NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

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

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

        • 3.
          Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


            • 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.

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


                  • 6.
                    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 \( x = 2 \).

                      CBSE CLASS XII Previous Year Papers

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