Arithmetic Mean

If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by

Which of the following is not true?
(A) If a, b, c are in AP and a, 2b, c are in GP then a, 4b, c are in HP
(B) The number 361 is not a term of the sequence a_n = n² + 2n+1.
(C) If p,q are the roots of (x-a)(x-b)-m=0, then a, b are roots of (x-p)(x-q)+m=0.
(D) The expression 9^x-3^x+1 can assume all real values for x ∈ R.
Choose the correct answer from the options given below :

The H.P. of two numbers is 4 and the arithmatic mean A and geometric mean G satisfy the relation 2A + G² = 27, the numbers are

If A₁, A₂ be two AM's and G₁, G₂ be two GM's between a and b, then is equal to

Which of the following is a correct relation if and only if all the n observations are equal?

Given below are two statements:
Statement I: Arithmetic mean of a given set of observations is their sum divided by the no. of observations.
Statement II: If in a series the sum of 5 number is 17, then the Arithmetic Mean of it will be 3.4±0.5. In the light of the above statements,
choose the correct answer from the options given below: