In a falling head permeability test on a clay sample,the following results were obtained. Sample length 120 m,sample diameter 80 mm, initial head 1200 mm, final head 400mm time for fall in head 6 minutes stand pipe diameter 4mm. Find the co-efficient of permeability of the soil in mm/sec.
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Solution
A pre-stressed concrete beam has a cross-section with the following properties:–
Area, A = 46400 mm2, I =75.8 × 107mm4, Ybottom=244m,Ytop = 156 mm. It is subjected to a pre-stressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of e is given by
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Solution
A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It is further subjected to a torque of 10 kNm. The maximum principal stress experienced on the shaft is closest to
A plane frame shown below is analyzed by neglecting axial deformation. Following statements are made with respect to the analysis.
1.Column AB carries axial force only.2.Vertical deflections at centre of beam BC is 1 mm.With reference to the above statements, which of the following applies?
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Solution
A column has a rectangular cross-section of 10 mm × 20mm and a length of 1 m. The slenderness ratio,
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Solution
The random variable x takes on the values 1, 2 and 3 with probabilities \(\frac{2+5P}{5},\frac{1+3P}{5}\) and \(\frac{1.5+2P}{5}\)respectively..The values of P and E(x) are respectively
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Solution
Consider the differential equation \(\frac{dy}{dx}\) = 1 + y2. Which one of the following can be particular solution of this differential equation?
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Solution
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Solution
Matching exercise. Choose the correct one out of the four alternatives.
Group I Group II
P.2nd order differential 1.Range-Kutta method equation
Q.Non-linear algebraic 2.Newton-Raphson method equation
R.Linear algebraic 3.Gauss elimination equation
S.Numerical integration 4.Simpson’s rule
The eigen values of the matrix \(\begin{bmatrix} 2 &-1 &0 &0 \\ 0 &3 &0 &0 \\ 0 &0 &-2 &0 \\ 0 &0 &-1 &4 \end{bmatrix}\) are
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Solution
Use the property, sum of eigen values equals sum of diagonal elements
Sum of diagonal elements = 2 + 3 – 2 + 4 = 7
Find sum of eigen values given in options.
(a)2 +– 2+ 1+ 1= 2
(b)2+ 3+ –2 +4 =7
(c)2 + 3 + 1 + 4 = 10
(d)1+ 1+ 1+ 1= 4
∴answer is(b)