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.

    Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as 

    (i) Find \(f'(x)\) for \(0<x>3\). 
    (ii) Find \(f'(4)\). 
    (iii)(a) Test for continuity of \(f(x)\) at \(x=3\). 
    OR 
    (iii)(b) Test for differentiability of \(f(x)\) at \(x=3\). 
     


      • 2.

        The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that 
        (i) target is hit. 
        (ii) at least one shot misses the target. 


          • 3.

            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. 


              • 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 : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]


                      • 6.
                        Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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