NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.2

CBSE CLASS XII Related Questions

  • 1.

    Evaluate :

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


      • 2.

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

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

        • 3.

          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

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


            • 4.

              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 :

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

              • 5.

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


                  • 6.

                    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

                    \[ 2x + y \geq 8 \]

                    \[ x + 2y \geq 10 \]

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

                      CBSE CLASS XII Previous Year Papers

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