Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2010 · Mathematics · Inverse Trigonometric Functions

Statement I : y= ^ -1 (x^ -1 )+1 is an increasing function of x ....

Statement I : y=tan⁡−1y=\tan ^{-1}\left(x^{-1}\right)+1isanincreasingfunctionofis an increasing function ofx.StatementII:. Statement II :\frac{d y}{d x}ispositiveforallvaluesofis positive for all values ofx. Which one of the following is correct in respect of the above statements?

Options

  1. ABoth statements I and II are independently correct and statement II is the correct explanation of statement I
  2. BBoth statements I and II are independently correct but statement II is not the correct explanation of statement I
  3. CStatement I is correct but statement II is false
  4. DStatement I is false but statement II is correct

Correct answer

A. Both statements I and II are independently correct and statement II is the correct explanation of statement I

Step-by-step solution

The correct answer is option (A).
Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

Consider the following in respect of inverse circular functions : I. ^ -1 (-x)=- ^ -1 x… NDA 2026What is [2 ^ -1 (1)/(2)-(π)/(4)] equal to ? NDA 2026If ^ -1 k + ^ -1 (1)/(2) = (π)/(4) , then what is the value of k ? NDA 2025What is the value of [(1)/(2) ^ -1 ( 2 3 )]? NDA 2025Consider the following for the two (02) items that follow: Let y = ^ -1 (x - (4x^3)/(27))… NDA 2025If k is a root of x^2 - 4x + 1 = 0 , then what is ^ -1 k + ^ -1 (1)/(k) equal to? NDA 2025What is ^ -1 9 + cosec^ -1 ( 41 4 ) equal to? NDA 2025What is ^2 ( ^ -1 2)+ ^2 (cosec^ -1 3) equal to? NDA 2024If ^ -1 x= ^ -1 x , then which one of the following is correct? NDA 2024What is 15+ ^2((π)/(4)-2 ^ -1 3) equal to? NDA 2024If 4 ^ -1 x+ ^ -1 x=π , then what is ^ -1 x+4 ^ -1 x equal to? NDA 2024What is ^ -1 ((a)/(b))- ^ -1 ((a-b)/(a+b))equal to? NDA 2024What is 2 ((1)/(2) ^ -1 5 3 )equal to? NDA 2023If ^ -1 p-cosec^ -1 q=0 , where p > 0, q > 0 ; then what is the value of ^ -2 + ^ -2 ? NDA 2023What is 1+ ^2 ( ^ -1 ( 3 17 ))equal to? NDA 2023What is ^ -1 (cosec^ -1 2) equal to? NDA 2022 Full Inverse Trigonometric Functions list Inverse Trigonometric Functions JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs