NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.3

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Jasmine Grover

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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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Class 12 Chapter 6 Applications of Derivatives Topics:

CBSE Class 12 Mathematics Study Guides:

CBSE CLASS XII Related Questions

  • 1.
    For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

      • local maximum value is 2
      • local minimum value is \( -2 \)
      • local maximum value is \( -2 \)
      • local minimum value \( < \) local maximum value

    • 2.
      Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]


        • 3.
          Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
          Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

            • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
            • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
            • Assertion (A) is true and Reason (R) is false.
            • Assertion (A) is false and Reason (R) is true.

          • 4.
            A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.


              • 5.
                The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

                  • \( e^{-3} \)
                  • \( -1 \)
                  • \( 1 \)
                  • \( -e^3 \)

                • 6.

                  If \[ B(\operatorname{adj} B)= \begin{bmatrix} \frac{1}{3} & 0 & 0\\ 0 & \frac{1}{3} & 0\\ 0 & 0 & \frac{1}{3} \end{bmatrix}, \] then the value of \[ \det(B^{-1}) \] is: 

                    • \(\frac{1}{3}\)
                    • \(\frac{1}{9}\)
                    • \(3\)
                    • \(9\)
                  CBSE CLASS XII Previous Year Papers

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