NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.2

CBSE CLASS XII Related Questions

  • 1.

    For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :

    Minimize \(Z = 18x + 10y\)

    subject to constraints

    \[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]


      • 2.

        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

        \[ 2x + y \geq 8 \]

        \[ x + 2y \geq 10 \]

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


          • 3.

            Evaluate :

            \[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]


              • 4.

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


                  • 5.

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

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


                      • 6.

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

                          • \( \log \cos 2x + C \)
                          • \( \sec^{2} 2x + C \)
                          • \( e^{x}\tan x + C \)
                          • \( e^{x}\cot x + C \)
                        CBSE CLASS XII Previous Year Papers

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