CBSE Class 12 Mathematics Question Paper 2012 (Set 65-2-1)

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.

  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.

  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.

  Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
  Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

  • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
    
  • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
    
  • Assertion (A) is true and Reason (R) is false.
    
  • Assertion (A) is false and Reason (R) is true.
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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.

  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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