NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.4

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Class 11 Maths NCERT Solutions Chapter 9 Sequence and Series Exercise 9.4 is based on Sum to n Terms of Special Series. 

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CBSE CLASS XII Related Questions

  • 1.
    Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).


      • 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 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.


              • 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.

                    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 \(x=3\). 
                     


                      • 6.

                        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 \(P,O,Q\). 
                         

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