CBSE Class 12 Mathematics Question Paper 2007

CBSE CLASS XII Questions

• 1.

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

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• 2.

  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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• 3.

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

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• 4.

  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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• 5.

  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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• 6.

  If \[ B(\operatorname{adj} B)= \begin{bmatrix} \frac{1}{3} & 0 & 0\\ 0 & \frac{1}{3} & 0\\ 0 & 0 & \frac{1}{3} \end{bmatrix}, \] then the value of \[ \det(B^{-1}) \] is: 

  • \(\frac{1}{3}\)
    
  • \(\frac{1}{9}\)
    
  • \(3\)
    
  • \(9\)
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