Download App

6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
Coffee is draining from a conical filter, height and diameter both $15 \,\,cms$ into a cylinderical coffee pot diameter $15 \,\,cm$. The rate at which coffee drains from the filter into the pot is $100 \,\,cu cm /min$.The rate in $cm s/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \,\,cm$, is
  • A
    $\frac{9}{16\pi }$
  • B
    $\frac{25}{9\pi }$
  • C
    $\frac{5}{3\pi }$
  • ✓
    $\frac{16}{9\pi }$
✓

Answer

Correct option: D.
$\frac{16}{9\pi }$
d
For cylindrical pot  $V = \pi r^2h$

$\frac{{dV}}{{dt}} = \pi \left[ {{r^2}\frac{{dh}}{{dt}} + h\,\cdot\,2r\frac{{dr}}{{dt}}} \right]$(r = constant, $\frac{{dr}}{{dt}} = 0$)

hence,$100 = \pi r^2\frac{{dh}}{{dt}}$

$100 = \pi · \frac{{225}}{4} · \frac{{dh}}{{dt}}$(r = $\frac{{15}}{{2}} cm$)

$\frac{{dh}}{{dt}} = \frac{{400}}{{225\pi }} = \frac{{16}}{{9\pi }} cm/min$

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 6. Application of derivatives→6. Application of derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_{}^{} {\frac{{{e^x}(x + 1)}}{{{{\cos }^2}(x{e^x})}}dx = } $
→
If $f(x)$ = $sin^2x + xsin2x.logx$, then $f(x)$ = $0$ has
→
Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations

$x+y+z=5$    ;    $x+2 y+3 z=\mu$   ;     $x+3 y+\lambda z=1$

is constructed. If $\mathrm{p}$ is the probability that the system has a unique solution and $\mathrm{q}$ is the probability that the system has no solution, then :

→
Evaluate: $\int_0^2(x-[x]) d x$
→
If the function $\text{f}(\text{x})=2\tan\text{x}+(2\text{a}+1)\log_\text{e}|\sec\text{x}|+(\text{a}-2)\text{x}$ is increasing on R, then:
  1. $\text{a}\in\Big(\frac{1}{2},\infty\Big)$
  2. $\text{a}\in\Big(-\frac{1}{2},\frac{1}{2}\Big)$
  3. $\text{a}=\frac{1}{2}$
  4. $\text{a}\in\text{R}$
→
A die is tossed $5$ times. Getting an odd number is considered a success. Then the variance of distribution of success is
→
The set of all values of $\lambda $ for which the system of linear equations $x - 2y - 2z = \lambda x$ ; $x + 2y + z = \lambda y$ ; $-x - y = \lambda z$ has non zero solutions.
→
The function $f$ defined by $f(x)=4 x^4-2 x+1$ is increasing for
→
The roots of the equation $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right| = 0$ are equal to
→
Let R be a relation on the set N given by R = {(a, b): a = b - 2, b > 6}. Then,
  1. (2, 4) ∈ R
  2. (3, 8) ∈ R
  3. (6, 8) ∈ R
  4. (8, 7) ∈ R
→