The smallest and largest Eigen values of the
following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr 2 & { - 3} & 5 \cr } } \right]$$

In a catchment, there are four rain-gauge stations, P, Q, R, and S. Normal annual precipitation values at these stations are 780 mm, 850 mm, 920 mm, and 980 mm, respectively. In the year 2013, stations Q, R, and S, were operative but P was not. Using the normal ratio method, the precipitation at station P for the year 2013 has been estimated as 860 mm. If the observed precipitation at stations Q and R for the year 2013 were 930 mm and 1010 mm, respectively; what was the observed precipitation (in mm) at station S for that year?

The two columns below show some parameters and their possible values.

Parameters	Value
P-Gross Command Area	I-100 hectares/cumec
Q-Permanent Wilting Point	II-6℃
R-Duty of canal water	III-1000 hectares
S-Delta of wheat	IV-1000 cm
	V-40 cm
	VI-0.12

Which of the following options matches the parameters and the values correctly?

The development length of a deformed reinforcement bar can be expressed as $$\left( {1/k} \right)\left( {\phi {\sigma _s}/{\tau _{bd}}} \right).$$

From the $$IS:$$ $$456$$-$$2000,$$ the value of $$k$$ can be calculated as _________________.