NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

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.

        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.

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

            • \( e^{-3} \)
            • \( -1 \)
            • \( 1 \)
            • \( -e^3 \)

          • 4.
            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.


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

                      CBSE CLASS XII Previous Year Papers

                      Comments


                      No Comments To Show