NCERT Solutions Class 11 Maths Chapter 1 Sets Miscellaneous Exercises

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.

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

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

        • 3.
          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.


            • 4.

              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:


                • 5.
                  If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


                    • 6.

                      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: 

                        • \(\frac{1}{3}\)
                        • \(\frac{1}{9}\)
                        • \(3\)
                        • \(9\)
                      CBSE CLASS XII Previous Year Papers

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