NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.2

CBSE CLASS XII Related Questions

  • 1.
    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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]


      • 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.

            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 \(x=3\). 
             


              • 4.
                Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


                  • 5.
                    Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]


                      • 6.
                        A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.

                          CBSE CLASS XII Previous Year Papers

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