NCERT Solutions Class 11 Maths Chapter 1 Sets Miscellaneous Exercises

CBSE CLASS XII Related Questions

  • 1.

    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

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


      • 2.

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

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

        • 3.

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

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

          • 4.

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


              • 5.

                Evaluate :

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


                  • 6.

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

                      CBSE CLASS XII Previous Year Papers

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