NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.2

CBSE CLASS XII Related Questions

  • 1.
    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 \( \cos^{-1}(x^2) \).


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


          • 3.
            Find:

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


              • 4.

                At a birthday party, children are being served orange juice in conical cups, as shown in the figure. 


                Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
                On the basis of the above information, answer the following questions :


                  • 5.
                    Find:

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

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

                    • 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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