NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.3 is based on Quadratic Equations.

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CBSE CLASS XII Related Questions

  • 1.
    \[ \int \frac{\tan^2 \sqrt{x}}{\sqrt{x}} \, dx \text{ is equal to:} \]

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

    • 2.
      Three students run on a racing track such that their speeds add up to 6 km/h. However, double the speed of the third runner added to the speed of the first results in 7 km/h. If thrice the speed of the first runner is added to the original speeds of the other two, the result is 12 km/h. Using the matrix method, find the original speed of each runner.


        • 3.
          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.


            • 4.

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


                • 5.
                  The domain of the function \( f(x) = \cos^{-1}(2x) \) is:

                    • \([-1, 1]\)
                    • \(\left[0, \frac{1}{2}\right]\)
                    • \([-2, 2]\)
                    • \(\left[-\frac{1}{2}, \frac{1}{2}\right]\)

                  • 6.

                    Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
                    \[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.

                      CBSE CLASS XII Previous Year Papers

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