Consider the lines give by `L_1: x+3y -5=0, L_2:3x - ky-1=0, L_3: 5x +2y -12=0`

Consider the lines given by : L_1 : x+3y-5=0, L_2 : 3x-ky-1=0, L_3 : 5x+2y-12=0 If a be the value of k for which lines L_1, L_2, L_3 do not form a triangle and c be the value of k for which one of L_1, L_2, L_3 is parallel to at least one of the other lines, then abc=

Consider the lines given by L_(1):x+3y-5=0," "L_(2):3x-ky-1=0" "L_(3):5x+2y-12=0 {:(,"Column-I",,"Column-II"),((A),","L_(1)","L_(2)","L_(3)" are concurrent, if",(p),k=-9),((B)," One of "L_(1)","L_(2)","L_(3)" is parallel to at least one of the other two, if",(q),k=-6/5),((C),L_(1)","L_(2)","L_(3)" from a triangle, if",(r),k=5/6),((D),L_(1)","L_(2)","L_(3)" do not from a triangle, if",(s),k=5):}

Consider the lines given by L_1 = x + 3y – 5 = 0 L_2 = 3x – ky – 1 = 0 L_3 = 5x + 2y – 12 = 0 Match the statements/Expression in Column-I with the statements/Expressions in Column-II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in OMR.

L_(1)=x+3y-5=0,L_(2)=3x-ky-1=0,L_(3)=5x+2y-12=0 are concurrent if k=

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where pa n dq are relatively prime numbers, then the value of p+q is (a)500 (b) 450 (c) 230 (d) 465