The recursion relation to solve x = e–x using Newton-Raphson method is
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A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ‘3’ is observed for the first time. Let X denote the number of times the dies is thrown. The expected value of X is _____.
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The variance of the random variable X with probability density function f(x) = 12|x|e–|x|is _____.
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The Newton-Raphs on method is used to solve the equation f(x) = x3– 5x2+ 6x – 8 =0. Taking the initial guess as x = 5, the solution obtained at the end of the first iteration is_____.
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Consider the differential equation
\(\frac{d^{2}x(t)}{dt^{2}}+3\frac{dx(t)}{dt}+2x(t)=0\)Given x(0) =20 and x(1) =10/e, where e = 2.718, the value of x(2) is _____.
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A hydrometer has a stem of diameter 1 cm and weight 0.3082N. The distance on the stem 10 cm corresponds to the markings between the relative density 1.0 and S.Then the value of S is.
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If a place L × B is towed through a fluid so that the boundary layer is entirely laminar, the ratio of towing speeds so that the drag forceremains constant regardless of whether length or breadth is in flow direction is given by
\(\frac{U_{L}}{U_{B}}= \left ( \frac{L}{B} \right )^{\frac{1}{K}}\)then the value of K is ________.
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A water tank supported on rigid foundation. The outer diameter of ring is 10m and its inner diameter is 8m. The intensity of loading being 100 kN/m2. What is the vertical stress at a depth of 5m below the centre of foundation in kN/m2.
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Determine the safe height of a slope which is to be constructed at an angle of 30° with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has the following properties; C = 10 kN/m2, f= 22.5° and density= 20 kN/m3.Taylor’s stability numbers for mobilised friction angles of 22.5° and 15° are, respectively,0.016 and 0.046. Safe height is ______ m.
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A purely cohesive soil was tested by unconfined compression. The mean unconfined compression strength was obtained as 50 kN/m2. Estimate the ratio of ultimate bearing capacity b/w the square footing of side 0.4m and circular footing of diameter 0.3m.