Download App

INVERSE TRIGNOMETRIC FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
Choose the correct answer from the given four options.The domain of the function defined by $\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$ is:
  1. [1, 2]
  2. [-1, 1]
  3. [0, 1]
  4. none of these.
✓

Answer

  1. [1, 2]
Solution:
$\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$
$\Rightarrow\ 0\leq\text{x}-1\leq1$ $[\because\ \sqrt{\text{x}-1}\geq0\ \text{and}\ -1\leq\sqrt{\text{x}-1}\leq1]$
$\Rightarrow\ 1\leq\text{x}\leq2$
$\therefore\ \text{x}\in[1,2]$

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 INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let $\text{A}=\{\text{x}\in\text{R}:\text{x}\leq1\}$ and $f : A \rightarrow A$ be defined as $f(x) = x(2 - x)$. Then $f^{-1}(x)$ is :
→
Choose the correct answer from the given four options.
If $\text{P}(\text{A})=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$ is equal to:
  1. $\frac{1}{10}$
  2. $\frac{1}{8}$
  3. $\frac{7}{8}$
  4. $\frac{17}{20}$
→
The value of $ \cos^{-1} (\cos 12) - \sin^{-1} (\sin 14)$ is
  1. 0
  2. 8π - 26
  3. 4π + 2
  4. None of these
→
The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in Column A and Column B.
Column A
Column B
Maximum of Z
325
→
A set of vectors taken in a given order gives a closed polygon.Then the resultant of these vectors is:
  1. scalar quantity
  2. pseudo vector
  3. unit vector
  4. null vector
→
If $A$ is a square matrix such that $A^2=A$, then $(I-A)^3+A$ is equal to
→
Order of $\Big(\frac{\text{dy}}{\text{dx}}+3\text{x}\Big)^\frac{3}{2}=\text{x}+\frac{3\text{dy}}{\text{dx}}$ is:
  1. 3
  2. 2
  3. 1
  4. 4
→
Given a system of inequation: $2\text{y}-\text{x}\leq4$ $-2\text{x}+\text{y}\geq-4$Find the value of s, which is the greatest possible sum of the x and y co - ordinates of the point which satisfies the following inequalities as graphed in the xy plane.
→
Which of the following transformation reduce the differential quation  into the form $\frac{\text{du}}{\text{dx}}+\text{P}(\text{x})\text{u}=\text{Q}(\text{x})$ into the from $\frac{\text{dz}}{\text{dx}}+\frac{\text{z}}{\text{x}}\log\text{z}=\frac{\text{z}}{\text{x}^{2}}(\log\text{z})^{2}$
  1. $\text{u}=\log\text{x}$
  2. $\text{u}=\text{e}^{\text{z}}$
  3. $\text{u}=(\log\text{z})^{-1}$
  4. $\text{u}=(\log\text{z})^{2}$ 
→
If $y = ax^2 + b,$ then $\frac{\text{dy}}{\text{dx}}$ at $x = 2$ is equal to:
→