For a certain value of \( c\),\( \underset{x\xrightarrow{} -\infty }{lim}\left[({x}^{5}+7{x}^{4}+2{)}^{c}-x\right]\) , is finite and non zero and has the value equal to l. Find the value of \( (l-2c)\).
Consider a family of straight lines \( \left(x+y\right)+\lambda \left(2x-y+1\right)=0\). Find the equation of the straight line belonging to this family that is farthest from \( \left(1, -3\right)\).
In how many ways a committee of 5 members can be formed out of 8 gentlemen and 4 ladies, if one particular lady is always to be taken a.140 b.330 c.560 d.None of these