12th Class Mathematics Applications of Derivatives Question Bank

done Assertion And Reason (MCQs) - Applications of Derivatives Total Questions - 11

• question_answer1)

  Directions: (1 - 11) 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 function \[x+\frac{5}{x},\,\,x\ne 0\] is strictly decreasing

  Reason [R]: For strictly decreasing function\[~f'\left( x \right)<0.\]

  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
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• question_answer2)

  Assertion [A]: The function \[f(x)={{x}^{3}}-12x\] is strictly  increasing in\[\left( -\infty ,-2 \right)\cup \left( 2,\text{ }\infty  \right)\].

  Reason [R]: For strictly increasing function \[f'\left( x \right)>0\].

  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
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• question_answer3)

  Assertion [A]: The function \[f\left( x \right)~={{x}^{2}}+2x+1\] is strictly increasing on (1, 2).

  Reason [R]: The least value of x is 1 in interval (1, 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
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• question_answer4)

  Assertion [A]: The intervals is which \[f\left( x \right)\text{ }=\text{ }log\text{ }sinx\], \[0\le \text{ }x\text{ }\le \pi \] is increasing is \[\left( 0,\frac{\pi }{2} \right)\].

  Reason [R]: The function tan x is + ve in first quadrant

   
  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]: The intervals in which\[f(x)=log\,\,cosx,\,\,0\le x\,\,\pi \] is decreasing is \[\left( 0,\frac{\pi }{2} \right)\].

  Reason [R]: The function \[\tan \,x\] is +ve in 3rd quadrant.

  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]: Tangent to the curve \[y={{x}^{2}}-7x+12\] at the points (3, 0) and (4, 0) are at right angles.

  Reason [R]: For perpendicular lines, product of slopes of lines is -1.

  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 tangent to the curve \[y={{x}^{3}}-{{x}^{2}}-x+2\] at (1, 1) is parallel to the X-axis.

  Reason [R]: The slope of the tangent to the above curve at (1, 1) is zero.

   
  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_answer8)

  Assertion [A]: The tangent to curve \[y=4{{x}^{3}}-3x+5\] at \[x\text{ }=\text{ }1\] is perpendicular to the line \[x+9y+3=0.\]

  Reason [R]: Slope of line \[ax+by+c=0\] is

  \[-\frac{Coeff\,.\,of\,x}{Coeff\,.\,of\,y}\]

  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 local maximum value of

  \[f\left( x \right)={{x}^{3}}-6{{x}^{2}}+9x+15\] at \[x=1\]is 19.

  Reason [R]: For local maximum, \[f''\left( x \right)<0.\]

  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
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• question_answer10)

  Assertion [A]: The point of local maxima of function \[f\left( x \right)={{x}^{3}}-3x+3\text{ }\] is \[x=-1\].

  Reason [R]: For local minima, \[f''\left( x \right)\text{ }>\text{ }0.\]

  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_answer11)

  Assertion [A]: Let

  \[f:\text{ }R\to R,\text{ }f\left( x \right)={{x}^{3}}+{{x}^{2}}\text{+3x+ }sin\text{ }x,\text{ f(x)}\]is one-one.

  Reason [R]: f(x) is decreasing function.

  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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