NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.3

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.

        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:


          • 3.

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


              • 4.

                For two vectors \(\vec{a}\) and \(\vec{b}\):  

                Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

                  • 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, but Reason (R) is false.
                  • Assertion (A) is false, but Reason (R) is true.

                • 5.
                  If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


                    • 6.
                      For a square matrix \(A\), \[ (3A)^{-1}= \]

                        • \( 3A^{-1} \)
                        • \( 9A^{-1} \)
                        • \( \frac{1}{3} A^{-1} \)
                        • \( \frac{1}{9} A^{-1} \)
                      CBSE CLASS XII Previous Year Papers

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