KVPY Sample Paper KVPY Stream-SX Model Paper-22

The limiting position of the point of intersection of the straight lines, \[3x+5y=1\] and \[(2+c)\,x+5{{c}^{2}}y=1\] as c tends to one is:

A) \[\left( \frac{2}{5},\,\,-\frac{1}{25} \right)\]

B) \[\left( \frac{1}{2},\,\,-\frac{1}{10} \right)\]

C) \[\left( \frac{3}{8},\,\,-\frac{1}{40} \right)\]

D) none of these

Correct Answer: A

Solution :

\[x=\underset{c\,\to \,1}{\mathop{Limit}}\,\frac{5\,(c-1)\,\,(c+1)}{5\,(c-1)\,\,(3c-2)}=\frac{2}{5};\]

\[y=\underset{c\,\to \,1}{\mathop{Limit}}\,\frac{1-c}{5\,(c-1)\,\,(3c+2)}=-\frac{1}{25}\]