JEE Mains · Maths · STD 12 - 1. relation and function
The range of \(f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)\) is
- A \([0, \pi]\)
- B \([0,2 \pi)\)
- C \([0, \pi)\)
- D \([0,2 \pi]\)
Answer & Solution
Correct Answer
(B) \([0,2 \pi)\)
Step-by-step Solution
Detailed explanation
\(f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)\) \(\frac{x^2+1-1}{x^2+1}=1-\frac{1}{x^2+1} \Rightarrow[0,1)\) Range of \(f(x)=[0,2 \pi)\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Consider a matrix \(A =\left[\begin{array}{ccc}\alpha & \beta & \gamma \\ \alpha^{2} & \beta^{2} & \gamma^{2} \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta\end{array}\right]\), where \(\alpha, \beta, \gamma\) are three distinct natural numbers. If \(\frac{\operatorname{det}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))))}{(\alpha-\beta)^{16}(\beta-\gamma)^{16}(\gamma-\alpha)^{16}}=2^{32} \times 3^{16}\), then the number of such \(3 -\) tuples \((\alpha, \beta, \gamma)\) is \(.....\)JEE Mains 2022 Hard
- If the system of equations
\(\begin{aligned}
& x+2 y-3 z=2 \\
& 2 x+\lambda y+5 z=5 \\
& 14 x+3 y+\mu z=33
\end{aligned}\)
has infinitely many solutions, then \(\lambda+\mu\) is equal to :JEE Mains 2025 Easy - If \(m\) and \(n\) respectively are the number of local maximum and local minimum points of the function \(f ( x )=\int_{0}^{ x ^{2}} \frac{ t ^{2}-5 t +4}{2+ e ^{ t }} dt\), then the ordered pair \(( m , n )\) is equal toJEE Mains 2022 Hard
- Let the product of \(\omega_1=(8+i) \sin \theta+(7+4 i) \cos \theta\) and \(\omega_2=(1+8 i) \sin \theta+(4+7 i) \cos \theta\) be \(\alpha+i \beta\), \(\mathrm{i}=\sqrt{-1}\). Let p and q be the maximum and the minimum values of \(\alpha+\beta\) respectively.JEE Mains 2025 Medium
- If a random variable x has the probability distribution
then \(P (3< x \leq 6)\) is equal tox 0 1 2 3 4 5 6 7 p(x) 0 2k k 3k \(2 k ^2\) 2k \(k ^2+ k\) \(7 k ^2\) JEE Mains 2026 Medium - The product of all possible values of \(\alpha\), for which \(\displaystyle\lim_{x \to 0}\left(\dfrac{1 - \cos(\alpha x)\cos((\alpha+1)x)\cos((\alpha+2)x)}{\sin^2((\alpha+1)x)}\right) = 2\), is:JEE Mains 2026 Hard
More PYQs from JEE Mains
- For a triangle \(ABC\), the value of \(\cos 2 A +\cos 2 B +\cos 2 C\) is least. If its inradius is \(3\) and incentre is \(M\), then which of the following is NOT correct?JEE Mains 2023 Hard
- Let the line \(\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}\) intersect the plane containing the lines \(\frac{x-4}{1}=\frac{y+1}{-2}=\frac{z}{1}\) and \(4 a x-y+5 z-7 a=0=2 x -5 y - z -3, a \in R\) at the point \(P(\alpha, \beta, \gamma)\). Then the value of \(\alpha+\beta+\gamma\) equals\(...\)JEE Mains 2022 Hard
- If \(\left| {z - 3 + 2i} \right| \leq 4\) then the difference between the greatest value and the least value of \(\left| z \right|\) isJEE Mains 2018 Hard
- If \(sin^4\,\,\alpha + 4\,cos^4\,\,\beta + 2 = 4\sqrt 2\,\,sin\,\alpha \,cos\,\beta ;\) \(\alpha \,,\,\beta \, \in \,[0,\pi ],\) then \(cos( \alpha + \beta)\) is equal toJEE Mains 2019 Hard
- The integral \(\int\left(\left(\frac{x}{2}\right)^x+\left(\frac{2}{x}\right)^x\right) \log _2 x d x\) is equal toJEE Mains 2023 Hard
- Let \(A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right], \quad\) where \(x, y\) and \(z\) are real numbers such that \(x + y + z >0\) and \(xyz =2\) If \(A ^{2}= I _{3},\) then the value of \(x ^{3}+ y ^{3}+ z ^{3}\) is ............JEE Mains 2021 Hard