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

Trigonometric Functions and Equations question

2022 · Shift 1 · Q33
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Trigonometric Functions and Equations
  5. /2022 · Shift 1 · Q33

Trigonometric Functions and Equations question

2022 · Shift 1 · Q33

JEE AdvancedMathematicsTrigonometric Functions and EquationsMCQ+3 / −1

Consider the following lists :

List-I List-II
(I) {x∈[−2π3,2π3]:cos⁡x+sin⁡x=1}\left\{x \in\left[-\frac{2 \pi}{3}, \frac{2 \pi}{3}\right]: \cos x+\sin x=1\right\}{x∈[−32π​,32π​]:cosx+sinx=1} (P) has two elements
(II) {x∈[−5π18,5π18]:3tan⁡3x=1}\left\{x \in\left[-\frac{5 \pi}{18}, \frac{5 \pi}{18}\right]: \sqrt{3} \tan 3 x=1\right\}{x∈[−185π​,185π​]:3​tan3x=1} (Q) has three elements
(III) {x∈[−6π5,6π5]:2cos⁡(2x)=3}\left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\}{x∈[−56π​,56π​]:2cos(2x)=3​} (R) has four elements
(IV) {x∈[−7π4,7π4]:sin⁡x−cos⁡x=1}\left\{x \in\left[-\frac{7 \pi}{4}, \frac{7 \pi}{4}\right]: \sin x-\cos x=1\right\}{x∈[−47π​,47π​]:sinx−cosx=1} (S) has five elements
(T) has six elements

The correct option is:

  1. A
    (I) →(P)\rightarrow(\mathrm{P})→(P); (II) →(S)\rightarrow(\mathrm{S})→(S); (III) →(P)\rightarrow(\mathrm{P})→(P); (IV) →(S)\rightarrow(\mathrm{S})→(S)
  2. B
    (I) →\rightarrow→(P); (II) →\rightarrow→(P); (III) →\rightarrow→(T); (IV) →\rightarrow→ (R)
  3. C
    (I) →\rightarrow→(Q); (II) →(P)\rightarrow(\mathrm{P})→(P); (III) →\rightarrow→(T); (IV) →\rightarrow→ (S)
  4. D
    (I) →(Q)\rightarrow(\mathrm{Q})→(Q); (II) →(S);\rightarrow(\mathrm{S}) ;→(S);(III) →(P)\rightarrow(\mathrm{P})→(P); (IV) →(R)\rightarrow(\mathrm{R})→(R)
PreviousNext

More from Trigonometric Functions and Equations

  • Let α and β be real numbers such that −4π​<β<0<α<4π​. If sin(α+β)=31​ and cos(α−β)=32​, then the greatest integer less than or equal to (cosβsinα​+sinαcosβ​+sinβcosα​+cosαsinβ​)2…2022 · Numerical
  • Let PQRS be a quadrilateral in a plane, where QR=1,∠PQR=∠QRS=70∘,∠PQS=15∘ and ∠PRS=40∘. If ∠RPS=θ∘,PQ=α and PS=β, then the interval(s)…2022 · Multiple correct
  • For non-negative integers n, let f(n)=k=0∑n​sin2(n+2k+1​π)k=0∑n​sin(n+2k+1​π)sin(n+2k+2​π)​…2019 · Multiple correct
  • Let f(x) = sin(π cos x) and g(x) = cos(2 π sin x) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order: X = {x : f(x) = 0}, Y = {x : f'(x) = 0} Z = {x : g(x) = 0}, W =… Includes diagram2019 · MCQ
  • Let f(x) = sin(π cos x) and g(x) = cos(2 π sin x) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order : X = {x : f(x) = 0}, Y = {x : f'(x) = 0} Z = {x : g(x) = 0}, W =… Includes diagram2019 · MCQ
  • In a Δ PQR = 30 ∘ and the sides PQ and QR have lengths 10 3​ and 10, respectively. Then, which of the following statement(s) is(are) TRUE?2018 · Multiple correct
  • Let f : R → R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x) f'(y) + f'(x) f(y) for all x, y ∈ R. Then, the value of loge(f(4)) is ...........2018 · Numerical
  • Let α and β be non zero real numbers such that 2(cosβ−cosα)+cosαcosβ=1. Then which of the following is/are true?2017 · Multiple correct