NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.
    If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


      • 2.

        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 :


          • 3.
            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 \( x = 2 \).


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


                  • 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:

                      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 \(q\).

                        • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
                        • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
                        • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
                        • \(p = 0, \, q = 0\)
                      CBSE CLASS XII Previous Year Papers

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