NCERT Solutions for Class 11 Maths Chapter 16 Miscellaneous Exercises

CBSE CLASS XII Related Questions

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


      • 2.
        Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).


          • 3.
            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 \(k\).

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

            • 4.
              Find:

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

                • \(-\frac{\pi}{2}\)
                • \(-\frac{\pi}{4}\)
                • \(\frac{\pi}{4}\)
                • \(\frac{\pi}{2}\)

              • 5.
                Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


                  • 6.

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

                      CBSE CLASS XII Previous Year Papers

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