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

Prove that ((a_1)/(a_2)+(a_3)/(a_4)+(a_5)/(a_6)) ((a_2)/(a_1)+(a_4)/(a_3)+(a_6)/(a_5)) geq 9

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

If a_1,a_2,….a_n are in H.P then (a_1)/(a_2+,a_3,…,a_n),(a_2)/(a_1+a_3+….+a_n),…,(a_n)/(a_1+a_2+….+a_(n-1)) are in

If a_1,a_2,a_3……..a_n are in H.P. and f(k) = sum_(r=1)^na_r-a_k then (f(1))/a_1, (f(2))/a_3 ….f(n)/a_n are (A) A.P. (B) G.P. (C) H.P. (D) none of these

If x,a_1,a_2,a_3,…..a_n epsilon R and (x-a_1+a_2)^2+(x-a_2+a_3)^2+…….+(x-a_(n-1)+a_n)^2le0 , then a_1,a_2,a_3………a_n are in (A) AP (B) GP (C) HP (D) none of these

If a_1,a_2, a_3………. are in H.P. and f(k) =sum_(r=1)^n a_r-a_k, the a_1/(f(1)), a_2/(f(2)), a_3/(f(3)), …….., a_n/(f(n)) are in (A) A.P. (B) G.P (C) H.P. (D) none of these

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

The equation A/(x-a_1)+A_2/(x-a_2)+A_3/(x-a_3)=0 where A_1,A_2,A_3gt0 and a_1lta_2lta_3 has two real roots lying in the invervals. (A) (a_1,a_2) and (a_2,a_3) (B) (-oo,a_1) and (a_3,oo) (C) (A_1,A_3) and (A_2,A_3) (D) none of these