NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.

    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 :


      • 2.
        Find:

        If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

          • \(0\)
          • \(-2\)
          • \(-1\)
          • \(2\)

        • 3.
          Which of the following equations is NOT a Linear Differential Equation?

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

          • 4.
            If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


              • 5.
                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 \(q\).

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

                • 6.
                  Find:

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

                    • \(-\frac{\pi}{2}\)
                    • \(-\frac{\pi}{4}\)
                    • \(\frac{\pi}{4}\)
                    • \(\frac{\pi}{2}\)
                  CBSE CLASS XII Previous Year Papers

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