NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.1

CBSE CLASS XII Related Questions

  • 1.
    Find:

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

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

    • 2.
      Find:

      If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

        • \(0\)
        • \(-2\)
        • \(-1\)
        • \(2\)

      • 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.
            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 \(q\).

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

            • 5.

              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 :


                • 6.
                  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 \( x = 2 \).

                    CBSE CLASS XII Previous Year Papers

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