CBSE Class 12 Mathematics Question Paper 2014

CBSE CLASS XII Questions

• 1.

  If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]

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• 2.

  Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \] 

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• 3.

  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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• 4.

  For a square matrix \(A\), \[ (3A)^{-1}= \]

  • \( 3A^{-1} \)
    
  • \( 9A^{-1} \)
    
  • \( \frac{1}{3} A^{-1} \)
    
  • \( \frac{1}{9} A^{-1} \)
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• 5.

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

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

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

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