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.

    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 \(A'\).

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

    • 2.
      Find:

      If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

        • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
        • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
        • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
        • \(p = 0, \, q = 0\)

      • 3.

        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 :


          • 4.

            An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.  
            Based on the above information, answer the following questions :


              • 5.
                Which of the following equations is NOT a Linear Differential Equation?

                  • \((1 + x^2) \, dy + 2xy \, dx = \cot x \, dx\)
                  • \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\)
                  • \(x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0\)
                  • \(y \, dx - (x + 3y^2) \, dy = 0\)

                • 6.
                  Find:

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

                    CBSE CLASS XII Previous Year Papers

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