Harmonic Mean

Q.

If $H$ be the harmonic mean between $a$ and $b$, then the value of $\frac{1}{H-a}+\frac{1}{H-b}$ is

1. $a+b$

2. $ab$

3. $\frac{1}{a}+\frac{1}{b}$

4. $\frac{1}{a}-\frac{1}{b}$

Q.

The harmonic mean between two numbers is $14\frac{2}{5}$and the geometric mean is $24$. The greater number between them is

1. $72$

2. $54$

3. $36$

4. None of these

Q.

Dividing $2x^2$$y$$z^5$ by $8x^2$$z^3$ gives $\frac{1}{4}xy{z}^2$.

1. True

2. False

Q.

Solve and show steps. Solve the formula for the indicated variable.

$T=\frac{3U}{E}$, solve for $U$.

Q. If H is the harmonic mean between p and q, then the value of $\frac{H}{p}+\frac{H}{q}$ is
[MNR 1990; UPSEAT 2000, 01]

1. None of these
2. 2
3. $\frac{pq}{p+q}$
4. $\frac{p+q}{pq}$

Q. If $x>1,y>1,z>1$ are in GP, then $\frac{1}{1+lnx},\frac{1}{1+lny},\frac{1}{1+lnz}$ are in

1. AP
2. HP
3. GP
4. None of these

Q. If the A.M. between a and b is m times their H.M. then a:b =

1. $\sqrt{m}+\sqrt{m-1}:\sqrt{m}-\sqrt{m-1}$
2. $\sqrt{m}-\sqrt{m-1}:\sqrt{m+1}+\sqrt{m-1}$
3. $\sqrt{m}+\sqrt{m+1}:\sqrt{m}-\sqrt{m+1}$
4. None of these

Q. The harmonic mean of $\frac{a}{1-ab}$ and $\frac{a}{1+ab}$ is
[MP PET 1996; Pb. CET 2001]

1. a
2. $\frac{a}{\sqrt{1-a^2{b}^2}}$
3. $\frac{a}{1-a^2{b}^2}$
4. $\frac{1}{1-a^2{b}^2}$

Q. If the harmonic mean between a and b be H, then the value of $\frac{1}{H-a}+\frac{1}{H-b}$ is

1. a+b
2. ab
3. $\frac{1}{a}+\frac{1}{b}$
4. $\frac{1}{a}-\frac{1}{b}$