NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercises

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


          • 3.
            Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]


              • 4.
                Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]


                  • 5.

                    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. 


                      • 6.
                        Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

                          CBSE CLASS XII Previous Year Papers

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