NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

CBSE CLASS XII Related Questions

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


      • 2.
        Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


          • 3.

            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 \(P,O,Q\). 
             


              • 4.
                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.


                  • 5.
                    Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


                      • 6.

                        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. 

                          CBSE CLASS XII Previous Year Papers

                          Comments


                          No Comments To Show