Suppose p - q - r are in A-P- and p 2- q 2- r 2 are in G-P- If p - q - r and p - q - r -3-2- then the value of p isA- 1-2 -2B-C- 1-2-1-3 -1-2-1-2

The correct option is D 12 1√(2)q^4=p^2r^2⇒ q^2=± pr ⋯(1) Given that p+q+r=32 ⇒ q=12 nbsp; For q^2=pr, p=q=r=12, this is not possible. ⇒ q^2= pr and p+ ...

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Byju's Answer

Standard XII

Mathematics

Adjoint of a Matrix

Suppose p , q...

Question

Suppose $p, q, r$ are in A.P. and $p^{2}, q^{2}, r^{2}$ are in G.P. If $p < q < r$ and $p + q + r = \frac{3}{2},$ then the value of $p$ is

\frac{1}{2 \sqrt{2}}

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\frac{1}{2}

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\frac{1}{2} - \frac{1}{\sqrt{3}}

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\frac{1}{2} - \frac{1}{\sqrt{2}}

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Solution

The correct option is D $\frac{1}{2} - \frac{1}{\sqrt{2}}$
$q^{4} = p^{2} r^{2} \Rightarrow q^{2} = \pm p r \dots (1)$
Given that $p + q + r = \frac{3}{2}$
$\Rightarrow q = \frac{1}{2}$

For $q^{2} = p r, p = q = r = \frac{1}{2}$ , this is not possible.
$\Rightarrow q^{2} = - p r and p + r = 1 \Rightarrow p = \frac{1}{2} - \frac{1}{\sqrt{2}}$

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Similar questions

Q. If

p, q, r

are in A.P. and

p^{2}, q^{2}, r^{2}

are in G.P, where

p < q < r

and

p + q + r = \frac{3}{2},

then the value of

p

Q. If

\frac{1}{q + r}

\frac{1}{r + p}

and

\frac{1}{p + q}

are in AP, then

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Q. If

p = - 2, q = 1

and

r = 3

find the value of
( a )

p^{2} + q^{2} - r^{2}

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p^{3} + q^{3} + r^{3} + 3 p q r

Q. If

a, b, c, p, q, r

are three complex numbers such that

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1 + i

and

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0

then value of

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

Q. If p = −2, q = −1 and r = 3, find the value of
(i) p² + q² − r²
(ii) 2p² − q² + 3r²
(iii) p − q − r
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(v) 3p²q + 5pq² + 2pqr
(vi) p⁴ + q⁴ − r⁴

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Suppose p,q,r are in A.P. and p2,q2,r2 are in G.P. If p<q<r and p+q+r=32, then the value of p is

The correct option is D 12−1√2q4=p2r2⇒q2=±pr ⋯(1) Given that p+q+r=32 ⇒q=12 For q2=pr, p=q=r=12, this is not possible. ⇒q2=−pr and p+r=1⇒p=12−1√2

Suppose $p, q, r$ are in A.P. and $p^{2}, q^{2}, r^{2}$ are in G.P. If $p < q < r$ and $p + q + r = \frac{3}{2},$ then the value of $p$ is