Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $\sec ^{-1}\left(\frac{1+x}{1-y}\right)=a$, then $\frac{d y}{d x}$ is equal to
  • A
    $\frac{x-1}{y-1}$
  • B
    $\frac{x-1}{y+1}$
  • C
    $\frac{y-1}{x+1}$
  • D
    $\frac{y+1}{x-1}$
✓

Answer

Given, $\sec ^{-1}\left(\frac{1+x}{1-y}\right)=a \Rightarrow \sec a=\frac{1+x}{1-y}$
On differentiating, we get
$\frac{(1-y)+(1+x) \frac{d y}{d x}}{(1-y)^2}=0 \Rightarrow(1+x) \frac{d y}{d x}=y-1 \Rightarrow \frac{d y}{d x}=\frac{y-1}{1+x}
$

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 Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $z = {y \over x}\left[ {\sin {x \over y} + \cos \left( {1 + {y \over x}} \right)} \right]$, then $x{{\partial z} \over {\partial x}} = $
→
If $A = \left[ {\begin{array}{*{20}{c}}
3&7\\
1&2
\end{array}} \right]$ then $|A^{2011} -5A^{2010}|$ is equal to
→
The number of matrices with order $3 \times 2$ whose each entries are 1 or 2 , is ____________ .
→
If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}+\overrightarrow{\text{OD}}=$
  1. $2\overrightarrow{\text{OG}}$
  2. $4\overrightarrow{\text{OG}}$
  3. $5\overrightarrow{\text{OG}}$
  4. $3\overrightarrow{\text{OG}}$
→
For the differentiable function $f: R -\{0\} \rightarrow R$, let $3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10$, then $\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|$ is equal to
→
Let $\vec p\, = \,2\hat i\, + \,3\hat j\, + \,a\hat k$, $\vec q\, = \,b\hat i\, + \,5\hat j\, - \hat k$, $\vec r\, = \,\hat i\, + \,\hat j\, + 3\hat k$ . If $\vec p,\vec q,\vec r$ are coplanar and $\vec p,\vec q$= $20$ , then the ordered pair $(a, b)$ is 
→
Let $\vec a = \hat i + \hat j + \hat k,\,\,\,\vec c = \hat j - \hat k$ and a vector $\vec b$ be such that $\vec a \times \vec b = \,\vec c$ and $\vec a\, \cdot \,\vec b = \,3.$ Then $\left| {\vec b} \right|$ equals?
→
Choose the correct answer from the given four options.
The distance of the plane $\vec{\text{r}}\Big(\frac{2}{7}\hat{\text{i}}+\frac{3}{7}\hat{\text{j}}-\frac{6}{7}\hat{\text{k}}\Big)=1$ from the origin is:
  1. 1.
  2. 7.
  3. $\frac{1}{7}.$
  4. None of these.
→
$4tan^{-1} \frac{1}{5} -tan^{-1} \frac{1}{239}$ is equal to
→
A value of $c$ for which conclusion of Mean Value Theorem holds for the function $f\left( x \right) = \log x$ on the interval $[1,3]$ is
→