# Tutor profile: Niraj B.

## Questions

### Subject: Number Theory

If 7x + 3y = 240 Which of the following option is true. A. X & Y both are odd B. Sum of X & Y is even C. If X is odd, Y is Even D. None of these.

Solution. 240 is Even => either even + even = Even OR Odd + Odd = Even. If X is Odd then 7X is odd. => 3Y has to be odd to make 7X + 3Y even. => Y is odd. Similarly, if X is even, Y has to be even => X & Y both are odd or both are even. => X + Y is Even in both the cases. Option B is correct

### Subject: Construction

Perform the Earned Value Analysis and comment on the project status from the following information. Details about the Project It is a high rise building having 30 Floors. Budgeted cost = 1,000,000 USD Project Duration = 36 months The project team has achieved 18 floors within 20 months. The Actual cost of the project until today is 550,000 USD

Solution Earned Value Cost = Budgeted cost x Activity % complete = 1000000 x (18/30) = 600,000 USD Planned Value Cost = Budgeted cost * Schedule % complete = 1000000 x (20/36) = 555,555 USD Schedule Variance (SV) = Earned Value Cost - Planned Value Cost =600,000-555,555 = 44,445 USD Cost Variance (CV) = Earned Value Cost – Actual Cost = 600,000-550,000 = 50,000 USD Schedule Performance Index (SPI) (Earned Value Cost/Planned Value Cost) = 600,000/555,555 = 1.08 Cost Performance Index (CPI) (Earned Value Cost /Actual Cost) = 600,000/550,000 = 1.09 Using above values we can say that our CV is positive & CPI > 1 & our SV is positive having SPI >1 Conclusion Which means that the project is under Budget and ahead of schedule.

### Subject: Algebra

Find the domain of the following function f(x)=√(-4-2x)/((x+3)(x-1))

For Numerator -4-2x ≥ 0 => -4 ≥ 2x => -2 ≥ x For Denominator Denominator ≠ 0 (because for zero denominator the function f(x) will become undefined) => (x+3) (x-1) ≠ 0 => x≠ -3 & x≠ 1 Final Solution domain of the function f(x) is X ≤ -2 and X ≠ -3,1

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