The minimum volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution (K_sp of PbCl₂ = 3.2 $$ \times $$ 10^-8 atomic mass of Pb = 207 u ) is :

n$$-$$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :

If x₁, x₂, . . ., x_n and $${1 \over {{h_1}}}$$, $${1 \over {{h_2}}}$$, . . . , $${1 \over {{h_n}}}$$ are two A.P..s such that x₃ = h₂ = 8 and x₈ = h₇ = 20, then x₅.h₁₀ equals :

Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y $$-$$ z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :