12th Class Mathematics Inverse Trigonometric Functions Question Bank

done Assertion And Reason (MCQs) - Inverse Trigonometric Functions Total Questions - 10

• question_answer1)

  Directions : (1 - 10)

  The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options.

  Assertion [A]: The principal value of \[{{\sin }^{-1}}\left( -\frac{1}{2} \right)\] is \[-\frac{\pi }{6}\].

  Reason [R]: The principal value of \[{{\sin }^{-1}}\left( -x \right)\] is \[-{{\sin }^{-1}}x\] if \[x\in \left[ -1,\,\,1 \right]\]

   
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
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• question_answer2)

  Assertion [A]: The principal value of \[{{\cos }^{-1}}\left( \frac{-1}{\sqrt{2}} \right)\] is \[-\frac{\pi }{4}\]

  Reason [R]: The principal value of \[{{\cos }^{-1}}\left( -x \right)\] is \[\pi -{{\cos }^{-1}}x\] if \[x\in \left[ -1,\,\,1 \right]\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
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• question_answer3)

  Assertion [A]: The principal value, of \[{{\tan }^{-1}}\left( \tan \frac{3\pi }{4} \right)\] is \[-\frac{\pi }{4}\].

  Reason [R]: The range of \[{{\tan }^{-1}}x\] is \[\left[ \frac{-\pi }{2},\,\frac{\pi }{2} \right]\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
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• question_answer4)

  Assertion [A]: The principal value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)=\frac{\pi }{3}\]

  Reason [R]: The range of \[{{\cos }^{-1}}x\] is \[\left[ 0,\,\,\pi  \right]\]

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false.                                                       done clear
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• question_answer5)

  Assertion [A]: \[{{\tan }^{-1}}\left( -x \right)=-{{\tan }^{-1}}x,\,x\in R\]

  Reason [R]: \[{{\sec }^{-1}}\left( -x \right)=\pi -{{\sec }^{-1}}x,\,x\in R\]

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer6)

  Assertion [A]: The value of \[\cos \left( {{\sec }^{-1}}\left( \frac{5}{3} \right) \right)\] is, \[\frac{3}{5}\].

  Reason [R]: Value of \[{{\sec }^{-1}}x\] is \[{{\cos }^{-1}}\frac{1}{x}\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer7)

  Assertion [A]: The value of \[{{\tan }^{-1}}\sqrt{3}-{{\sec }^{-1}}(-2)\] is \[\frac{\pi }{3}\].

  Reason [R]: If \[{{\cos }^{-1}}x=y\] then principal value of y is \[0\,\le \,\,y\,\,\le \,\,\pi \].

   
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer8)

  Assertion [A]: The principal value of \[{{\cos }^{-1}}\left( \cos \frac{13\pi }{6} \right)\]is \[\frac{\pi }{6}\].

  Reason [R]: The principal value of \[{{\tan }^{-1}}\left( \tan \,\frac{5\pi }{6} \right)\] is \[\frac{5\pi }{6}\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer9)

  Assertion [A]: The value of \[\sin \left( {{\tan }^{-1}}\frac{a}{b} \right)\] is \[\frac{a}{\sqrt{{{b}^{2}}-{{a}^{2}}}}\].

  Reason [R]: The value of \[\tan \left( {{\cot }^{-1}}\frac{a}{b} \right)\] is \[\frac{b}{a}\].

   
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer10)

  Assertion [A]: The value of \[{{\sin }^{-1}}\left( \cos \left( {{\sin }^{-1}}\frac{1}{2} \right) \right)\] is \[\frac{\pi }{3}\].

  Reason [R]: The value of \[{{\sin }^{-1}}\left( \cos \,x \right)\] is x.

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
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