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

CBSE CLASS XII Questions

• 1.

  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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• 2.

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

  • \( 3A^{-1} \)
    
  • \( 9A^{-1} \)
    
  • \( \frac{1}{3} A^{-1} \)
    
  • \( \frac{1}{9} A^{-1} \)
  View Solution

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• 3.

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

  View Solution

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• 4.

  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
  View Solution

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• 5.

  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.
  View Solution

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• 6.

  For two vectors \(\vec{a}\) and \(\vec{b}\):  
  
  Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

  • 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, but Reason (R) is false.
    
  • Assertion (A) is false, but Reason (R) is true.
  View Solution