Hi Akhil, though the question was right, the answer was incorrectly explained. As the question asks about the points of intersection rather than the lines themselves, the use of the word coincident is correct. The lines are concurrent as stated by you.

Hi Sir , I tried this sum and i know that first three options cant be the answer but I dont know how option 4 is the answer. Kindly explain this sir

Hi Selva,

These are linear equations in two variable. We have three of them and thus we’ll get $${}^3C_2=3$$ pairs. You can find the value of $$x$$ and $$y$$ for each such pair and analyse them accordingly to get the answer.
$$2x+3y=5$$ and $$5x-7y=-2$$ give $$x=y=1$$
$$2x+3y=5$$ and $$9x-5y=4$$ give $$x=y=1$$
$$5x-7y=-2$$ and $$9x-5y=4$$ give $$x=y=1$$
Thus the three possible points of intersection are coincident.

Hope this helps, feel free to ask if you have any doubts

Hi Sourajya,
The determinant in this question is the determinant of the matrix formed by the coefficients of the three equations.

The given 3 lines do not form a triangle. 
A triangle would be would be formed only the intersection points of the 3 lines are 3 distinct points. 

Find intersection points of first line and second line. It comes out to be (1,1)
Find intersection points of first line and third line. It comes out to be (1,1)

Hence, the 3 lines are concurrent. Not coincident.