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:

    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 \(k\).

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

    • 2.
      If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


        • 3.
          Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]


            • 4.
              Which of the following equations is NOT a Linear Differential Equation?

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

              • 5.

                An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.  
                Based on the above information, answer the following questions :


                  • 6.

                    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 \(A'\).

                      • \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
                      • \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
                      • \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
                      • \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)
                    CBSE CLASS XII Previous Year Papers

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