NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

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CBSE CLASS XII Related Questions

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


      • 2.
        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 \(P(E/F)\).


          • 3.

            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. 


              • 4.
                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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]


                  • 5.
                    Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]


                      • 6.
                        Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

                          CBSE CLASS XII Previous Year Papers

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