NCERT Solutions for Class 12 Chapter 13 Probability Exercise 13.1

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Class 12 Maths NCERT Solutions Chapter 13 Probability Exercise 13.1 is based on following concepts: Conditional Probability and Properties of conditional probability.

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


          • 3.
            Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


              • 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.
                    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. 

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