NCERT Solutions for Class 12 Maths Chapter 13 Probability Miscellaneous Exercises

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Class 12 Maths NCERT Solutions Chapter 13 Probability Miscellaneous Exercises cover all important concepts of Chapter 13. 

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CBSE CLASS XII Related Questions

  • 1.
    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:
    \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]


      • 2.

        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. 


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


              • 4.

                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 \(x=3\). 
                 


                  • 5.
                    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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]


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

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