NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

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.

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


            • 4.

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

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


                • 5.

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

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


                    • 6.

                      Evaluate :

                      \[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

                        CBSE CLASS XII Previous Year Papers

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