If `|(1+a_1,a_2,a_3),(a_1,1+a_2,a_3),(a_1,a_2,1+a_3)|=0,` then `a_1+a_2+a_3=`

If a_1,a_2,a_3,………….a_12 are in A.P. and /_\_1 =|(a_1a_5, a_1,a_2),(a_2a_6,a_2,a_3),(a_3a_7,a_3,a_4)|, |(a_2a_10, a_2,a_3),(a_3a_11,a_3,a_4),(a_4_12,a_4,a_5)| then /_\_1:/_\_2= (A) 1:2 (B) 2:1 (C) 1:1 (D) none of these

If (1 + ax + b x^2)^4 = a_0 +a_1 x + a_2 x^2 +...+a_8 x^8 when a,b,a_0,a_1,a_2...,a_8 in R such that a_0+a_1+a_2 != 0 and |(a_0,a_1,a_2),(a_1,a_2,a_3),(a_2,a_0,a_1)| then the value of 5a/b (A) 6 (B) 8 (C) 10 (D) 12

Evaluate: /_\ |[1+a_1, a_2, a_3],[a_1, 1+a_2, a_3],[a_1, a_2, 1+a_3]|

If (a_2 a_3)/(a_1 a_4) = (a_2 + a_3)/(a_1 + a_4) = 3 ((a_2 - a_3)/(a_1 - a_4)) then a_1, a_2, a_3, a_4 are in

If (a_2a_3)/(a_1a_4) = (a_2+a_3)/(a_1+a_4)=3 ((a_2 -a_3)/(a_1-a_4)) then a_1,a_2, a_3 , a_4 are in :

If p(x),q(x) and r(x) be polynomials of degree one and a_1,a_2,a_3 be real numbers then |(p(a_1), p(a_2),p(a_3)),(q(a_1), q(a_2),q(a_3)),(r(a_1), r(a_2),r(a_3))|= (A) 0 (B) 1 (C) -1 (D) none of these

If 2^(a1),2^(a2),2^(a3).......2^(ar) are in geometric progression , then |{:(a_1,a_2,a_3),(a_(n+1),a_(n+2),a_(n+3)),(a_(2n+1),a_(2n+2),a_(2n+3)):}| is equal to

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and Delta_1=|(a_1+pb_1,b_1+qc_1,c_1+ra_1),(a_2+pb_2,b_2+qc^2,c^2+ra^2),(a_3+pb_3,b_3+qc_3,c_3+ra_3)| then Delta_1=