Home
Class 12
MATHS
If m is the A.M. of two distinct real nu...

If m is the A.M. of two distinct real numbers `l and n(l, n>1) and G_1, G_2 and G_3`, are three geometric means between `I and n`, then `G_1^4+2G_2^4+G_3^4` equals-

A

`4 lmn^(2)`

B

`4 l^(2)m^(2)n^(2)`

C

`4 l^(2)mn`

D

`4 lm^(2)n`

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise (JA)|12 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise S-2|12 Videos

  • RACE

    ALLEN|Exercise Race 21|10 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|8 Videos

Similar Questions

Explore conceptually related problems

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G_1, G_2 and G_3 are three geometric means between l and n, then G_1^4+2G_2^4+G_3^4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

if m is the AM of two distinct real number l and n and G_(1),G_(2) and G_(3) are three geometric means between l and n, then (G_(1)^(4)+G_(2)^(4)+G_(3)^(4)) equals to

Knowledge Check

  • If m is the AM of two distinct real numbers l and n (l,ngt1) and G_(1),G_(2)" and "G_(3) are three geometric means between l and n, then G_(1)^(4)+2G_(2)^(4)+G_(3)^(4) equals

    A
    `4l^(2)m^(2)n^(2)`
    B
    `4l^(2)mn`
    C
    `4lm^(2)n`
    D
    `4lmn^(2)`

  • If G_(1) . G_(2) , g_(3) are three geometric means between two positive numbers a and b , then g_(1) g_(3) is equal to

    A
    `g_(2)`
    B
    `2g_(2)`
    C
    `g_(2)^(2)`
    D
    `g_(2)^(3)`

  • If A is the arithmetic mean and G_1, G_2 be two geometric means between any two numbers, then G_1^2/G_2+G_2^2/G_1 is equal to

    A
    2A
    B
    A
    C
    3A
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    If a be one A.M and G_(1) and G_(2) be then geometric means between b and c then G_(1)^(3)+G_(2)^(3)=

    Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The value of Sigma_(r=1)^(n) G_r is

    Lef a, b be two distinct positive numbers and A and G their arithmetic and geometric means respectively. If a, G_(1),G_(2) , b are in G.P. and a, H_(1),H_(2) , b are in H.P., prove that (G_(1)G_(2))/(H_(1)H_(2))lt (A^(2))/(G^(2)) .

    Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The number 2 A_(171,G_5^2+1,2A_(121)

    Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The n umber of arithmetic means is

    Home
    Profile