NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.1

CBSE CLASS XII Related Questions

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


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


              • 4.
                Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


                  • 5.

                    A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 

                    (i) Express \(y\) as a function of \(x\) from the given equation of ellipse. 
                    (ii) Integrate the function obtained in (i) with respect to \(x\). 
                    (iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration. 
                    OR 
                    (iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\). 
                     


                      • 6.

                        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. 

                          CBSE CLASS XII Previous Year Papers

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