If (b+c),(c+a),(a+b) are in H.P , then a^2,b^2,c^2 are in....... - Vidyadip

MCQ

If $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in.......

✓
$A.P.$
B
$G.P.$
C
$H.P.$
D
None

✓

Answer

Correct option: A.

$A.P.$

a
$(b+c)^{-1}, (c+a)^{-1}, (a+b)^{-1}$ are in $A.P$ so by using properties of $AP$ , we can show that $2b^2= a^2+b^2$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\frac{1}{x}}}}}{{{e^{\left( {\frac{1}{x} + 1} \right)}}}} = $

$\left( {\int_{\,0}^{\,a} {x\,dx} } \right) \le (a + 4),$ then

A fair coin is tossed $n$ times. Let $X$ be the number of times head is observed. If $P(X = 4),\,\,P(X = 5)$ and $P(X = 6)$ are in $H.P.$, then $n$ is equal to

The value of $\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{n^3}{\left(n^2+k^2\right)\left(n^2+3 k^2\right)}$ is

Let the tan gents drawn to the circle, $x^2 + y^2 = 16$ from the point $P(0, h)$ meet the $x-$ axis at point $A$ and $B.$ If the area of $\Delta APB$ is minimum, then $h$ is equal to

Let $A$ and $B$ be two sets. Then

If the sum of the roots of the equation $a{x^2} + bx + c = 0$ be equal to the sum of the reciprocals of their squares, then $b{c^2},\;c{a^2},\;a{b^2}$ will be in

The value of ${\left[ {\frac{{1 - \cos \frac{\pi }{{10}} + i\sin \frac{\pi }{{10}}}}{{1 - \cos \frac{\pi }{{10}} - i\sin \frac{\pi }{{10}}}}} \right]^{10}} = $

The incentre of triangle formed by the lines $x = 0,$ $y = 0$ and $3x + 4y = 12$ is

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are