Goodmarks

Mathematics · JEE

Important Questions: Inverse trigonometrical functions and their properties for JEE

14+ syllabus-aligned questions available

Quick answer

The most important Inverse trigonometrical functions and their properties questions for JEE cover conceptual traps, standard results, and numerical patterns from Inverse trigonometrical functions and their properties. Goodmarks provides 14+ high-yield MCQs with full solutions.

Focus on what matters most. These important Inverse trigonometrical functions and their properties questions cover high-weightage concepts from Inverse trigonometrical functions and their properties — the topics JEE repeats every year.

Syllabus context

Part of Trigonometry in JEE Main Mathematics.

Free sample questions

Attempt 8 free MCQs for Inverse trigonometrical functions and their properties. Unlock 6+ more with Pro.

Unlock full bank
Q1MathsUnit 14: Trigonometry
Assertion Consider f(x)=sin⁡−1(sec⁡(tan⁡−1x)+\boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. cos⁡−1(cosec⁡(cot⁡−1x)\cos ^{-1}\left(\operatorname{cosec}\left(\cot ^{-1} x\right)\right. Statement-1: Domain of f(x)f(x) is a singleton. Reason Statement-2: Range of the function f(x)\boldsymbol{f}(\boldsymbol{x}) is a singleton.
Q2MathsUnit 14: Trigonometry
The number of real solutions of the equation tan⁡−1x(x+1)+\tan ^{-1} \sqrt{x(x+1)}+ sin⁡−1x2+x+1=π2\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2} is
Q3MathsUnit 14: Trigonometry
If value of x\mathbf{x} which satisfy equation (cot⁡−1x)2−3(cot⁡−1x)+2>0\left(\cot ^{-1} x\right)^{2}-3\left(\cot ^{-1} x\right)+2>0 is x<x< cot⁡a\cot a or x>cot⁡bx>\cot b Find the value of a+ba+b
Q4MathsUnit 14: Trigonometry
Statement I: The equation (sin⁡−1x)3+(cos⁡−1x)3−aπ3=0\left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0 has solution for all a⩾132a \geqslant \frac{1}{32} Statement II : For any xϵR,sin−1x+\boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{s} \boldsymbol{i n}^{-1} \boldsymbol{x}+ cos⁡−1x=π2\cos ^{-1} x=\frac{\pi}{2} and 0≤(sin⁡−1x−π4)2≤0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq 9π216\frac{9 \pi^{2}}{16}
Q5MathsUnit 14: Trigonometry
Assertion (A)(A) If 0<x<π20<x<\frac{\pi}{2} then sin⁡−1(cos⁡x)+cos⁡−1(sin⁡x)=π−2x\sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)=\pi-2 x Reason (R)cos⁡−1x=π2−sin⁡−1x∀x∈(\mathrm{R}) \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x \forall x \in [0,1][\mathbf{0}, \mathbf{1}]
Q6MathsUnit 14: Trigonometry
Assertion fi=12nsin⁡−1xi=nπ∀nϵNf_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi \forall n \epsilon N then ∑i=12nxi=\sum_{i=1}^{2 n} x_{i}= ∑i=12nxi2=∑i=12nxin=2n\sum_{i=1}^{2 n} x_{i}^{2}=\sum_{i=1}^{2 n} x_{i}^{n}=2 n Reason −π2≤sin⁡−1x≤π2∀xϵ[−1,1]-\frac{\pi}{2} \leq \sin ^{-1} x \leq \frac{\pi}{2} \forall x \epsilon[-1,1]
Q7MathsUnit 14: Trigonometry
Find the value of sin⁡−1x+sin⁡−11x+\sin ^{-1} x+\sin ^{-1} \frac{1}{x}+ cos⁡−1x+cos⁡−11x\cos ^{-1} x+\cos ^{-1} \frac{1}{x}
Q8MathsUnit 14: Trigonometry
If [sin⁡−1cos⁡−1sin⁡−1tan⁡−1θ]=1,\left[\sin ^{-1} \cos ^{-1} \sin ^{-1} \tan ^{-1} \theta\right]=1, where [.] denotes the greatest integer function, the θ\theta lies in the interval

Want unlimited Inverse trigonometrical functions and their properties practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started freeView Pro plans

Popular questions in Inverse trigonometrical functions and their properties

Frequently asked questions

What makes a Inverse trigonometrical functions and their properties question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Trigonometry are high-weightage?

Key areas include Inverse trigonometrical functions and their properties. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.

Related topics