NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.3

CBSE CLASS XII Related Questions

  • 1.

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

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

    • 2.

      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 \[ 3q(x)-\pi. \] 


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

            • \( 3A^{-1} \)
            • \( 9A^{-1} \)
            • \( \frac{1}{3} A^{-1} \)
            • \( \frac{1}{9} A^{-1} \)

          • 4.

            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. 


              • 5.
                Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
                Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

                  • 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 and Reason (R) is false.
                  • Assertion (A) is false and Reason (R) is true.

                • 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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