CBSE Class 12 Mathematics Question Paper 2004

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.

  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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• 4.

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

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• 5.

  Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not. 

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• 6.

  Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]

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