NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

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.

        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.

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


            • 4.

              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

              \[ 2x + y \geq 8 \]

              \[ x + 2y \geq 10 \]

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


                • 5.

                  The value of \( \left[ \tan^{-1}(-1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right) \right] \) is :

                    • \( \frac{7\pi}{12} \)
                    • \( \frac{5\pi}{12} \)
                    • \( -\frac{5\pi}{12} \)
                    • \( \frac{\pi}{3} \)

                  • 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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