NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3

CBSE CLASS XII Related Questions

  • 1.

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


      • 2.

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


          • 3.

            Find the value of \(x\) if \(A = B\), where

            \[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]


              • 4.

                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

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


                  • 5.

                    Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).


                      • 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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