NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercises

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercises are based on following concepts:

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CBSE CLASS XII Related Questions

  • 1.
    Find:

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


      • 2.
        If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


          • 3.
            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 \(q\).

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

            • 4.
              A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

                • Reflexive only
                • Reflexive and Transitive
                • Symmetric and Transitive
                • Symmetric only

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

                    CBSE CLASS XII Previous Year Papers

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