NCERT Solutions for Class 11 Maths Chapter 16 Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.

    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

    • 2.

      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

      \[ 2x + y \geq 8 \]

      \[ x + 2y \geq 10 \]

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


        • 3.

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

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

          • 4.

            If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

              • \(0.35\)
              • \(0.85\)
              • \(0.5\)
              • \(0.21\)

            • 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.

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

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

                    CBSE CLASS XII Previous Year Papers

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