Evaluate \(\int_{e}\frac{dz}{z^{2}+2z+2}\), is the source having vertices at (0, 0), (–2,–2), (–2, 0) and (0, –2) oriented in the anticlockwise direction.
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The probability that an event A occurs in one trial of an experiment is 0.4. Three independent trials of experiments are performed. The probability that A occurs at least once is______.
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Solution
p = 0.4, q = 1–0.4 =0.6 ,n = 3
Required probability =P(A occuring at least once)
= 1 – P(r= 0-)
= 1 –nCr pr qn–r
= 1 – 3C0(0.4)°(0.6)3
= 1 – 0.216 = 0.784
Expand the function f(z)= sin z about z = π⁄4 pin Taylor’s series.
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The minimum value of \(\left ( x^{2}+\frac{250}{x} \right )\) is _______.
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The system of equations 3x – y + z = 0, 15x – 6y + 5z = 0, λx– 2y + 2z= 0 has a non- zero solution, if λ is _____.
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The pressure drop for a relatively low Reynolds number flow in a 600 mm, 30 m long pipeline is 70 KPa. Then the wall shears tress will be ________.
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The wet bulb depression is zero, if relative humidity will be equal to
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Solution
At 100% Relative Humidity (RH), the wet bulb temperature (WBT) becomes equal to dry bulb temperature (DBT)
So, wet bulb depression =DBT – WBT = 0 at RH = 100%
In a small engineering project, for an activity, the optimistic time is 2min, the most likely time is 5 min and the pessimistic time is 8 min, then the expected time of activity will be________.
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In orthogonal cutting, cutting force and thrust force are 1000N and 500 N respectively. If the rake angle of tool is zero, the coefficient of friction in chip-tool interface will be ________.
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Plane stress at a point in a body is described by principal stresses 3σ and σ. Then, the ratio (σn/τman) on the plane of maximum shear stress is ________. (where σn= normal stress,τmax= maximum shear stress).
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