CBSE Class 12 Mathematics Question Paper 2009

CBSE CLASS XII Questions

• 1.

  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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• 2.

  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.
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• 3.

  The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

  • \( e^{-3} \)
    
  • \( -1 \)
    
  • \( 1 \)
    
  • \( -e^3 \)
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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.

  A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

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• 6.

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

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