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

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Miscellaneous Exercise is provided in this article. Chapter 6 Miscellaneous Exercise Solutions covers the concepts of rate of change of quantities, increasing and decreasing functions, maxima and minima, and approximations.

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Check out the Class 12 Maths NCERT solutions chapter 6 Applications of Derivatives Miscellaneous Exercise Solutions

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Class 12 Chapter 6 Applications of Derivatives Topics:

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CBSE CLASS XII Related Questions

  • 1.

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


      • 2.
        Which of the following equations is NOT a Linear Differential Equation?

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

        • 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 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 \(k\).

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

              • 5.
                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 \(q\).

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

                • 6.
                  A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

                    • Reflexive only
                    • Reflexive and Transitive
                    • Symmetric and Transitive
                    • Symmetric only
                  CBSE CLASS XII Previous Year Papers

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