CBSE Class 12 Mathematics Question Paper 2012

CBSE CLASS XII Questions

• 1.

  Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not. 

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• 2.

  The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

  • \( e^{-3} \)
    
  • \( -1 \)
    
  • \( 1 \)
    
  • \( -e^3 \)
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• 3.

  The domain of \[ f(x)=\cos^{-1}(2x-5) \] is: 

  • \([-1, 1]\)
    
  • \([4, 6]\)
    
  • \([-7, -3]\)
    
  • \([2, 3]\)
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• 4.

  Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

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• 5.

  Sports car racing is a form of motorsport which uses sports car prototypes.The competition is held on special tracks designed in various shapes. 

  

  The equation of a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:

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• 6.

  For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

  • local maximum value is 2
    
  • local minimum value is \( -2 \)
    
  • local maximum value is \( -2 \)
    
  • local minimum value \( < \) local maximum value
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