NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2

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CBSE CLASS XII Related Questions

  • 1.
    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:
    \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]


      • 2.
        Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]


          • 3.
            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 \(P(E/F)\).


              • 4.

                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 \(x=3\). 
                 


                  • 5.
                    Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).


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

                          CBSE CLASS XII Previous Year Papers

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