NCERT Solutions for Class 12 Chapter 13 Probability Exercise 13.4

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Class 12 Maths NCERT Solutions Chapter 13 Probability Exercise 13.4 is based on Random Variables and its Probability Distributions. Key topics covered under these concepts are:

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CBSE CLASS XII Related Questions

  • 1.
    Find:

    The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

      • \(-\frac{\pi}{2}\)
      • \(-\frac{\pi}{4}\)
      • \(\frac{\pi}{4}\)
      • \(\frac{\pi}{2}\)

    • 2.
      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 \( x = 2 \).


        • 3.

          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 \(A'\).

            • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
            • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
            • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
            • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)

          • 4.

            At a birthday party, children are being served orange juice in conical cups, as shown in the figure. 


            Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
            On the basis of the above information, answer the following questions :


              • 5.

                Evaluate:
                \[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]


                  • 6.
                    Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

                      CBSE CLASS XII Previous Year Papers

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