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.
    Find:

    If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

      • \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
      • \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
      • \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
      • \(p = 0, \, q = 0\)

    • 2.
      Find:

      The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

        • \(-\frac{\pi}{2}\)
        • \(-\frac{\pi}{4}\)
        • \(\frac{\pi}{4}\)
        • \(\frac{\pi}{2}\)

      • 3.
        Which of the following equations is NOT a Linear Differential Equation?

          • \((1 + x^2) \, dy + 2xy \, dx = \cot x \, dx\)
          • \(y + \frac{d}{dx}(xy) = x(\sin x + \log x)\)
          • \(x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0\)
          • \(y \, dx - (x + 3y^2) \, dy = 0\)

        • 4.

          An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.  
          Based on the above information, answer the following questions :


            • 5.
              If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).


                • 6.
                  Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

                    CBSE CLASS XII Previous Year Papers

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