NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

CBSE CLASS XII Related Questions

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


      • 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:

                    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 \(k\).

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

                    • 6.
                      Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

                        CBSE CLASS XII Previous Year Papers

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