Commerce Exam  >  Commerce Tests  >  Mathematics (Maths) Class 11  >  Test: Relation Between AM And GM - Commerce MCQ

Test: Relation Between AM And GM - Commerce MCQ


Test Description

10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Relation Between AM And GM

Test: Relation Between AM And GM for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The Test: Relation Between AM And GM questions and answers have been prepared according to the Commerce exam syllabus.The Test: Relation Between AM And GM MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Relation Between AM And GM below.
Solutions of Test: Relation Between AM And GM questions in English are available as part of our Mathematics (Maths) Class 11 for Commerce & Test: Relation Between AM And GM solutions in Hindi for Mathematics (Maths) Class 11 course. Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free. Attempt Test: Relation Between AM And GM | 10 questions in 10 minutes | Mock test for Commerce preparation | Free important questions MCQ to study Mathematics (Maths) Class 11 for Commerce Exam | Download free PDF with solutions
Test: Relation Between AM And GM - Question 1

The G.M. between the numbers: 56 and 14 is:

Detailed Solution for Test: Relation Between AM And GM - Question 1

Geometric mean of two numbers a and b is √ab
As two numbers are 14 and 56
Geometric mean is √14×56
= ± √2×7×2×2×2×7
= ±(2×2×7)
= ±28

Test: Relation Between AM And GM - Question 2

Three geometric means between the numbers 1/4 and 64 are:

Detailed Solution for Test: Relation Between AM And GM - Question 2

nth G.M. between a and b is
Gn = arn
Where common ratio is r = (b/a)(1/(n+1))
​So, to insert 3 geometric means between 1/4 and 64
 r = (b/a)(1/(n+1))
r = (64/(¼)(1/(3+1))
r = (256)1/4
r  = (4)(4)1/4
r = 4
Gn = 1 * (4)n
G0 = 1 * (4)0 = 1
G1 = 1 * (4)1 = 4
G2 = 1 * (4)2 = 16
The terms are 1, 4, 16

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Relation Between AM And GM - Question 3

The three numbers between 1 and 256 such that the sequence is in GP are

Detailed Solution for Test: Relation Between AM And GM - Question 3

nth G.M. between a and b is
Gn = arn
Where common ratio is r = (b/a)(1/(n+1))
​So, to insert 3 geometric means between 1 and 256
 r = (b/a)(1/(n+1))
r = (256/(1)(1/(3+1))
r = (256)1/4
r  = (4)(4)1/4
r = 4
Gn = 1 * (4)n
G1 = 1 * (4)1 = 4
G2 = 1 * (4)2 = 16
G3 = 1 * (4)3 = 64
The terms are  4, 16, 64

Test: Relation Between AM And GM - Question 4

If A and G are A.M. and G.M. of two real numbers a and b, then

Detailed Solution for Test: Relation Between AM And GM - Question 4

A=a+b/2. ,G=√ab
A-G=(a+b/2)-√ab
=(a+b-2√ab)/2
=(√a-√b)2/2 is greater than or equal to zero
A-G is greater than or equal to zero so
So A is greater than equal to zero

Test: Relation Between AM And GM - Question 5

The sum of the series 2 + 6 + 18 + ….+ 4374 is:

Detailed Solution for Test: Relation Between AM And GM - Question 5

The given series is a geometric series in which a=2,r=3,l=4374.
Therefore,
Required sum = (lr−a)/(r−1)
​= (4374×3−2)/(3−1)
​= 6560

Test: Relation Between AM And GM - Question 6

If a, b, c are in A.P. and k is any non zero numbre, then ka, kb, kc are in

Detailed Solution for Test: Relation Between AM And GM - Question 6

a, b, c are in AP
Let d be the common difference.
b = a + d,
c = a + 2d 

There are in GP with common ratio: kd
 

Test: Relation Between AM And GM - Question 7

The A.M. between two numbers is 34 and their G.M. is 16.The numbers are

Detailed Solution for Test: Relation Between AM And GM - Question 7

Let the numbers be x, y 

Then arithmatic mean = (x+y)/2 =34 

→x+y =68 

Also geometric mean =√(xy)=16 

oy xy=16^2=256 

Hence 

x(68−x)=256 

or x^2−68x+256=0 

(x−64)(x−4)=0 

Hence x=64 or x=4 

and y=4 or 64 

Larger number is 64

Test: Relation Between AM And GM - Question 8

Two geometric means g and g’ and one arithmetic mean A is inserted between two numbers, then

Detailed Solution for Test: Relation Between AM And GM - Question 8


Test: Relation Between AM And GM - Question 9

The G.M. between 3/2 and 27/2 is

Detailed Solution for Test: Relation Between AM And GM - Question 9

b2 = ac
a = 3/2, c = 27/2
⇒ b2 = 3/2 * 27/2
⇒ b = (√81/4)
⇒ b = 9/2

Test: Relation Between AM And GM - Question 10

How many terms of geometric progression 4 , 16 , 64 , are required to give the sum 5460?

Detailed Solution for Test: Relation Between AM And GM - Question 10

a(rn-1)/(r-1) = 5460
=> 4(4n-1)/4-1 = 5460
=> 4n = 4096
=> 22n = 212
=> n = 6

75 videos|238 docs|91 tests
Information about Test: Relation Between AM And GM Page
In this test you can find the Exam questions for Test: Relation Between AM And GM solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Relation Between AM And GM, EduRev gives you an ample number of Online tests for practice

Top Courses for Commerce

75 videos|238 docs|91 tests
Download as PDF

Top Courses for Commerce