NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2

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CBSE CLASS XII Related Questions

  • 1.

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


      • 2.

        The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :

          • \( -6 \) unit/sec
          • \( 0 \) unit/sec
          • \( 18 \) unit/sec
          • \( 6 \) unit/sec

        • 3.

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

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


            • 4.

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


                • 5.

                  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

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


                    • 6.

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

                        CBSE CLASS XII Previous Year Papers

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