NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

CBSE CLASS XII Related Questions

  • 1.
    Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]


      • 2.
        Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]


          • 3.
            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 \(2p(x)+\frac{\pi}{2}\).


              • 4.

                A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 

                (i) Express \(y\) as a function of \(x\) from the given equation of ellipse. 
                (ii) Integrate the function obtained in (i) with respect to \(x\). 
                (iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration. 
                OR 
                (iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\). 
                 


                  • 5.
                    Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]


                      • 6.
                        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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

                          CBSE CLASS XII Previous Year Papers

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