Related InterviewSolutions

• If `(a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0)`, then show that `a , b , c a n d d`are in G.P.
• If p, q, r are in G.P. and the equations, `p x^2+2q x+r=0`and `dx^2+2e x+f=0`have a common root, then show that `d/p`,`e/q`,`f/r`are in A.P.
• If `a a n d b`are the roots of `x^2-3x+p=0 a n d c , d`are the roots `x^2-12 x+q=0`where `a , b , c , d`form a G.P. Prove that `(q+p):(q-p)=17 : 15.`
• 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 G.P.?
• If `a ,b ,c`are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)`
• If `S`be the sum, `P`the product and `R`the sum of the reciprocals of `n`terms of a G.P. prove that `(S/R)^n=P^2dot`
• If `(a-b), (b-c),(c-a)`are in G.P. then prove that `(a+b+c)^2=3(a b+b c+c a)`
• Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that `P^2R^n=S^n`.
• Which of the foliowing statement(s) is/are true? (A) If `a^x =b^y=c^z and a,b,c` are in GP, then x, y, z are in HP (B) If `a^(1/x)=b^(1/y)=c^(1/z)` and `a,b,c` are in GP, then `x,y,z` are in AP
• Find the sum of each of the following infinite series : `6+1.2+0.24+oo`