NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2

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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 a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:


      • 2.
        If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


          • 3.
            Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]


              • 4.

                Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not. 


                  • 5.
                    Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
                    Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

                      • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
                      • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
                      • Assertion (A) is true and Reason (R) is false.
                      • Assertion (A) is false and Reason (R) is true.

                    • 6.
                      A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

                        CBSE CLASS XII Previous Year Papers

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