If - 9 r- 1 4 - 3- 3 -r 3- 3 -r -m- then find the value of m is

The correct option is B 3 ^ 2 √(9^(r+14)√(3× 3^ r)3×√(3^ r))=m ⇒√(9^(r+14)√(3)·√(3^ r)3×√(3^ r))=m ⇒ r√(9^(r+14)·√(3)3√(3))=m ⇒[(3^2)^r ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Parametric Differentiation

If √ 9 r+ 1...

Question

If $\sqrt[r]{\frac{9^{(r + \frac{1}{4})} \sqrt{3 \times 3^{- r}}}{3 \times \sqrt{3^{- r}}}} = m$ , then find the value of $m$ is

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt[r]{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $3^{2}$
$\sqrt[r]{\frac{9^{⎛ ⎝ r + \frac{1}{4} ⎞ ⎠} \sqrt{3 \times 3^{- r}}}{3 \times \sqrt{3^{- r}}}} = m$
$\Rightarrow \sqrt[r]{\frac{9^{⎛ ⎝ r + \frac{1}{4} ⎞ ⎠} \sqrt{3} \cdot \sqrt{3^{- r}}}{3 \times \sqrt{3^{- r}}}} = m$
$\Rightarrow r \sqrt{\frac{9^{⎛ ⎝ r + \frac{1}{4} ⎞ ⎠} \cdot \sqrt{3}}{3 \sqrt{3}}} = m$
$\Rightarrow {⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{(3^{2})^{r + \frac{1}{4}}}{3^{\frac{1}{2}}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{\frac{1}{r}} = m$
$\Rightarrow {⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{3^{2 r + \frac{2}{4}}}{3^{\frac{1}{2}}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{\frac{1}{r}} = m \Rightarrow {⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{3^{2 r + \frac{1}{2}}}{3^{\frac{1}{2}}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{\frac{1}{r}} = m$
$\Rightarrow {⎡ ⎢ ⎣ 3^{2 r + \frac{1}{2}} - \frac{1}{2} ⎤ ⎥ ⎦}^{\frac{1}{r}} = m$
$\Rightarrow [3^{2 r}]^{\frac{1}{r}} = m$
$3^{2} = m$
$∴ m = 3^{2}$ .

Suggest Corrections

Similar questions

Question 1
If the radius of a sphere is 2r, then its volume will be:

A) $\frac{4}{3} π r^{3}$
B) $4 π r^{3}$
C) $\frac{8}{3} π r^{3}$
D) $\frac{32}{3} π r^{3}$

Q. If

\frac{^{n} C_{r} + 4^{n} C_{r + 1} + 6^{n} C_{r + 2} + 4^{n} C_{r + 3} +^{n} C_{r + 4}}{^{n} C_{r} + 3^{n} C_{r + 1} + 3^{n} C_{r + 2} +^{n} C_{r + 3}} = \frac{n + k}{r + k}

, then the value of k is

Q. If

f; R \to R, g; R \to R

and

g (x) = x + 3

and

(f o g) (x) = (x + 3)^{2}

, then the value of

f (- 3)

Q. If

\sum_{r = 1}^{10} t a n^{- 1} [\frac{3}{9 r^{2} + 3 r - 1}] = c o t^{- 1} [\frac{m}{n}]

(where m and n are coprime), then find the value of (m - n). ___

Q. If the sum of the series

1 + 2 r + 3 r^{2} + 4 r^{3} + \dots \infty

\frac{9}{4},

then the value of

r

Join BYJU'S Learning Program

If r   ⎷9(r+14)√3×3−r3×√3−r=m, then find the value of m is

If $\sqrt[r]{\frac{9^{(r + \frac{1}{4})} \sqrt{3 \times 3^{- r}}}{3 \times \sqrt{3^{- r}}}} = m$ , then find the value of $m$ is