Harmonic Progression

Q.

Subtract $3\mathrm{xy}+5\mathrm{yz}-7\mathrm{zx}$ from $5\mathrm{xy}-2\mathrm{yz}-2\mathrm{zx}+10\mathrm{xyz}$.

Q.

If $a,a_1,a_2,,...,a_{2n},b$are in arithmetic progression and $a,g_1,g_2,..,g_{2n},b$are in geometric progression and is the harmonic mean of $a$ and $b$ is

1. $2nh$

2. $n/h$

3. $nh$

4. $2n/h$

Q.

If $1/(b-a)+1/(b-c)=(1/a)+(1/c),$then $a,b,c$are in

1. $AP$

2. $GP$

3. $HP$

4. none of these

Q.

If $x_1,x_2,\dots ..x_n$ are $n$ observations such that $\sum _{i=1^n}{x_i}^2=400$ and $\sum _{i=1^n}{x}_i=80$, the possible value of $n$ is

1. $18$

2. $12$

3. $15$

4. $16$

Q.

Write $\frac{1}{2}$with denominator as $10,16,26,102,5000$. Can you write $\frac{1}{2}$ with denominator equal to $5.$

Q.

If $2x+3=5$, then value of $3x+2$ is _______

Q. If $a_1,a_2,a_3$ are in A.P., $a_2,a_3,a_4$ are in G.P., and $a_3,a_4,a_5$ are in H.P., then $\ln a_1,\ln a_3,\ln a_5$ are in

1. G.P.
2. A.P.
3. H.P.
4. None of these

Q.

If a₁, a₂, a₃.....a_n are in H.P., then $\frac{a_1}{a_2+a_3+......a_n}$ . $\frac{a_2}{a_1+a_3+.....+a_n}$, ...... $\frac{a_n}{a_1+a_2+.......+a_{n-1}}$

are in

1. H.P.

2. A.P.

3. G.P.

4. A.G.P

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. 1/19

2. 1/29

3. 1/27

4. 1/17

Q.

$\frac{1}{9}of\frac{6}{5}$is ………..

Q.

Prove $\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\cdots +\frac{1}{(3n-2)(3n+1)}=\frac{n}{(3n+1)}$

Q.

Which ratio is greater: $7˸9$ and $2˸11$

Q.

$\frac{1}{3}$ and $\frac{1}{5}$ are first 2 terms of H.P. the 15th term of H.P is

1. 

2. 

3. 

4. 

Q. If a, b, c, d are in H.P. , then ab +bc+cd =

1. ad
2. 2ad
3. 3ad
4. 4ad

Q.

Subtract :

$-5pq$ from$-12pq$

Q. The minimum value of f(x) = $|x-1|$ +$|x-2|$ + $|x-3|$

1. 1

2. 2

3. 3

4. 0

Q.

Which ratio is greater: $3˸7$ and $2˸5$

Q.

Which ratio is greater: $2˸3$ and $11˸15$

Q.

Which ratio is greater: $2˸15$ and $7˸12$

Q.

If a, b, c are in H.P then $4^{-a},4^{-b},4^{-c}$ are in

1. A.P
2. G.P
3. H.P
4. none of these

Q.

If a, b, and c are in G.P. and x, y, respectively, be arithmetic means between a, b and b, c, then the value of $\frac{a}{x}+\frac{c}{y}$is

1. 1

2. 2

3. 1/2

4. none of these

Q.

The correct statement about the roots of the equation $x^2$ - 2ax - $b^2=0$ is

1. Real and same in sign

2. Real and equal

3. Real and opposite in sign

4. Imaginary

Q.

In $△ABC\frac{co{s}^2\frac{A}{2}}{a}+\frac{co{s}^2\frac{B}{2}}{b}+\frac{co{s}^2\frac{C}{2}}{c}$

1. 

2. 

3. 

4. None of these

Q. Paragraph for below question

नीचे दिए गए प्रश्न के लिए अनुच्छेद

A man started investing in a company. He started with Rs. 10 in 1^st month. In every succeeding month, he invested 2 times as of the proceeding month.

एक व्यक्ति ने एक कम्पनी में निवेश करना प्रारम्भ किया। प्रथम माह में उसने 10 रूपये से शुरूआत की, तथा प्रत्येक आने वाले माह में गत माह की तुलना में 2 गुना निवेश किया।

Q. At the end of 6^th month, total amount that he had invested in the company was

प्रश्न - 6^th महीने के अंत में, उसके द्वारा कंपनी में निवेश की गई कुल राशि थी

1. 1260
2. 630
3. 640
4. 1780

Q.

If $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c},$ then a, b, c, are in

1. A.P
2. G.P
3. H.P
4. none of these

Q. Let $a_1,a_2,a_3.$..... be in harmonic progression with $a_1=5$ and $a_{20}=25$. The least positive integer n for which $a_n<0$ is

1. 25
2. 22
3. 23
4. 24

Q.

If a, b, c, d are in H.P., then ab + bc + cd is equal to

1. 3ad

2. (a + b)(c + d)

3. 3ac

4. None of these

Q.

If the roots of $a(b-c)x^2+b(c-a)x+c(a-b)$ = 0 be equal then a, b, c are in

1. A.P

2. G.P

3. H.P

4. None of these

Q. If $x={\sum }_{n=0}^{\infty }{a}^n,y={\sum }_{n=0}^{\infty }{b}^n,z={\sum }_{n=0}^{\infty }{c}^n$ where a, b, c, are in AP
and |a| <1, |b|<1, |c|<1 then x, y, z are in

1. GP
2. AP
3. Arithmetic- Geometric progression
4. H.P

Q. Let $a_1,a_2................,a_{10}$ be in AP and $h_1,h_2,........h_{10}$ be in HP. If $a_1=h_1=2$ and $a_{10}=3$, then a$a_4{h}_7$ is

1. 2
2. 5
3. 3
4. 6