NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.1 Solutions 

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.
        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.
            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 \( x = 2 \).


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


                  • 5.

                    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 :


                      • 6.
                        Find:

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

                          CBSE CLASS XII Previous Year Papers

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