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

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

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

Given $$i = \sqrt { - 1} ,$$ the value of the definite integral, $$\,{\rm I} = \int\limits_0^{\pi /2} {{{\cos x + \sin x

The probability density function of a random variable, $$x$$ is $$$\matrix{ {f\left( x \right) = {x \over 4}\left( {

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

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

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

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

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

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

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

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.

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

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

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

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

Prying forces are

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

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

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

In a system, two connected rigid bars $$AC$$ and $$BC$$ are of identical length $$L$$ with pin supports at $$A$$ and $$B

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

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

A horizontal beam $$ABC$$ is loaded as shown in the figure below. The distance of the point of contraflexure from end $$

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

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

A superspeedway in New Delhi has among the highest super-elevation rates of any track on the Indian Grand Prix circuit.