12th Class Mathematics Applications of Derivatives Question Bank

done Assertion And Reason (MCQs) - Derivatives Total Questions - 6

• question_answer1)

  Directions:

  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.

  Let \[f\left( x \right)=2+cos\text{ }x\]for all real x

  Statement-1 : For each real 't', then exist a point C in \[\left[ t,t+\pi  \right]\] such that\[f'\left( C \right)\text{ }=\text{ }0\].

  Statement-2 : \[f\left( t \right)=f\left( t+2\pi  \right)\]for each real t

   
  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]: One root of \[{{x}^{3}}-2{{x}^{2}}-1=0\] and lies between 2 and 3.

  Reason [R]: If \[f\left( x \right)\] is continuous function and f [a], f[b] have opposite signs then at least one or odd number of roots of \[f\left( x \right)=0\] lies between a and b.

  [A] Statement-1 is true, Statement-2 is true; statement-I 2 is a correct explanation of statement-1.

  [B] Statement-1 is true, Statement-2 is true, statement- 2 is not correct explanation of Statement-1

  [C] Statement-1 is true, Statement-2 is false

  [D] Statement-1 is false, Statement-2 is True.

   
  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_answer3)

  Assertion [A]: \[f\left( x \right)\text{ }=\text{ }\left[ x \right]\]is not differentiable

  Reason [R]: \[f\left( x \right)\text{ }=\text{ }\left[ x \right]\]is not continuous at\[x=0\].

  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_answer4)

  Assertion [A]: \[f\left( x \right)=x\text{ }sin\left( \frac{1}{x} \right)\]is differentiable at x = 0.

  Reason [R]: f(x) is continuous at x = 0.

  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_answer5)

  Assertion [A]: If then \[f'\left( x \right)\]does not exist

  Reason [R]: \[f'\left( x \right)\]is not continuous at x =2.

  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]:  \[\frac{d}{dx}\left( {{x}^{{{x}^{x}}}} \right)={{x}^{{{x}^{x}}}}\,.\,x\left( 1+2\,\,\log \,x \right)\]

  Reason [R]: \[{{\left( {{x}^{x}} \right)}^{x}}={{x}^{{{x}^{2}}}}={{e}^{{{x}^{2}}}}={{e}^{{{x}^{2}}}}\log \,x\]

   
  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