NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.2 Solutions 

CBSE CLASS XII Related Questions

  • 1.
    Find the local maxima and local minima of the function \[ f(x) = \frac{8}{3} x^3 - 12x^2 + 18x + 5. \]


      • 2.
        \[ \int \frac{\tan^2 \sqrt{x}}{\sqrt{x}} \, dx \text{ is equal to:} \]

          • \(\sec \sqrt{x} + C\)
          • \(2\sqrt{x} \tan x - x + C\)
          • \(2\left( \tan \sqrt{x} - \sqrt{x} \right) + C\)
          • \(2 \tan \sqrt{x} - x + C\)

        • 3.

          A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.
          A school is organizing a debate competition


            • 4.

              Find the Derivative \( \frac{dy}{dx} \)
              Given:\[ y = \cos(x^2) + \cos(2x) + \cos^2(x^2) + \cos(x^x) \]


                • 5.
                  In a rough sketch, mark the region bounded by \( y = 1 + |x + 1| \), \( x = -2 \), \( x = 2 \), and \( y = 0 \). Using integration, find the area of the marked region.


                    • 6.
                      The domain of the function \( f(x) = \cos^{-1}(2x) \) is:

                        • \([-1, 1]\)
                        • \(\left[0, \frac{1}{2}\right]\)
                        • \([-2, 2]\)
                        • \(\left[-\frac{1}{2}, \frac{1}{2}\right]\)
                      CBSE CLASS XII Previous Year Papers

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