Correct Answer - Option 2 : 7
Group index, \(GI = 0.2\left( {F - 35} \right) + 0.005\left( {F - 35} \right)\left( {{w_l} - 40} \right) + 0.01\left( {F - 15} \right)\left( {{I_P} - 10} \right)\)
Where, F= percentage by mass passing 75μm sieve, expressed as whole number
wl=Liquid limit (%) expressed as whole number
Ip= Plasticity index
While calculating GI if any term in the parentheses become negative, it is not considered in calculation. The maximum value of (F-35) and (F-15) are taken as 40 and that of (wl-40) and (Ip-10) as 20.
Here F= 62%, wl=35%,
\({I_p} = 14\%\)
\(GI = 0.2\left( {62 - 35} \right) + 0.005\left( {62 - 35} \right)\left( {35 - 40} \right) + 0.01\left( {62 - 15} \right)\left( {14 - 10} \right)\)
\(\Rightarrow GI = 0.2 \times 27 + 0.005 \times 27 \times \left( { - 5} \right) + 0.01 \times \left( {47} \right) \times 4\)
\( \Rightarrow GI = 0.2 \times 27 + 0.005 \times 27 \times \left( 0 \right) + 0.01 \times \left( {40} \right) \times 4 = 7.0\)