NCERT Solutions for Class 11 Maths Chapter 7 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.
    Which of the following equations is NOT a Linear Differential Equation?

      • \((1 + x^2) \, dy + 2xy \, dx = \cot x \, dx\)
      • \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\)
      • \(x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0\)
      • \(y \, dx - (x + 3y^2) \, dy = 0\)

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


        • 3.
          Find:

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

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

          • 4.
            Find:

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


              • 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.
                    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 \(k\).

                      • \(0\)
                      • \(-2\)
                      • \(-1\)
                      • \(2\)
                    CBSE CLASS XII Previous Year Papers

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