Download App

Arithmetic Progressions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions3 Marks
Question
If $\text{a}\Big(\frac{1}{\text{b}}+\frac{1}{\text{c}}\Big),\ \Big(\frac{1}{\text{c}}+\frac{1}{\text{a}}\Big),\ \text{c}\Big(\frac{1}{\text{a}}+\frac{1}{\text{b}}\Big)$ are in A.P., proved that a, b, c are in A.P.
✓

Answer

$\text{a}\Big(\frac{1}{\text{b}}+\frac{1}{\text{c}}\Big),\ \Big(\frac{1}{\text{c}}+\frac{1}{\text{a}}\Big),\ \text{c}\Big(\frac{1}{\text{a}}+\frac{1}{\text{b}}\Big)$ are in A.P.
$\Rightarrow\text{a}\Big(\frac{1}{\text{b}}+\frac{1}{\text{c}}\Big)+1,\ \Big(\frac{1}{\text{c}}+\frac{1}{\text{a}}\Big)+1,\ \text{c}\Big(\frac{1}{\text{a}}+\frac{1}{\text{b}}\Big)+1$ are in A.P.
$\Rightarrow\Big(\frac{​​​​​​\text{ac}+​\text{ab}+​\text{bc}}{​\text{bc}}\Big),\ \Big(\frac{​\text{ab}+​\text{bc}+​\text{ac}}{​\text{ac}}\Big),\ \Big(\frac{​\text{cd}+​\text{ac}+​\text{ab}}{​\text{ab}}\Big)$ are in A.P.
$\Rightarrow\frac{1}{​\text{bc}},\ \frac{1}{​\text{ac}},\ \frac{1}{​\text{ab}}$ are in A.P.
$\Rightarrow\frac{​\text{abc}}{​\text{bc}},\ \frac{​\text{abc}}{​\text{ac}},\ \frac{​\text{abc}}{​\text{ab}}$ are in A.P.
$\Rightarrow​\text{a},​\text{b},​\text{c}$ are in A.P.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If A.M. and G.M. of two positive numbers a and b are 10 and 8 respectively, find the numbers.
→
Prove that:
$\sin4\text{x}=4\sin\text{x}\cos^3\text{x}-4\cos\text{x}\sin^3\text{x}$
→
Let $A = \{3, 6, 12, 15, 18, 21\}, B = \{4, 8, 12, 16, 20\}, C = \{2, 4, 6, 8, 10, 12, 14, 16\}, D = \{5 , 10, 15, 20\}.$ Find:
  1. $A - B$
  2. $A - C$
  3. $A - D$
  4. $B - A$
  5. $C - A$
  6. $D - A$
  7. $B - C$
  8. $B - D.$
→
One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?
→
How many automobile license plates can be made if each plate contains two different letters followed by three different digits?
→
Using binomial theorem write down the expansions of the following:
$(1-2\text{x}+3\text{x}^2)^3$
→
Find the mean and variance for each of the data First $n$ natural numbers.
→
Prove that: $\cos 2 x \cos \frac{x}{2}-\cos 3 x \cos \frac{9 x}{2}$ $=\sin 5 x \sin \frac{5 x}{2}$
→
The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the value of m and c.
→
Sketch the graphs of the following trigonometric functions:
$\text{g(x)}=\cos\Big(\text{x}+\frac{\pi}{4}\Big)$
→