Insertion of HP's between 2 Numbers

Q. If m is a root of the given equation $(1-ab)x^2-(a^2+b^2)x-(1+ab)=0$ and m harmonic means are inserted between a and b, then the difference between the last and the first of the means equals

1. b - a
2. ab(b - a)
3. a(b - a)
4. ab(a - b)

Q.

If a is first term of H.P and D is common difference of corresponding A.P, nth term of H.P is

1. 

2. 

3. + (n - 1)d

4. None of these

Q. Insert 2 no.s between 1 & $\frac{1}{3}$ so that the sequence becomes an Harmonic progression --

1. $\frac{5}{3},\frac{7}{3}$
2. $\frac{5}{7},1$
3. $\frac{1}{7},\frac{2}{7}$
4. $\frac{3}{5},\frac{3}{7}$

Q.

5 harmonic means are inserted between 5 and 10. The common difference of corresponding A.P is.

1. 

2. 

3. 

4. 

Q. If m is a root of the given equation $(1-ab)x^2-(a^2+b^2)x-(1+ab)=0$ and m harmonic means are inserted between a and b, then the difference between the last and the first of the means equals

1. b - a
2. ab(b - a)
3. a(b - a)
4. ab(a - b)

Q. Insert 2 no.s between 1 & $\frac{1}{3}$ so that the sequence becomes an Harmonic progression --

1. $\frac{5}{3},\frac{7}{3}$
2. $\frac{5}{7},1$
3. $\frac{3}{5},\frac{3}{7}$
4. $\frac{1}{7},\frac{2}{7}$