NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

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CBSE CLASS XII Related Questions

  • 1.

    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 :


      • 2.
        Find:

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

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

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


            • 4.
              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 \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


                • 5.
                  A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

                    • Reflexive only
                    • Reflexive and Transitive
                    • Symmetric and Transitive
                    • Symmetric only

                  • 6.
                    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 \(q\).

                      • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
                      • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
                      • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
                      • \(p = 0, \, q = 0\)
                    CBSE CLASS XII Previous Year Papers

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