NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.2 Solutions 

CBSE CLASS XII Related Questions

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


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


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

                          CBSE CLASS XII Previous Year Papers

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