If pv = 81, then dp dv is at v = 9 equal to - Vidyadip

MCQ

If $pv = 81$, then ${{dp} \over {dv}}$ is at $ v = 9 $ equal to

A
$1$
✓
$-1$
C
$2$
D
None of these

✓

Answer

Correct option: B.

$-1$

b
(b) $pv = 81 \Rightarrow \frac{{dp}}{{dv}} = \frac{{ - 81}}{{{v^2}}} = \frac{{ - 81}}{{81}} = - 1$.

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 "M.C.Q (1 Marks)" from 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int\limits_{\frac{\pi }{4}}^{\frac{\pi }{4}} {{{\log }_e}\left( {\sin x + \cos x} \right)\,dx}$ is equal to

Identify the statement(s) which is/are True.

$\mathop {Lim}\limits_{k \to 0} \,\,\frac{1}{k}\int\limits_0^k {{{(1 + \sin 2x)}^{\frac{1}{x}}}dx} $

If $A = [1\,\,2\,{\rm{ }}3]$and $B = \left[ {\begin{array}{*{20}{c}}{ - 5}&4&0\\0&2&{ - 1}\\1&{ - 3}&2\end{array}} \right]$, then $AB = $

If $f(x) = \left\{ \begin{array}{l}x,\,\,{\rm{when\,\,}}\,x\,\,{\rm{\,is\,}}\,{\rm{\,rational\,\,}}\\0{\rm{,}}\,\,{\rm{when\,\,}}x{\rm{ \,\,is\,\,\, irrational\,}}\end{array} \right.$;

$g(x) = \left\{ \begin{array}{l}0,\,\,\,\,{\rm{when\,\,}}\,x\,{\rm{\,\,is\,\,}}\,{\rm{\,\,rational\,}}\\x,\,\,\,\,{\rm{\,\,when\,\,}}\,x\,{\rm{\,\,is\,\, irrational\,}}\end{array} \right.$ then $(f - g)$ is

The value of $\tan^{-1}\Big(\frac{1}{2}\Big)+\tan^{-1}\Big(\frac{1}{3}\Big)+\tan^{-1}\Big(\frac{7}{8}\Big)$ is:

$\tan^{-1}\Big(\frac{7}{8}\Big)$
$\cot^{-1}(15)$
$\tan^{-1}(15)$
$\tan^{-1}\Big(\frac{25}{24}\Big)$

Area of the greatest rectangle that can be inscribed in the ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$ is

The function $F(x) = \int_0^x {\log \left( {\frac{{1 - x}}{{1 + x}}} \right)} \,dx$ is

If $y = x{\rm{ }}\left[ {\left( {\cos {x \over 2} + \sin {x \over 2}} \right){\rm{ }}\left( {\cos {x \over 2} - \sin {x \over 2}} \right) + \sin x} \right] + {1 \over {2\sqrt x }}$, then ${{dy} \over {dx}} = $

For real $x,$ let $f\left( x \right) = {x^3} + 5x + 1$,then