NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercises

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercises are based on following concepts:

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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.
        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.


          • 3.

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


              • 4.
                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.

                • 5.

                  The domain of \[ f(x)=\cos^{-1}(2x-5) \] is: 

                    • \([-1, 1]\)
                    • \([4, 6]\)
                    • \([-7, -3]\)
                    • \([2, 3]\)

                  • 6.
                    The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

                      • \( e^{-3} \)
                      • \( -1 \)
                      • \( 1 \)
                      • \( -e^3 \)
                    CBSE CLASS XII Previous Year Papers

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