GATE CE 2015 Set 2
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## GATE CE

Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and $${{a_{ij}} = i.j.}$$ The rank of $$A$$ i
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The two Eigen Values of the matrix $$\left[ {\matrix{ 2 &amp; 1 \cr 1 &amp; p \cr } } \right]$$ have a ratio
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$$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^{2x}}\,\,$$ is equal to
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Given $$i = \sqrt { - 1} ,$$ the value of the definite integral, $$\,{\rm I} = \int\limits_0^{\pi /2} {{{\cos x + \sin x View Question The probability density function of a random variable,$$x$$is$$\$\matrix{ {f\left( x \right) = {x \over 4}\left( {
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Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability
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Consider the following second order linear differential equation $${{{d^2}y} \over {d{x^2}}} = - 12{x^2} + 24x - 20$$
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For step-size, $$\Delta x = 0.4,$$ the value of following integral using Simpson's $$1/3$$ rule is ______
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In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while f
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A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %) present in the sample is ___
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A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top vertex of the gate is
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If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is
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A 588 $$cm^3$$ volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of solids, G is 2.67.
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The average surface area of a reservoir in the month of June is 20 km2. In the same month, the average rate of inflow is
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According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a structure is _______
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A column of size $$450\,mm \times 600\,mm$$ has unsupported length of $$3.0$$ $$m$$ and is braced against side sway in b
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In a pre-stressed concrete beam section shown in the figure, the net loss is $$10\%$$ and the final prestressing force
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Prying forces are
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A steel member ‘M’ has reversal of stress due to live loads, whereas another member ‘N’ has reversal of stress due to wi
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For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are:
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A simply supported reinforced concrete beam of length $$10$$ $$m$$ sags while undergoing shrinkage. Assuming a uniform c
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In a system, two connected rigid bars $$AC$$ and $$BC$$ are of identical length $$L$$ with pin supports at $$A$$ and $$B View Question A steel strip of length,$$L = 200mm$$is fixed at end$$A$$and rests at$$B$$on a vertical spring of stiffness, View Question A simply supported beam$$AB$$of span,$$L = 24m$$is subjected to two wheel loads acting at a distance,$$d = 5$$View Question A horizontal beam$$ABC$$is loaded as shown in the figure below. The distance of the point of contraflexure from end$$
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A fixed end beam is subjected to a load, W at $$1/3rd$$ span from the left support as shown in the figure. The collapse
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A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with
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A superspeedway in New Delhi has among the highest super-elevation rates of any track on the Indian Grand Prix circuit.
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