NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

CBSE CLASS XII Related Questions

  • 1.
    If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


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


          • 3.
            Find:

            If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

              • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
              • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
              • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
              • \(p = 0, \, q = 0\)

            • 4.

              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. 


                • 5.

                  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 :


                    • 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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