If ` | (a+1,a+2, a+p), (a+2, a+3,a+q), (a+3,a+4,a+r)|=0,then p ,q ,r` are in:

|(a+1, a+2, a+p), (a+2, a+3, a+q) ,(a+3, a+4, a+r)|=0 , then p, q r are in (A) A P (B) G P (C) H P (D) none of these

The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), and (r q ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are (1,2) (b) (2,-1) (c) (1,-1) (d) (2,3)

Let A= {p, q, r} . Which of the following is an equivalence relation on A ? (a) R_1 = {(p, q), (q, r), (p, r), (p, q)} (b) R_2 = {(r,q), (r, p), (r.r), (q, r)} (c) R_3 = {(p, p), (q,q), (r, r), (p, q)} (d) one of these

If a_(1),a_(2),a_(3),…. are in A.P., then a_(p),a_(q),a_(r) are in A.P. if p,q,r are in

If the roots of the equation px ^(2) +qx + r=0, where 2p , q, 2r are in G.P, are of the form alpha ^(2), 4 alpha-4. Then the value of 2p + 4q+7r is :

Show that |(1, 1+p, 1+p+q), (2, 3+2p, 4+3p+2q), (3, 6+3p, 10+6p+3q)|=1.

Find the value of : 2p + 3q + 4r + por when p =-1,q = 2 and r = 3

If p(q-r)x^(2) + q(r-p)x+ r(p-q) = 0 has equal roots, then show that p, q, r are in H.P.

Match the following lists (where [x] represents the greatest integer function) and then choose the correct code. Codes : {:(,"a b c d"),((1),"s r q p"),((2),"q p s p"),((3), "s r p q"),((4),"p p q r"):}

" if " a_(1) ,a_(2), a_(3)….." are in A.P, then find the value of the following determinant:" |{:(a_(p)+a_(p+m) +a_(p+2m),,2a_(p)+3a_(p+m)+4a_(p+2m),,4a_(p)+9a_(p+m)+16a_(p+2m)),(a_(p)+a_(q+m)+a_(q+2m),,2a_(q)+3a_(q+m) +4a_(q+2m),,4a_(q)+9a_(q+m)+16a_(q+2m)),(a_(r)+a_(r+m)+a_(r+2m),,2a_(r)+3a_(r+m)+4a_(r+2m),,4a_(r) +9a_(r+m)+16a_(r+2m)):}|