NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.3

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Class 11 Maths NCERT Solutions Chapter 9 Sequence and Series Exercise 9.3 is based on the following concepts:

  • Relationship Between A.M. and G.M.

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CBSE CLASS XII Related Questions

  • 1.

    \( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :

      • \( \log \cos 2x + C \)
      • \( \sec^{2} 2x + C \)
      • \( e^{x}\tan x + C \)
      • \( e^{x}\cot x + C \)

    • 2.

      For events A and B, if \(P(B)=\frac{3}{5}\), \(P(A/B)=\frac{1}{2}\) and \(P(A\cup B)=\frac{4}{5}\), then \(P(A)\) is :

        • \(\frac{1}{2}\)
        • \(\frac{3}{5}\)
        • \(\frac{1}{5}\)
        • \(\frac{3}{10}\)

      • 3.

        Solve the differential equation \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \).


          • 4.

            If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that

            \[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]


              • 5.

                For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.

                Minimize \(Z = 5x + 7y\)

                subject to constraints

                \[ 2x + y \geq 8 \]

                \[ x + 2y \geq 10 \]

                \[ x,\ y \geq 0. \]


                  • 6.

                    Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

                      CBSE CLASS XII Previous Year Papers

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