NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.5

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.5 is given in this article. Chapter 6 Exercise 6.5 includes questions that deal with concepts of maxima and minima and maximum and Minimum Values of a Function in a Closed Interval.

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Class 12 Chapter 6 Applications of Derivatives Topics:

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CBSE CLASS XII Related Questions

  • 1.

    Find:
    Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

      • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
      • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
      • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
      • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)

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


        • 3.
          Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).


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


                • 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.

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

                        CBSE CLASS XII Previous Year Papers

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