^ - 1 , ( 1 + x^2 2 + x^2 ) નો વિસ્તાર મેળવો. - Vidyadip

MCQ

${\sin ^{ - 1\,}}\left( {\frac{{1 + {x^2}}}{{2 + {x^2}}}} \right)$ નો વિસ્તાર મેળવો.

A
$\left[ { - \frac{\pi }{6},\frac{\pi }{6}} \right]$
B
$\left[ {0,\frac{\pi }{2}} \right)$
C
$\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]$
D
$\left[ { \frac{\pi }{6},\frac{\pi }{2}} \right]$

✓

Answer

$\sin ^{-1}\left(1-\frac{1}{\left(2+x^{2}\right)}\right)$

$y=\sin ^{-1}(1)$ when $x \rightarrow \infty=\frac{\pi}{2}$

When $x=0 \Rightarrow y=\sin ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}$

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 "MCQ" from 1. relation and functiion→1. relation and functiion — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

અહી $M=\left\{A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{\pm 3, \pm 2, \pm 1,0\}\right\} $ આપેલ છે. વિધેય $f: M \rightarrow z$ છે કે જેથી દરેક $A \in M$ માટે $f(A)=\operatorname{det}(A)$ કે જ્યાં $Z$ એ પૂર્ણાંક ગણ છે. તો $f(A)=15$ થાય તેવા $A \in M$ શ્રેણીકોની સંખ્યા મેળવો.

${\sin ^{ - 1}}\left[ {\frac{{\sin x - \cos x}}{{\sqrt 2 }}} \right] = ......$ (જયાં $- \frac{\pi }{4} < x < \frac{\pi }{4})$

$\sin \left(\tan ^{-1} x\right),|x|<1=$ .....................

જો $a + b + c = 0,$ તો આપેલ વિધાન પૈકી કયું સત્ય બને.

વિકલ સમીકરણ $\left( {1 + {e^{2y}}} \right){e^{{{\tan }^{ - 1}}x}}dx - \left( {1 + {x^2}} \right)\left( {{e^y} + {{\left( {{e^y} - 1} \right)}^2}} \right)dy = 0$ નો ઉકેલ મેળવો

જો$\begin{vmatrix}1&x&x^2\\1&y&y^2\\1&z&z^2\end{vmatrix}=(x-y)(y-z)(z-x)$ તો$\begin{vmatrix}1&(b+c-a-d)^2&(b+c-a-d)^4\\1&(c+a-b-d)^2&(c+a-b-d)^4\\1&(a+b-c-d)^2&(a+b-c-d)^4\end{vmatrix}=.......$

A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces $20 \%$ and plant $T_2$ produces $80 \%$ of the total computers produced. $7 \%$ of computers produced in the factory turn out to be defective. It is known that

$P$ (computer turns out to be defective given that it is produced in plant $T_1$ )

$=10 P\left(\right.$ computer turns out to be defective given that it is produced in plant $\left.T_2\right)$,

where $P(E)$ denotes the probability of an event $E$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_2$ is

જો $A=\left[\begin{array}{ccc}\sqrt{3} & 1 & -1 \\ 2 & 3 & 0\end{array}\right]$ અને $B=\left[\begin{array}{ccc}2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2}\end{array}\right]$ આપેલા હોય, તો $A + B$ શોધો.

ધારો કે વિકલ સમીકરણ

$\left[\frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}}\right] x \frac{d y}{d x}=x+\left[\frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}}\right] y$ નો ઉકેલ

વક્ર $y=y(x)$ એે બિંદુઓ $(1,0)$ અને $(2 \alpha, \alpha)$ માંથી પસાર થાય, તો $\alpha>0$ નુ............ મૂલ્ય છે

જો $P \equiv (0, 1, 0),$ અને $Q \equiv (0, 0, 1)$ હોય તો $PQ$ નો સમતલ $x + y +z = 3$ પરનો પ્રક્ષેપ કેટલો થાય ?