NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.4 Solutions 

CBSE CLASS XII Related Questions

  • 1.

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


      • 2.

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


          • 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.

                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.

                    Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).


                      • 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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