# Discrete Mathematics Questions and Answers – Arithmetic and Geometric Mean

This set of Discrete Mathematics Multiple Choice Questions & Answers focuses on “Arithmetic and Geometric Mean”.

1. Let A1, A2, be two AM’s and G1, G2 be two GM’s between a and b,then (A1 + A2) / G1G2 is equal to _______
a) (a+b) / 2ab
b) 2ab/(a+b)
c) (a+b)/(ab)
d) None of the mentioned

Explanation: A1 + A2 = a + b, G1G2 = ab.

2. The series a,(a+b)/2, b is in _______
a) AP
b) GP
c) HP
d) None of the mentioned

Explanation: (a+b)/2 is AM between a, b. Hence series is in AP.

3. The series a, (ab)1/2, b is in _______
a) AP
b) GP
c) HP
d) None of the mentioned

Explanation: (ab)1/2 is GM between a, b. Hence series is in GP.

4. If A and G be the A.M and G.M between two positive number then the numbers are A + (A2 – G2)1/2, A – (A2 – G2)1/2.
a) True
b) False

Explanation: The equation having its roots as given equation is
x2 – 2Ax + G2 = 0 which implies
x = A + (A2 – G2)1/2, A – (A2 – G2)1/2.

5. If one geometric mean G and two airthmetic mean A1, A2 are inserted between two numbers, then (2A1 – A2) (2A2 – A1) is equal to _______
a) 2G
b) G
c) G2
d) None of the mentioned

Explanation: Let a and b be two numbers then, G = (ab)1/2, A1 = (2a+b)/3, A2 = (a+2b)/3, (2A1 – A2) = a, (2A2 – A1) = b, (2A1 – A2)(2A2 – A1) = G2.

6. State whether the given statement is true or false.
AM ≤ GM.
a) True
b) False

Explanation: Airthmetic Mean is always greater or equal to the geometric mean.

7. If between two numbers which are root of given equation. x2 – 18x + 16 = 0, a GM is inserted then the value of that GM is?
a) 4
b) 5
c) 6
d) 16

Explanation: x2 – 2Ax + G2 = 0, here G2 = 16 and therefore G = 4.

8. If a1, a2, a3 are in airthemetic as well as geometric progression then which of the following is/are correct?
a) 2a2 = a1 + a3
b) a2 = (a1a3)1/2
c) a2 – a1 = a3 -a2
d) All of the mentioned are correct

Explanation: a2 is AM, GM between a1, a3, also the series is in AP so common difference should be same.

9. If a1, a2, a3 are in GP then 1/a1, 1/a2, 1/a3 are in ___________
a) AP
b) GP
c) HP
d) None of the mentioned

Explanation: Let the terms be ar, a, a/r then reciprocals are 1/(ar), 1/a, r/a. Still the terms are in GP.

10. If a1, a2, a3…….. are in AP then if a7 = 15, then the value of common difference that would make a2 a7 a12 greatest is?
a) 2
b) 0
c) 4
d) 9

Explanation: Let d be common difference of the AP. Then,
a2 a7 a12 = (15 – 5d)(15)(15 + 5d) = 375(9 – d2)
For maximum value d=0.

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