If `a_1,a_2,a_3,a_4` are in H.P. then `1/(a_1 a_4) sum_(r=1)^3 a_r a_(r+1)` is a root of (A) `x^2-2x-15=0` (B) `x^2+2x+15=0` (C) `x^2+2x-15=0` (D) `x^2-2x+15=0`

Let f:RrarrR such that f(x) is continuous and attains only rational value at all real x and f(3)=4. If a_1,a_2,a_3,a_4,a_5 are in H.P. then sum_(r=1)^4 a_r a_(r+1)= (A) f(3).a_1a_5 (B) f(3).a_4a_5 (C) f(3).a_1a_2 (D) f(2).a_1a_3

If a_1,a_2,a_3 are in G.P. having common ratio r such that sum_(k=1)^n a_(2k-1)= sum_(k=1)^na_(2k+2)!=0 then number of possible value of r is (A) 1 (B) 2 (C) 3 (D) none of these

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

The average of a_1, a_2, a_3, a_4 is 16. Half of the sum of a_2, a_3, a_4 is 23. What is the value of a_1

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let a_1,a_2,……a_10 be in A.P. and h_1,h_2,….h_10 be in H.P. If a_1=h_1=2 and a_10 = h_10 =3, then a_4 h_7 is (A) 2 (B) 3 (C) 5 (D) 6