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.
      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 \( x = 2 \).


        • 3.
          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 \(k\).

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

          • 4.

            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 :


              • 5.
                Find:

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


                  • 6.
                    If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

                      CBSE CLASS XII Previous Year Papers

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