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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CBSE CLASS XII Related Questions

  • 1.

    Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as 

    (i) Find \(f'(x)\) for \(0<x>3\). 
    (ii) Find \(f'(4)\). 
    (iii)(a) Test for continuity of \(f(x)\) at \(x=3\). 
    OR 
    (iii)(b) Test for differentiability of \(f(x)\) at \(x=3\). 
     


      • 2.
        Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]


          • 3.
            Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


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


                  • 5.
                    Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]


                      • 6.
                        If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
                        \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]

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