):
  • Option A: ... more
    - This expression does not lead to a straightforward evaluation with f(x). It's not feasible to determine if it's a factor using simple substitution.
  • Option B: (x - 1)
    - Substitute x = 1 into f(x):
    - f(1) = 2(1)^7 + 3(1) - 5 = 2 + 3 - 5 = 0
    - Since f(1) = 0, (x - 1) is a factor.
  • Option C: (2x - 5)
    - Substitute x = 5/2 into f(x):
    - f(5/2) is complex and does not yield a simple check for being a factor.
  • Option D: (x + 1)
    - Substitute x = -1 into f(x):
    - f(-1) = 2(-1)^7 + 3(-1) - 5 = -2 - 3 - 5 = -10, which is not zero.

Conclusion
Only option B, (x - 1), gives us a value of zero when substituted into f(x), confirming that it is indeed a factor of the polynomial function. Hence, the correct answer is option B.

If the BOD of a diluted sample in 1 : 100 ratio is 11 PPM in the beginning and 8 PPM at the end of 5 days, then the BOD of the sample is
  • a)
    300 PPM
  • b)
    950 PPM
  • c)
    137.5 PPM
  • d)
    73 PPM
Correct answer is option 'A'. Can you explain this answer?

Om Pillai answered  •  15 hours ago
Understanding BOD Calculation
Biochemical Oxygen Demand (BOD) is a critical parameter in assessing the organic pollution level in water. In this scenario, we analyze a diluted sample to determine the original BOD concentration.
Given Data
- Initial BOD of diluted sample: 11 PPM
- Final BOD after 5 days: 8 PPM
- Dilution factor: 1:100
Calculation Steps
... more
1. Determine the change in BOD:
- Change in BOD = Initial BOD - Final BOD
- Change in BOD = 11 PPM - 8 PPM = 3 PPM
2. Calculate the BOD of the original sample:
- The change in BOD reflects the oxygen consumed by the sample. Since the sample was diluted 100 times, we need to multiply the change in BOD by the dilution factor to find the original concentration.
- Original BOD = Change in BOD × Dilution factor
- Original BOD = 3 PPM × 100 = 300 PPM
Conclusion
The BOD of the original sample is therefore 300 PPM, confirming that option 'A' is correct. This indicates a significant level of organic material present in the sample, which is crucial for water quality assessment in civil engineering and environmental management.

The effect of arching a beam, is
  • a)
    to reduce the bending moment throughout
  • b)
    to increase the bending moment throughout
  • c)
    nothing on the bending throughout
  • d)
    all the above.
Correct answer is option 'A'. Can you explain this answer?

Bibek Mukherjee answered  •  17 hours ago
Understanding Beam Arching
Arching a beam refers to the intentional curvature introduced into a beam's shape, which significantly influences its structural behavior, particularly concerning bending moments.
Reduction of Bending Moments
- When a beam is arched, it alters the distribution of internal forces.
- The curvature helps in redistributing loads applied to t
... more

Cavity wall is generally provided for
  • a)
    heat insulation
  • b)
    sound insulation
  • c)
    prevention of dampness
  • d)
    all the above
Correct answer is option 'D'. Can you explain this answer?

Nilesh Kapoor answered  •  20 hours ago
Cavity Wall Overview
Cavity walls are a popular construction technique in modern buildings, designed with two separate wall sections (outer and inner) with a space or cavity in between. This design serves multiple purposes, making it a versatile choice for various climates and building requirements.
Heat Insulation
- Energy Efficiency: The cavity creates an air
... more

The steel used for rails under heavy traffic and on sharp curves, is
  • a)
    Nickel steel
  • b)
    Chrome steel
  • c)
    Magnese steel
  • d)
    Vanadium steel
Correct answer is option 'C'. Can you explain this answer?

Varun Mukherjee answered  •  22 hours ago
Importance of Steel in Rail Construction
The type of steel used in rail construction is crucial, particularly for rails subjected to heavy traffic and sharp curves. The properties of steel must ensure durability, strength, and resistance to wear.
Why Manganese Steel?
Manganese steel, often referred to as Hadfield steel, is known for its unique properties that make it i
... more
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