NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

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CBSE CLASS XII Related 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. 


      • 2.
        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.


          • 3.

            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 \[ 3q(x)-\pi. \] 


              • 4.

                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: 

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

                • 5.
                  The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

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

                  • 6.
                    Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

                      CBSE CLASS XII Previous Year Papers

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