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# When a sample of human blood is diluted $200$ times its initial volume and microscopically examined in a layer $0.10\;mm$ thick , an average of $30\;RBC$ are found in $100 \times 100$ micrometer square. The number of RBC in $1 \;mm^3$ of undiluted blood is

$(a)\; 3 \times 10^6 \\ (b)\;6 \times 10^6\\(c)\;10^6\\(d)\;2 \times 10^6$

Volume of blood= Area $\times$ thickness
or Volume $= (100 \; \mu m) \times (100 \; \mu m) \times (0.10\;mn)$
But $1 \;\mu m =10^{-3} mm$
$\therefore 100 \;\mu m= 100 \times 10^{-3} =0.1 \;m$
Volume $= (0.10 \;mm)^3=1.0 \times 10^{-3}$
$1 \times 10^{-3} \;mm$ of blood contain $=30\;RBC$
Therefore 200 mm of blood contain
$\qquad= 30 \times 1.0 \times 10^{3} mm^3 \times 200 \;mm^3= 6 \times 10^{6}$
Hence b is the correct answer.