JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The domain of the function \(\operatorname{cosec}^{-1}\left(\frac{1+\mathrm{x}}{\mathrm{x}}\right)\) is :
- A \(\left(-1,-\frac{1}{2}\right] \cup(0, \infty)\)
- B \(\left[-\frac{1}{2}, 0\right) \cup[1, \infty)\)
- C \(\left(-\frac{1}{2}, \infty\right)-\{0\}\)
- D \(\left[-\frac{1}{2}, \infty\right)-\{0\}\)
Answer & Solution
Correct Answer
(D) \(\left[-\frac{1}{2}, \infty\right)-\{0\}\)
Step-by-step Solution
Detailed explanation
\(\frac{1+x}{x} \in(-\infty,-1] \cup[1, \infty)\) \(\frac{1}{x} \in(-\infty,-2] \cup[0, \infty)\) \(x \in\left[-\frac{1}{2}, 0\right) \cup(0, \infty)\) \(x \in\left[-\frac{1}{2}, \infty\right)-\{0\}\)
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
- The line of shortest distance between the lines \(\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}\) and \(\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1}\) makes an angle of \(\cos ^{-1}\left(\sqrt{\frac{2}{27}}\right)\) with the plane \(P: a x-y-\) \(z=0\), \((a>0)\). If the image of the point \((1,1,-5)\) in the plane \(P\) is \((\alpha, \beta, \gamma)\), then \(\alpha+\beta-\gamma\) is equal to \(........\)JEE Mains 2022 Hard
- If \(A\) and \(B\) are two events such that \(P(A \cap B)=0.1\), and \(P(A \mid B)\) and \(P(B \mid A)\) are the roots of the equation \(12 x^2-7 x+1=0\), then the value of \(\frac{\mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}})}{\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})}\) is :JEE Mains 2025 Hard
- Let the area of the triangle formed by the lines \(x+2=y-1=z, \frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}\) and \(\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}\) be \(A\). Then \(A^2\) is equal to ________JEE Mains 2025 Medium
- A boy needs to select five courses from \(12\) available courses, out of which \(5\) courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses isJEE Mains 2023 Medium
- The mean and variance of \(8\) observations are \(10\) and \(13.5,\) respectively. If \(6\) of these observations are \(5,7,10,12,14,15,\) then the absolute difference of the remaining two observations isJEE Mains 2020 Hard
- If \(0 \le x < 2\pi \) , then the number of real values of \(x,\) which satisfy the equation \(\cos x + \cos 2x + \cos 3x + \cos 4x = 0\) is . . .JEE Mains 2016 Hard
More PYQs from JEE Mains
- Let \(P_{1}\) be a parabola with vertex \((3,2)\) and focus \((4,4)\) and \(P _{2}\) be its mirror image with respect to the line \(x +2 y =6\). Then the directrix of \(P _{2}\) is \(x +2 y\) =JEE Mains 2022 Hard
- Let the direction cosines of two lines satisfy the equations: \( 4l+m-n=0 \) and \( 2mn+10nl+3lm=0 \). Then the cosine of the acute angle between these lines is:JEE Mains 2026 Easy
- The sum of all the real values of \(x\) satisfying the equation \({2^{\left( {x - 1} \right)\left( {{x^2} + 5x - 50} \right)}} = 1\) isJEE Mains 2017 Hard
- For three positive integers \(p , q , r , x ^{ pq p ^2}= y ^{ qr }= z ^{ p ^2 r }\) and \(r=p q+1\) such that \(3,3 \log _y x, 3 \log _z y, 7 \log _x z\) are in A.P. with common difference \(\frac{1}{2}\). Then \(r - p - q\) is equal toJEE Mains 2023 Hard
- Let \((2,3)\) be the largest open interval in which the function \(f(x)=2 \log _{\mathrm{e}}(x-2)-x^2+a x+1\) is strictly increasing and (b, c) be the largest open interval, in which the function \(\mathrm{g}(x)=(x-1)^3(x+2-\mathrm{a})^2\) is strictly decreasing. Then \(100(a+b-c)\) is equal to :JEE Mains 2025 Medium
- Consider the differential equation \(\frac{{dy}}{{dx}} = \frac{{{y^3}}}{{2(x{y^2} - {x^2})}}\) Statement \(-1:\) The substitution \(z = y^2\) transforms the above equation into a first order homogenous differential equation. Statement \(-2:\) The solution of this differential equation is \({y^2}{e^{ - {y^2}/x}} = C\).JEE Mains 2013 Hard