GATE 2010 Civil Engineering
20 questions across 1 session
The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is
The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \over {\partial x}},q = {{\partial z} \over {\partial y}}} \ri...
The inverse of the matrix $$\left[ {\matrix{ {3 + 2i} & i \cr { - i} & {3 - 2i} \cr } } \right]$$ is
A doubly reinforced rectangular concrete beam has a width of $$300$$ $$mm$$ and an effective depth of $$500$$ $$mm.$$ the beam is reinforced with $$2200\,m{m^2}$$ of steel in tensi...
Ion concentrations obtained for a groundwater sample (having pH=8.1) are given below. Ion $$Ca^{2+}$$ $$Mg^{2+}$$ $$Na^+$$ $$HCO_3^-$$ $$SO_4^{2-}$$ $$Cl^{-}$$ Ionconcentration(mg/...
Ion concentrations obtained for a groundwater sample (having pH=8.1) are given below. Ion $$Ca^{2+}$$ $$Mg^{2+}$$ $$Na^+$$ $$HCO_3^-$$ $$SO_4^{2-}$$ $$Cl^{-}$$ Ionconcentration(mg/...
Two coins are simultaneously tossed. The probability of two heads simultaneously appearing
The $$\mathop {Lim}\limits_{x \to 0} {{\sin \left( {{2 \over 3}x} \right)} \over x}\,\,\,$$ is
The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \right)}^3} + {y^2}} = 0$$ are respectively
A parabolic cable is held between two supports at the same level. The horizontal span between the supports is $$L.$$ The sag at the mid-span is $$h.$$ The equation of the parabola...
Given a function $$f\left( {x,y} \right) = 4{x^2} + 6{y^2} - 8x - 4y + 8,$$ the optimal values of $$f(x,y)$$ is
The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is
A doubly reinforced rectangular concrete beam has a width of $$300$$ $$mm$$ and an effective depth of $$500$$ $$mm.$$ the beam is reinforced with $$2200\,m{m^2}$$ of steel in tensi...
The number of independent elastic constants for a linear elastic isotropic and homogeneous material is
Two people weighing W each are sitting on a plank of length $$L$$ floating on water at $$L/4$$ from either end. Neglecting the weight of the plank, the bending moment at the center...
The major and minor principal stresses at a point are $$3MPa$$ and $$-3MPa$$ respectively. The maximum shear stress at the point is
The effective length of a column of length $$L$$ fixed against rotation and translation at one end is
A solid circular shaft of diameter d and length $$L$$ is fixed at one end and free at the other end. A torque t is applied at the free end. The shear modulus of the material is $$G...
The moisture holding capacity of the soil in a 100 hectare farm is 18 cm/m. the field is to be irrigated when 50 percent of the available moisture in the root zone is depleted. The...
The moisture holding capacity of the soil in a 100 hectare farm is 18cm/m. the field is to be irrigated when 50 percent of the available moisture in the root zone is depleted. The...