Discrete Mathematics Questions and Answers – Arithmetic and Geometric Mean

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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
View Answer

Answer: c
Explanation: A1 + A2 = a + b, G1G2 = ab.
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2. The series a,(a+b)/2, b is in _______
a) AP
b) GP
c) HP
d) None of the mentioned
View Answer

Answer: a
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
View Answer

Answer: b
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
View Answer

Answer: a
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
View Answer

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

Answer: b
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
View Answer

Answer: a
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
View Answer

Answer: d
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
View Answer

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

Answer: b
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn