NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

CBSE CLASS XII Related Questions

  • 1.
    Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


      • 2.
        Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).


          • 3.
            Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


              • 4.
                Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]


                  • 5.

                    A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle. 


                      • 6.

                        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 one such track is given as 

                        (i) Find \(f'(x)\) for \(0<x>3\). 
                        (ii) Find \(f'(4)\). 
                        (iii)(a) Test for continuity of \(f(x)\) at \(x=3\). 
                        OR 
                        (iii)(b) Test for differentiability of \(f(x)\) at \(x=3\). 
                         

                          CBSE CLASS XII Previous Year Papers

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