JEE Main & Advanced Mathematics Trigonometric Equations Question Bank

done Periodic functions Total Questions - 20

• question_answer1)
  Period of \[|\sin 2x|\] is [MP PET 1989]
  A)
  \[\frac{\pi }{4}\] done clear
  B)
  \[\frac{\pi }{2}\] done clear
  C)
  \[\pi \] done clear
  D)
  \[2\pi \] done clear
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• question_answer2)
  Period of \[\sin \theta \cos \theta \]is
  A)
  \[\frac{\pi }{2}\] done clear
  B)
  \[\pi \] done clear
  C)
  \[2\pi \] done clear
  D)
  None of these done clear
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• question_answer3)
  Period of \[\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }\]is
  A)
  \[2\pi \] done clear
  B)
  \[\pi \] done clear
  C)
  \[\frac{2\pi }{3}\] done clear
  D)
  \[\frac{\pi }{3}\] done clear
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• question_answer4)
  Period of \[\cos (7x-5)\]is
  A)
  \[\frac{2\pi -5}{7}\] done clear
  B)
  \[2\pi -5\] done clear
  C)
  \[\frac{2\pi }{7}\] done clear
  D)
  \[\frac{\pi }{7}\] done clear
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• question_answer5)
  Period of \[\sin \theta -\sqrt{3}\cos \theta \]is  [MP PET 1990]
  A)
  \[\frac{\pi }{4}\] done clear
  B)
  \[\frac{\pi }{2}\] done clear
  C)
  \[\pi \] done clear
  D)
  \[2\pi \] done clear
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• question_answer6)
  Period of \[\sin \frac{x}{2}-\cos \frac{x}{3}\] is
  A)
  \[2\pi \] done clear
  B)
  \[4\pi \] done clear
  C)
  \[8\pi \] done clear
  D)
  \[12\pi \] done clear
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• question_answer7)
  Period of cot \[3x-\cos (4x+3)\]is
  A)
  \[\frac{\pi }{3}\] done clear
  B)
  \[\frac{\pi }{4}\] done clear
  C)
  \[\pi \] done clear
  D)
  \[2\pi \] done clear
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• question_answer8)
  Period of \[|2\sin 3\theta +4\cos 3\theta |\]is
  A)
  \[\frac{2\pi }{3}\] done clear
  B)
  \[\pi \] done clear
  C)
  \[\frac{\pi }{2}\] done clear
  D)
  \[\frac{\pi }{3}\] done clear
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• question_answer9)
  The period of \[{{\sin }^{4}}x+{{\cos }^{4}}x\]is       [RPET 1997]
  A)
  \[\pi /2\] done clear
  B)
  \[\pi \] done clear
  C)
  \[2\pi \] done clear
  D)
  \[3\pi /2\] done clear
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• question_answer10)
  The period of the function \[f(\theta )=\sin \frac{\theta }{3}+\cos \frac{\theta }{2}\]is [EAMCET 2001]
  A)
  \[3\pi \] done clear
  B)
  \[6\pi \] done clear
  C)
  \[9\pi \] done clear
  D)
  \[12\pi \] done clear
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• question_answer11)
  If the period of the function \[f(x)=\sin \left( \frac{x}{n} \right)\]is \[4\pi \], then n is equal to [Pb. CET 2000]
  A)
  1 done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  2 done clear
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• question_answer12)
  Period of \[{{\sin }^{2}}x\]is [UPSEAT 2002; AIEEE 2002]
  A)
  \[\pi \] done clear
  B)
  \[2\pi \] done clear
  C)
  \[\frac{\pi }{2}\] done clear
  D)
  None of these\[\] done clear
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• question_answer13)
  The period of the function \[y=\sin 2x\]is  [Kerala (Engg.) 2002]
  A)
  \[2\pi \] done clear
  B)
  \[\pi \] done clear
  C)
  \[\pi /2\] done clear
  D)
  \[4\pi \] done clear
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• question_answer14)
  Which of the following functions has period \[2\pi \]  [Pb. CET 2004]
  A)
  \[y=\sin \left( 2\pi t+\frac{\pi }{3} \right)+\]\[2\sin \left( 3\pi t+\frac{\pi }{4} \right)+3\sin 5\pi t\] done clear
  B)
  \[y=\sin \frac{\pi }{3}t+\sin \frac{\pi }{4}t\] done clear
  C)
  \[y=\sin t+\cos 2t\] done clear
  D)
  None of these done clear
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• question_answer15)
  The period of the function \[\sin \left( \frac{2x}{3} \right)+\sin \left( \frac{3x}{2} \right)\]is  [Orissa JEE 2004]
  A)
  \[2\pi \] done clear
  B)
  \[10\pi \] done clear
  C)
  \[6\pi \] done clear
  D)
  \[12\pi \] done clear
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• question_answer16)
  Let \[f(x)=\cos px+\sin x\] be periodic, then p must be
  A)
  Rational done clear
  B)
  Irrational done clear
  C)
  Positive real number done clear
  D)
  None of these done clear
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• question_answer17)
  The period of the function \[\sin \left( \frac{\pi x}{2} \right)+\cos \left( \frac{\pi x}{2} \right)\] is  [EAMCET 1990]
  A)
  4 done clear
  B)
  6 done clear
  C)
  12 done clear
  D)
  24 done clear
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• question_answer18)
  The function \[f(x)=\sin \frac{\pi x}{2}+2\cos \frac{\pi x}{3}-\tan \frac{\pi x}{4}\] is period with period  [EAMCET 1992; RPET 2001]
  A)
  6 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  12 done clear
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• question_answer19)
  The period of the function |sinp x| is [AMU 1999]
  A)
  \[{{\pi }^{2}}\] done clear
  B)
  \[2\pi \] done clear
  C)
  2 done clear
  D)
  1 done clear
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• question_answer20)
  The period of \[f(x)=\sin \left( \frac{\pi x}{n-1} \right)+\cos \,\left( \frac{\pi x}{n} \right)\,\,,\,n\in Z\], \[n>2\] is [Orissa JEE 2002]
  A)
  \[2\pi n(n-1)\] done clear
  B)
  \[4n\,(n-1)\] done clear
  C)
  \[2n\,(n-1)\] done clear
  D)
  None of these done clear
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