NCERT Solutions for Class 11 Maths Chapter 15 Miscellaneous Exercises

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CBSE CLASS XII Related Questions

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


      • 2.

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

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

        • 3.
          For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

            • local maximum value is 2
            • local minimum value is \( -2 \)
            • local maximum value is \( -2 \)
            • local minimum value \( < \) local maximum value

          • 4.
            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.

            • 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.
                  In a school, the probability of holding a debate competition is \( \frac{1}{3} \) and that of a quiz competition is \( \frac{2}{3} \). In the two participating teams, A has 4 girls and 6 boys and B has 7 girls and 3 boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.

                    CBSE CLASS XII Previous Year Papers

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