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.
    Solve the following linear programming problem graphically: Maximise \( Z = x + 2y \) Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]


      • 2.
        The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:


          • 3.
            Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?

              • $f$ has a minimum value at $x = 0$
              • $f$ has no maximum value in $\mathbb{R}$
              • $f$ is continuous at $x = 0$
              • $f$ is differentiable at $x = 0$

            • 4.

              A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
              A person buys a smartphone from this shop

              (i) Find the probability that it was defective.


                • 5.
                  Let the polished side of the mirror be along the line \[ \frac{x}{1} = \frac{1 - y}{2} = \frac{2z - 4}{6}. \] A point \( P(1, 6, 3) \), some distance away from the mirror, has its image formed behind the mirror. Find the coordinates of the image point and the distance between the point \( P \) and its image.


                    • 6.
                      If $f : \mathbb{N} \rightarrow \mathbb{W}$ is defined as \[ f(n) = \begin{cases} \frac{n}{2}, & \text{if } n \text{ is even} \\ 0, & \text{if } n \text{ is odd} \end{cases} \] then $f$ is :

                        • injective only
                        • surjective only
                        • a bijection
                        • neither surjective nor injective
                      CBSE CLASS XII Previous Year Papers

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