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.
    Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).


      • 2.
        Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


          • 3.
            If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


              • 4.
                Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).


                  • 5.
                    Find:

                    The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]


                      • 6.

                        Find:
                        Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

                          • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
                          • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
                          • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
                          • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)
                        CBSE CLASS XII Previous Year Papers

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