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

View Question The two Eigen Values of the matrix $$\left[ {\matrix{
2 & 1 \cr
1 & p \cr
} } \right]$$ have a ratio

View Question $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^{2x}}\,\,$$ is equal to

View Question 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( {

View Question Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability

View Question Consider the following second order linear differential equation $${{{d^2}y} \over {d{x^2}}} = - 12{x^2} + 24x - 20$$

View Question For step-size, $$\Delta x = 0.4,$$ the value of following integral using Simpson's $$1/3$$ rule is ______

View Question In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while f

View Question A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ___

View Question 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

View Question If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is

View Question 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.

View Question 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

View Question According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a
structure is _______

View Question A column of size $$450\,mm \times 600\,mm$$ has unsupported length of $$3.0$$ $$m$$ and is braced against side sway in b

View Question In a pre-stressed concrete beam section shown in the figure, the net loss is $$10\% $$ and the final prestressing force

View Question Prying forces are

View Question A steel member ‘M’ has reversal of stress due to live loads, whereas another member ‘N’ has reversal of stress due to wi

View Question For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are:

View Question A simply supported reinforced concrete beam of length $$10$$ $$m$$ sags while undergoing shrinkage. Assuming a uniform c

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

View Question A simply supported beam $$AB$$ of span, $$L = 24$$ $$m$$ 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 $$

View Question 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

View Question A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with

View Question 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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