NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.

    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 \[ 3q(x)-\pi. \] 


      • 2.
        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

        • 3.

          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.

          • 4.
            The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

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

            • 5.

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

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

              • 6.

                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. 

                  CBSE CLASS XII Previous Year Papers

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