NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.3

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.3 is provided in this article. Chapter 6 Exercise 6.3 includes questions that deal with concepts of tangents and normals. The exercise includes a total of 27 questions.

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CBSE CLASS XII Related Questions

  • 1.
    Find:

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


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


          • 3.
            Which of the following equations is NOT a Linear Differential Equation?

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

            • 4.
              If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


                • 5.

                  Evaluate:
                  \[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]


                    • 6.
                      Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

                        CBSE CLASS XII Previous Year Papers

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