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Piyush P.
Electrical and Electronics Engineer and Master's Student
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Calculus
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Question:

Calculate deirvative of Dx ln(x^2 + 1) ?

Piyush P.

Use CHAIN RULE, Dx ln(x^2 + 1) = 2x * 1/(x^2 + 1) =2x/(x^2 + 1) is the answer.

Electrical Engineering
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Question:

What is “pu” in electrical engineering?

Piyush P.

Pu stands for per unit and this will be used in single line diagram of power distribution and it is like a huge electrical circuit with no of components (generators, transformers, loads) with different ratings (in MVA and KV). To bring all the ratings into the common platform we use pu concept in which, in general, largest MVA and KV ratings of the component is considered as base values, then all other component ratings will get back into this basis.Those values are called as pu values. (p.u=actual value/base value).

Algebra
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Question:

If x^3+y^3=9 and x+y=3 then the value of x^4+y^4 is, 1. 81 2. 32 3. 27 4. 17

Piyush P.

Whenever you meet x^3+y^3=9 and x+y=3 together straightway go for the expression x^3+y^3=(x+y)×(x2−xy+y^2) which results in, 9 = 3×((x+y)^2−3xy) =3×(9−3xy) =27−9xy or, xy = 2. Now easiest way to get x^4+y^4 is to multiply the first two given expressions together, giving, x4+y^4+xy(x^2+y^2 )= 27. So, x^4+y^4 = 27−2×((x+y)^2−2xy) =27−2×(9−4) =17 Answer: Option 4: 17. Key concepts used: Use of x^3+y^3=9 and x+y=3 together to get the value of xy -- get target value by direct multiplication of given two expressions and using the value of xy.

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