NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.3

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Class 11 Maths NCERT Solutions Chapter 9 Sequence and Series Exercise 9.3 is based on the following concepts:

  • Relationship Between A.M. and G.M.

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CBSE CLASS XII Related Questions

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


      • 2.

        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. 


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

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

                • 5.
                  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.


                    • 6.

                      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.
                      CBSE CLASS XII Previous Year Papers

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