In a levelling survey, a reading is taken as 2.25 m. However, along the line of sight there is deflection of 20 cm with respect to vertical position of the staff. The correct reading, in m is_____. (round off to two decimal places)

Water flows through a vertical sand column of cross sectional area 4000 mm² and length 300 mm. For a water head of 600 mm, quantity of seepage water is 100 mm³/min. The hydraulic conductivity of the sand column, in mm/min is_____. (round off to three decimal places)

The value of $lim_{x\to0}\frac{(1-x)^n - 1}{x}$ is

A velocity field in Cartesian coordinate system is expressed as $v = x\hat{i} + y\hat{j} + p(z)\hat{k}, \text{ where } p(0) = 0$

If div $v = 0$, $p(z)$ is

The constant term of the Fourier coefficients of the periodic function

$f(x) = \begin{cases} -k, & \text{for } -pi < x < 0 \\ k, & \text{for } 0 < x < pi \end{cases}, \quad f(x + 2\pi) = f(x) \text{ and } k = \text{constant}$

is

Two vectors $x$ and $y$ are shown in the figure. The projection vector of $x$ on $y$ is

A deposit has the grade attribute $X in [0, 30]$ with a density function $f(x)$. For a cut-off grade $x_c$, the proportion of the ore in the deposit is given by

Match the rock with its metamorphosed form

A square pattern of blasting is shown in the figure. For the case of simultaneous blast, identify the zone of no fragmentation

The correct vertical stress profile in the case of tributary area method for pillar design is