NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.4

CBSE CLASS XII Related Questions

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


      • 2.
        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 \(q\).

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

        • 3.
          Find:

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


            • 4.
              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 \( x = 2 \).


                • 5.
                  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 \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).


                    • 6.

                      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 :

                        CBSE CLASS XII Previous Year Papers

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