NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.2 is based on following concepts:

  • Argand Plane
  • Polar representation of a complex number

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CBSE CLASS XII Related Questions

  • 1.

    A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle. 


      • 2.
        Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


          • 3.

            A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 

            (i) Express \(y\) as a function of \(x\) from the given equation of ellipse. 
            (ii) Integrate the function obtained in (i) with respect to \(x\). 
            (iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration. 
            OR 
            (iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\). 
             


              • 4.
                If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
                \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]


                  • 5.
                    Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


                      • 6.
                        Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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