NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.4

CBSE CLASS XII Related Questions

  • 1.

    A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length. 


      • 2.
        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 \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


          • 3.
            If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


              • 4.

                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 :


                  • 5.
                    Find:

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


                      • 6.
                        Find:

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

                          • \(-\frac{\pi}{2}\)
                          • \(-\frac{\pi}{4}\)
                          • \(\frac{\pi}{4}\)
                          • \(\frac{\pi}{2}\)
                        CBSE CLASS XII Previous Year Papers

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