NCERT Solutions for Class 11 Maths Chapter 9 Miscellaneous Exercises

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Class 11 Maths NCERT Solutions Chapter 9 Sequence and Series Miscellaneous Exercises is based on the following concepts:

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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.

        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 \(x=3\). 
         


          • 3.
            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 \(P(E/F)\).


              • 4.
                Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]


                  • 5.
                    If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
                    \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]


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

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