The common difference of the A.P. `1/(2b),(1-6b)/(2b),(1-12 b)/(2b),...` is
(a)`2b` (b) `-2b` (c) `3` (d) `-3`

The common difference of the A.P. 1/3,(1-3b)/3,(1-6b)/3,\ dot is (a) 1/3 (b) -1/3 (c) - b (d) b

If a=2b ,\ then a : b= (a) 2:1 (b) 1:2 (c) 3:4 (d) 4:3

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is (a) (ab^(2))/((2a-b)^(2)) (b) (a^(2)b)/((2a-b)^(2)) (c) (a^(2)b^(2))/((2a-b)^(2)) (d) None of these

The product (a+b)(a-b)(a^2-a b+b^2)(a^2+a b+b^2) is equal to: (a) a^6+b^6 (b) a^6-b^6 (c) a^3-b^3 (d) a^3+b^3

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

If a ,b ,c are in A.P., prove that the following are also in A.P. (i) 1/(b c),1/(c a),1/(a b), (ii) b+c ,c+a ,a+b (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) (iv) a^2(b+c),b^2(c+a),c^2(a+b) (v) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

If a^2,b^2,c^2 are in A.P. prove that 1/(b+c),1/(c+a),1/(a+b) are in A.P.

The sum of the coefficients in the monomials 3a^2b and -2a b^2 is (a)5 (b) -1 (c) 1 (d) -6

If a ,1/b ,c and 1/p ,q ,1/r form two arithmetic progressions of the common difference, then a ,q ,c are in A.P. if p ,b ,r are in A.P. b. 1/p ,1/b ,1/r are in A.P. c. p ,b ,r are in G.P. d. none of these