NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.3

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Class 11 Maths NCERT Solutions Chapter 11 Conic Sections Exercise 11.3 is based on the following topics:

  • Relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse
  • Special cases of an ellipse
  • Eccentricity
  • Standard equations of an ellipse
  • Latus rectum

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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.

        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.
            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:
            \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]


              • 4.

                Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions: 

                (i) What is the probability that selected person is a female? 
                (ii) If a male person is selected, what is the probability that he will not be suffering from lung problems? 
                (iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female. 
                OR 
                (iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male. 
                 


                  • 5.
                    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 \(P(E/F)\).


                      • 6.
                        A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.

                          CBSE CLASS XII Previous Year Papers

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