GATE CE 2015 Set 2

## 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 $$\left[ {\matrix{
2 & 1 \cr
1 & p \cr
} } \right]$$ 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

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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

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A steel strip of length, $$L = 200$$ $$mm$$ is fixed at end $$A$$ and rests at $$B$$ on a vertical spring of stiffness,

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A simply supported beam $$AB$$ of span, $$L = 24$$ $$m$$ is subjected to two wheel loads acting at a distance, $$d = 5$$

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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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