Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Inverse Trigonometric Functions question

2018 · Shift 2 · Q19
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Inverse Trigonometric Functions
  5. /2018 · Shift 2 · Q19

Inverse Trigonometric Functions question

2018 · Shift 2 · Q19

JEE AdvancedMathematicsInverse Trigonometric FunctionsMultiple correct+4 / −2
For any positive integer n, define fn:(0,∞)→R{f_n}:(0,\infty ) \to Rfn​:(0,∞)→R as fn=∑j=1ntan⁡−1(11+(x+j)(x+j−1)){f_n} = \sum\limits_{j = 1}^n {{{\tan }^{ - 1}}} \left( {{1 \over {1 + (x + j)(x + j - 1)}}} \right)fn​=j=1∑n​tan−1(1+(x+j)(x+j−1)1​) for all x ∈\in∈(0, ∞\infty∞). (Here, the inverse trigonometric function tan −-− 1 x assumes values in (−π2,π2)\left( { - {\pi \over 2},{\pi \over 2}} \right)(−2π​,2π​)). Then, which of the following statement(s) is (are) TRUE?
  1. A
    ∑j=15tan⁡2(fj(0))=55\sum\limits_{j = 1}^5 {{{\tan }^2}({f_j}(0)) = 55}j=1∑5​tan2(fj​(0))=55
  2. B
    ∑j=110(1+fj′(0))sec⁡2(fj(0))=10\sum\limits_{j = 1}^{10} {(1 + f{'_j}(0)){{\sec }^2}({f_j}(0)) = 10}j=1∑10​(1+fj′​(0))sec2(fj​(0))=10
  3. C
    For any fixed positive integer n, lim⁡x→∞tan⁡(fn(x))=1n\mathop {\lim }\limits_{x \to \infty } \tan ({f_n}(x)) = {1 \over n}x→∞lim​tan(fn​(x))=n1​
  4. D
    For any fixed positive integer n, lim⁡x→∞sec⁡2(fn(x))=1\mathop {\lim }\limits_{x \to \infty } {\sec ^2}({f_n}(x)) = 1x→∞lim​sec2(fn​(x))=1
PreviousNext

More from Inverse Trigonometric Functions

  • If α =3sin−1(116​) and β=3cos−1(94​), where the inverse trigonimetric functions take only the principal values, then the correct options(s) is (are)2015 · Multiple correct
  • Let f : [0, 4 π] →[0, π] be defined by f(x) = cos − 1 (cos x). The number of points x ∈ [0, 4 π] satisfying the equation f(x)=1010−x​ is2014 · Numerical
  • Match List I with List II and select the correct answer using the code given below the lists: List-I (P.) Let y(x)=cos(3cos−1x),x∈[−1,1],xe±23​​.…2014 · MCQ
  • The value of cot(n=1∑23​cot−1(1+k=1∑n​2k)) is2013 · MCQ
  • Match List I with List II and select the correct answer using the code given below the lists: List IP. (y21​(cot(sin−1y)+tan(sin−1y)cos(tan−1y)+ysin(tan−1y)​)2+y4)1/2…2013 · MCQ
  • If 0<x<1, then 1+x2​[{xcos(cot−1x)+sin(cot−1x)}2−1]1/2=2008 · MCQ
  • Let F(x) be an indefinite integral of sin2x. Statement 1 : The function F(x) satisfies F(x+π) = F(x) for all real x. Statement 2 : sin2(x+π)=sin2x for all real x.2007 · MCQ
  • The total number of real solutions of the equation θ=tan−1(2tanθ)−21​sin−1(9+tan2θ6tanθ​) is (Here, the inverse trigonometric functions sin−1x and $\tan^{-1}…2025 · MCQ