NCERT Solutions Class 11 Maths Chapter 1 Sets Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.
    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 \(q\).

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

    • 2.

      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 :


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


            • 4.

              Evaluate:
              \[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]


                • 5.
                  Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


                    • 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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