nth Term of HP

Q.

If the 7th term of a H.P is $\frac{1}{10}$ and the 12th term is $\frac{1}{25}$, then the 20th term is

1. $\frac{1}{37}$

2. $\frac{1}{41}$

3. $\frac{1}{45}$

4. $\frac{1}{49}$

Q.

The first term of a harmonic is $\frac{1}{7}$ and the second term is $\frac{1}{9}$. The ${12}^{th}$ term is

1. $\frac{1}{19}$

2. $\frac{1}{29}$

3. $\frac{1}{17}$

4. $\frac{1}{27}$

Q. If the $7^{\text{th}}$ and ${12}^{\text{th}}$ terms of a H.P. are $\frac{1}{10}$ and $\frac{1}{25}$ respectively, then the ${20}^{\text{th}}$ term of H.P. is

1. $\frac{1}{37}$
2. $\frac{1}{42}$
3. $\frac{1}{45}$
4. $\frac{1}{49}$

Q.

The fifth of the H.P. 2, $\frac{5}{2}$, $\frac{10}{3}$, ................. will be

1. $5\frac{1}{5}$

2. $3\frac{1}{5}$

3. $\frac{1}{10}$

4. 10

Q.

If $\alpha ,\beta ,\gamma$ are the roots of the equation $x^3+4x+1=0$, then ${\left(\alpha +\beta \right)}^{-1}+{\left(\beta +\gamma \right)}^{-1}+{\left(\gamma +\alpha \right)}^{-1}$ is equal to

1. $2$

2. $3$

3. $4$

4. $5$

Q. If $(1+2!)$ is a root of the equation $x^2+bx+c=0,$ where b and c are real then (b, c) is given by

1. (2, -15)
2. (-3, 1)
3. (3, 1)
4. (-2, 5)

Q.

If the roots of $x^3-12x^2+12x-28=0$ are in A.P, their common difference is

1. $\pm 3$

2. $\pm 2$

3. $\pm 1$

4. None of these

Q.

If the $7^{th}$ term of a harmonic progression is 8 and the $8^{th}$ term is 7, then its ${15}^{th}$ term is

1. 16

2. 14

3. $\frac{27}{14}$

4. $\frac{56}{15}$