If s-p-q-r- then the value of - s-r p q- r s-p q- r p s-q - isA- 3 s 3B- 2 s 3C- s 3D- 2 s 2

The correct option is B 2s^3Δ =s+r amp;p amp;q r amp;s+p amp;q r amp;p amp;s+q C_1→ C_1+C_2+C_3 ⇒ nbsp; Δ=s+r+p+q amp;p amp;q s+r+p+q amp; ...

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Standard XII

Mathematics

Distance Formula

If s=p+q+r, t...

Question

If $s = p + q + r$ , then the value of $∣ ∣ ∣ ∣ \begin{matrix} s + r & p & q r & s + p & q r & p & s + q \end{matrix} ∣ ∣ ∣ ∣$ is

3 s^{3}

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2 s^{3}

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s^{3}

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2 s^{2}

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Solution

The correct option is B $2 s^{3}$
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} s + r & p & q r & s + p & q r & p & s + q \end{matrix} ∣ ∣ ∣ ∣$

$C_{1} \to C_{1} + C_{2} + C_{3}$
$\Rightarrow Δ = ∣ ∣ ∣ ∣ \begin{matrix} s + r + p + q & p & q s + r + p + q & s + p & q s + r + p + q & p & s + q \end{matrix} ∣ ∣ ∣ ∣$

$\Rightarrow Δ = (s + r + p + q) ∣ ∣ ∣ ∣ \begin{matrix} 1 & p & q 1 & s + p & q 1 & p & s + q \end{matrix} ∣ ∣ ∣ ∣$

$R_{2} \to R_{2} - R_{1}, R_{3} \to R_{3} - R_{1}$
$\Rightarrow Δ = 2 s ∣ ∣ ∣ ∣ \begin{matrix} 1 & p & q 0 & s & 0 0 & 0 & s \end{matrix} ∣ ∣ ∣ ∣$

$\Rightarrow Δ = 2 s \cdot s^{2} = 2 s^{3}$

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Similar questions

If $p > q > 0 a n d p r < - 1 < q r$ , then find the value of

{tan}^{- 1} \frac{p - q}{1 + p q} + {tan}^{- 1} \frac{q - r}{1 + q r} + {tan}^{- 1} \frac{r - p}{1 + r p} .

If every pair of the equations $x^{2} + p x + q r = 0, x^{2} + q x + r p = 0, x^{2} + r x + p q = 0$ have a common root, then the sum of three common roots is

Q. If the

p^{t h}, q^{t h}

and

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terms of an A. P. are P, Q, R respectively, then

P (q - r) + Q (r - p) + R (p - q)

equals ______.

The factors of $(p - q)^{3} + (q - r)^{3} + (r - p)^{3}$ are:

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△ R S T

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and

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. If

R P = 4, P S = 8, R Q = 3

, then find

Q T

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If s=p+q+r, then the value of ∣∣ ∣∣s+rpqrs+pqrps+q∣∣ ∣∣ is

The correct option is B 2s3Δ=∣∣ ∣∣s+rpqrs+pqrps+q∣∣ ∣∣ C1→C1+C2+C3 ⇒Δ=∣∣ ∣∣s+r+p+qpqs+r+p+qs+pqs+r+p+qps+q∣∣ ∣∣ ⇒Δ=(s+r+p+q)∣∣ ∣∣1pq1s+pq1ps+q∣∣ ∣∣ R2→R2−R1, R3→R3−R1 ⇒Δ=2s∣∣ ∣∣1pq0s000s∣∣ ∣∣ ⇒Δ=2s⋅s2=2s3

If $s = p + q + r$ , then the value of $∣ ∣ ∣ ∣ \begin{matrix} s + r & p & q r & s + p & q r & p & s + q \end{matrix} ∣ ∣ ∣ ∣$ is