NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

CBSE CLASS XII Related 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:


      • 2.
        Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


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

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

            • 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.
                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

                • 6.

                  Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not. 

                    CBSE CLASS XII Previous Year Papers

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