NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.4

CBSE CLASS XII Related Questions

  • 1.
    Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]


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


              • 4.
                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.


                  • 5.

                    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. 


                      • 6.

                        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. 
                         

                          CBSE CLASS XII Previous Year Papers

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