NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.5 Solutions 

CBSE CLASS XII Related Questions

  • 1.

    Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not. 


      • 2.
        Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


          • 3.

            Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \] 


              • 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 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:


                  • 5.

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

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

                    • 6.
                      If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]

                        CBSE CLASS XII Previous Year Papers

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