NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.2

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

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

        • 3.

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

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

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


                • 6.

                  If \[ B(\operatorname{adj} B)= \begin{bmatrix} \frac{1}{3} & 0 & 0\\ 0 & \frac{1}{3} & 0\\ 0 & 0 & \frac{1}{3} \end{bmatrix}, \] then the value of \[ \det(B^{-1}) \] is: 

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

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