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.

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

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

        • 3.

          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

          \[ 2x + y \geq 8 \]

          \[ x + 2y \geq 10 \]

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


            • 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.

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


                    • 6.

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

                        CBSE CLASS XII Previous Year Papers

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