Question

There are n lines in a plane, no two of which are parallel and no three of them are concurrent. Let plane be divided in $U_n$ parts by these n lines. Then

• A. $U_4=11$
• B. $U_3=7$
• C. $U_2=3$
• D. $U_n=U_{n-1}+4$

Answer 1

Answer: (A), (B)

The correct options are
A $U_4=11$
B $U_3=7$

The $n^{th}$ line will rise to n additional parts when $U_{n-1}$ parts are already there.

$\Rightarrow U_n=U_{n-1}+n\Rightarrow$

Choice (D) is incorrect.

Again $U_0=1,U_1=2$

We easily get $U_2=4,U_3=7,U_4=11$