Let `a ,b >0,` let `5a-b ,2a+b ,a+2b` be in A.P. and `(b+1)^2, a b+1,(a-1)^2` are in G.P., then the value of `(a^(-1)+b^(-1))` is _______.

Let a, b, c be in an AP and a^2, b^2, c^2 be in GP. If a < b < c and a + b+ c=3/2 then the value of a is

If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-zero then

Suppose a, b, c are in a.P and a^(2), b^(2), c^(2) are in G.P. If a lt b lt c and a + b + c = 3/2 then the value of a Is

If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a,c,e are in GP.

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

Let A and B are two square matrices of order 3 such that det. (A)=3 and det. (B)=2 , then the value of det. (("adj. "(B^(-1) A^(-1)))^(-1)) is equal to _______ .

If a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

If a , b ,a n dc are in G.P., then a+b ,2b ,a n db+c are in a. A.P b. G.P. c. H.P. d. none of these

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9