For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?

For the two equations to have infinite number of solutions, the two lines must overlap one another.

Lines having equation $$a_1x+b_1y+c_1=0$$ and $$a_2x+b_2y+c_2=0$$ are said to be collinear if $$\frac{a_1}{a_2}$$ $$=\frac{b_1}{b_2}$$ $$=\frac{c_1}{c_2}$$

Thus, for the equations : 6x + 12y + 9 = 0 and 2x + gy + 3 = 0

=> $$\frac{6}{2}=\frac{12}{g}=\frac{9}{3}$$

=> $$\frac{12}{g}=3$$

=> $$g=\frac{12}{3}=4$$

=> Ans - (B)